Prof. Maria EkielJeżewska, Ph.D., Dr. Habil. 

Habilitation thesis
20050929  Oddziaływania hydrodynamiczne a współczynniki transportu zawiesin 
Professor
20140219  Title of professor 
Supervision of doctoral theses
1.  20160929  Gruca Marta  Ruch regularnych układów wielu cząstek oddziałujących hydrodynamicznie w polu grawitacyjnym  1255  
2.  20120628  Myłyk Anna  Dynamika układów wielocząstkowych opadających grawitacyjnie w lepkim płynie  648 
Recent publications
1.  EkielJeżewska M.L., Adamczyk Z.^{♦}, Bławzdziewicz J.^{♦}, Streaming Current and Effective ζPotential for ParticleCovered Surfaces with Random Particle Distributions, The Journal of Physical Chemistry C, ISSN: 19327447, DOI: 10.1021/acs.jpcc.8b10068, Vol.123, No.6, pp.35173531, 2019 Abstract: A detailed theoretical and experimental study is presented concerning the streaming current and the derivative effective ζpotential for a planar surface covered by a monolayer of adsorbed particles. Precise simulation results are obtained for the equilibrium and randomsequentialadsorption (RSA) distributions of monodisperse spherical particles interacting via the excludedvolume potential. The streaming current is calculated in the thindoublelayer regime for all physically accessible particle area fractions. The results are expressed as a linear combination of the interface and particle contributions DI and DP weighted by the interface and particle ζpotentials ζI and ζP. We find that in the areafraction regime where both particle distributions exist, the equilibrium and RSA results for the streaming current are nearly indistinguishable. Our numerical data show that DI exponentially decays to zero when the particle area fraction θ is increased, whereas DP exponentially tends to a linear behavior. The results are described (with the accuracy better than 1.5% of the maximal value) by the exponential and linear plus exponential approximations, with only one fitting parameter. The numerical and theoretical predictions are in agreement with experimental data obtained for a wide range of ζpotentials of the interface and the particles. Results obtained for a rough surface with spherical asperities indicate that the roughness can reduce the effective ζpotential (as evaluated from the streaming current) by more than 25%; this prediction is also confirmed by experiments. Affiliations:
 
2.  Gruziel M., Thyagarajan K.^{♦}, Dietler G.^{♦}, Stasiak A.^{♦}, EkielJeżewska M.L., Szymczak P.^{♦}, Periodic Motion of Sedimenting Flexible Knots, PHYSICAL REVIEW LETTERS, ISSN: 00319007, DOI: 10.1103/PhysRevLett.121.127801, Vol.121, No.12, pp.12780116, 2018 Abstract: We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. We then recover this motion numerically and find out that it is accompanied by a very slow rotation around the vertical symmetry axis. We analyze the dependence of the characteristic timescales on the chain flexibility and aspect ratio. It is observed in the experiments that this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. In numerical simulations, the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops. Affiliations:
 
3.  Trombley C.I., EkielJeżewska M.L., Stable configurations of charged sedimenting particles, PHYSICAL REVIEW LETTERS, ISSN: 00319007, DOI: 10.1103/PhysRevLett.121.254502, Vol.121, pp.25450212545026, 2018 Abstract: The qualitative behavior of charged particles in a vacuum is given by Earnshaw’s Theorem which states that there is no steady configuration of charged particles in a vacuum which is asymptotically stable to perturbations. In a viscous fluid, examples of stationary configurations of sedimenting uncharged particles are known, but they are unstable or neutrally stable  they are not attractors. In this paper, it is shown by example that two charged particles settling in a fluid may have a configuration which is asymptotically stable to perturbations, for a wide range of charges, radii and densities. The existence of such "bound states" is essential from a fundamental point of view and it can be significant for dilute charged particulate systems in various biological, medical and industrial contexts. Affiliations:
 
4.  Bukowicki M., EkielJeżewska M.L., Different bending models predict different dynamics of sedimenting elastic trumbbells, SOFT MATTER, ISSN: 1744683X, DOI: 10.1039/C8SM00604K, Vol.14, pp.57865799, 2018 Abstract: The main goal of this paper is to examine theoretically and numerically the impact of a chosen bending model on the dynamics of elastic filaments settling in a viscous fluid under gravity at lowReynoldsnumber. We use the beadspring approximation of a filament and the Rotne–Prager mobility matrix to describe hydrodynamic interactions between the beads. We analyze the dynamics of trumbbells, for which bending angles are typically larger than for thin and long filaments. Each trumbbell is made of three beads connected by springs and it exhibits a bending resistance, described by the harmonic or – alternatively – by the ‘cosine’ (also called the Kratky–Porod) bending models, both often used in the literature. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and attraction of two elastic trumbbells towards a periodic longlasting orbit. As the most significant result of this paper, we show that for very elastic trumbbells at the same initial conditions, the Kratky–Porod bending potential can lead to qualitatively and quantitatively different spurious dynamics, with artificially large bending angles and unrealistic shapes. We point out that for the bead models of an elastic filament, the range of applicability of the Kratky–Porod model might not go beyond bending angles smaller than π/2 for touching beads and beyond an even much lower value for beads wellseparated from each other. The existence of stable stationary configurations of elastic trumbbells and a family of periodic oscillations of two elastic trumbbells are very important findings on their own. Affiliations:
 
5.  EkielJeżewska M.L., Boniecki R., Bukowicki M., Gruca M., Stokes velocity generated by a point force in various geometries, EUROPEAN PHYSICAL JOURNAL E, ISSN: 12928941, DOI: 10.1140/epje/i2018117273, Vol.41, No.120, pp.17, 2018 Abstract: In this short review, we visualize the fluid velocity generated by a point force close to a plane free surface or a plane rigid wall. We present separately contributions from all the multipoles which form the corresponding classical systems of images. Such graphical images might be useful in the theoretical and numerical modeling of the dynamics of microobjects moving close to an interface. Affiliations:
 
6.  EkielJeżewska M.L., Wajnryb E., Motion of a particle with stickslip boundary conditions towards a flat interface: hard wall or free surface, Physicochemical Problems of Mineral Processing, ISSN: 16431049, DOI: 10.5277/ppmp1849, Vol.54, No.1, pp.203209, 2018 Abstract: Motion of a particle with stickslip boundary conditions towards a hard wall or free surface is investigated in the range of Reynolds numbers much smaller than unity, based on the multipole expansion of the Stokes equations. The slip parameter can be interpreted as a measure of a solid particle roughness or as the effect of a surfactant on the motion of a small spherical nondeformable bubble. The particle friction coefficient is evaluated as a function of the distance from its center to the wall, based on the inverse power series expansion, and the results are used to derive explicit lubrication expressions for the friction coefficient, in a wide range of the slip parameters. It is pointed out that for a very small thickness of the fluid film, the lubrication expressions are more accurate than the series expansion. The drainage time is calculated and analyzed, and estimated in terms of explicit lubrication expressions. Keywords:particle, boundary conditions, hard wall, free surface Affiliations:
 
7.  EkielJeżewska M.L., Konferencje naukowe nauczycieli, PAUZA AKADEMICKA, ISSN: 1689488X, Vol.421, pp.23, 2018  
8.  EkielJeżewska M.L., Profesor Krzysztof Zanussi z wizytą u nauczycieli, PAUZA AKADEMICKA, ISSN: 1689488X, Vol.434, pp.34, 2018  
9.  Cichocki B.^{♦}, EkielJeżewska M.L., Wajnryb E., Translational and rotational Brownian displacements of colloidal particles of complex shapes, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.69, No.3, pp.257267, 2017 Abstract: The exact analytical expressions for the timedependent crosscorrelations of the translational and rotational Brownian displacements of a particle with arbitrary shape were derived by us in [3, 4]. They are in this work applied to construct a method to analyze the Brownian motion of a particle of an arbitrary shape, and to extract accurately the selfdiffusion matrix from the measurements of the crosscorrelations, which in turn allows to gain some information on the particle structure. As an example, we apply our new method to analyze the experimental results of D. J. Kraft et al. for the micrometersized aggregates of the beads [8]. We explicitly demonstrate that our procedure, based on the measurements of the timedependent crosscorrelations in the whole range of times, allows to determine the selfdiffusion (or alternatively the friction matrix) with a much higher precision than the method based only on their initial slopes. Therefore, the analytical timedependence of the crosscorrelations serves as a useful tool to extract information about particle structure from trajectory measurements. Keywords:Brownian motion, Smoluchowski equation, hydrodynamic interactions, selfdiﬀusion matrix, friction coeﬃcients, crosscorrelations of translational and rotational Brownian displacements Affiliations:
 
10.  EkielJeżewska M.L., Jak żyli nauczyciele w II Rzeczypospolitej?, Mińskie Zeszyty Muzealne, ISSN: 22993827, Vol.5, pp.171176, 2017  
11.  Feuillebois F.^{♦}, EkielJeżewska M.L., Wajnryb E., Sellier A.^{♦}, Bławzdziewicz J.^{♦}, Highfrequency eﬀective viscosity of a dilute suspension of particles in Poiseuille ﬂow between parallel walls, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, DOI: 10.1017/jfm.2016.378, Vol.800, pp.111139, 2016 Abstract: It is shown that the formal expression for the effective viscosity of a dilute suspension of arbitraryshaped particles in Poiseuille flow contains a novel quadrupole term, besides the expected stresslet. This term becomes important for a very confined geometry. For a highfrequency flow field (in the sense used in Feuillebois et al. (J. Fluid Mech., vol. 764, 2015, pp. 133–147), the suspension rheology is Newtonian at first order in volume fraction. The effective viscosity is calculated for suspensions of Nbead rods and of prolate spheroids with the same length, volume and aspect ratio (up to 6), entrained by the Poiseuille flow between two infinite parallel flat hard walls. The numerical computations, based on solving the Stokes equations, indicate that the quadrupole term gives a significant positive contribution to the intrinsic viscosity [μ] if the distance between the walls is less than ten times the particle width, or less. It is found that the intrinsic viscosity in bounded Poiseuille flow is generally smaller than the corresponding value in unbounded flow, except for extremely narrow gaps when it becomes larger because of lubrication effects. The intrinsic viscosity is at a minimum for a gap between walls of the order of 1.5–2 particle width. For spheroids, the intrinsic viscosity is generally smaller than for chains of beads with the same aspect ratio, but when normalized by its value in the bulk, the results are qualitatively the same. Therefore, a rigid chain of beads can serve as a simple model of an orthotropic particle with a more complicated shape. The important conclusion is that the intrinsic viscosity in shear flow is larger than in the Poiseuille flow between two walls, and the difference is significant even for relatively wide channels, e.g. three times wider than the particle length. For such confined geometries, the hydrodynamic interactions with the walls are significant and should be taken into account. Keywords:lowReynoldsnumber flows Affiliations:
 
12.  Farutin A.^{♦}, Piasecki T., Słowicka A.M., Misbah C.^{♦}, Wajnryb E., EkielJeżewska M.L., Dynamics of flexible fibers and vesicles in Poiseuille flow at low Reynolds number, SOFT MATTER, ISSN: 1744683X, DOI: 10.1039/c6sm00819d, Vol.12, pp.73077323, 2016 Abstract: The dynamics of flexible fibers and vesicles in unbounded planar Poiseuille flow at low Reynolds number is shown to exhibit similar basic features, when their equilibrium (moderate) aspect ratio is the same and vesicle viscosity contrast is relatively high. Tumbling, lateral migration, accumulation and shape evolution of these two types of flexible objects are analyzed numerically. The linear dependence of the accumulation position on relative bending rigidity, and other universal scalings are derived from the local shear flow approximation. Keywords:Poiseuille flow, Stokes equations, vesicles, flexible fibers Affiliations:
 
13.  Cichocki B.^{♦}, EkielJeżewska M.L., Wajnryb E., Note: Brownian motion of colloidal particles of arbitrary shape, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.4942119, Vol.144, pp.07610112, 2016 Abstract: The analytical expressions for the timedependent cross correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape are derived. The reference center is arbitrary, and the reference frame is such that the rotationalrotational diffusion tensor is diagonal. Keywords:Rotational correlation time, Tensor methods, Brownian motion, Colloidal systems, Matrix equations Affiliations:
 
14.  Feuillebois F.^{♦}, EkielJeżewska M.L., Wajnryb E., Sellier A.^{♦}, Bławzdziewicz J.^{♦}, Highfrequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, DOI: 10.1017/jfm.2014.690, Vol.764, pp.133147, 2015 Abstract: A general expression for the effective viscosity of a dilute suspension of arbitraryshaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to Nbead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of nonBrownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centreofmass distribution to be practically frozen, yet small enough for the flow to be quasisteady. It is known that for spheres, the intrinsic viscosity [μ] increases monotonically when the distance H between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a ‘weakly confined’ regime (for H>l, where l is the particle length), where [μ] is slightly larger for smaller H; (ii) a ‘semiconfined’ regime, when H becomes smaller than l, where [μ] rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a ‘strongly confined’ regime when H becomes smaller than 2–3 particle widths d, where [μ] rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5–6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid. Keywords:complex fluids, lowReynoldsnumber flows, suspensions Affiliations:
 
15.  Bukowicki M., Gruca M., EkielJeżewska M.L., Dynamics of elastic dumbbells sedimenting in a viscous fuid: oscillations and hydrodynamic repulsion, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, DOI: 10.1017/jfm.2015.31, Vol.767, pp.95108, 2015 Abstract: Hydrodynamic interactions between two identical elastic dumbbells settling under gravity in a viscous fluid at low Reynolds number are investigated using the pointparticle model. The evolution of a benchmark initial configuration is studied, in which the dumbbells are vertical and their centres are aligned horizontally. Rigid dumbbells and pairs of separate beads starting from the same positions tumble periodically while settling. We find that elasticity (which breaks the timereversal symmetry of the motion) significantly affects the system dynamics. This is remarkable when taking into account that elastic forces are always much smaller than gravity. We observe oscillating motion of the elastic dumbbells, which tumble and change their length nonperiodically. Independently of the value of the spring constant, a horizontal hydrodynamic repulsion appears between the dumbbells: their centres of mass move apart from each other horizontally. This motion is fast for moderate values of the spring constant k, and slows down when k tends to zero or to infinity; in these limiting cases we recover the periodic dynamics reported in the literature. For moderate values of the spring constant, and different initial configurations, we observe the existence of a universal timedependent solution to which the system converges after an initial relaxation phase. The tumbling time and the width of the trajectories in the centreofmass frame increase with time. In addition to its fundamental significance, the benchmark solution presented here is important to understanding general features of systems with a larger number of elastic particles, in regular and random configurations. Keywords:complex fluids, lowReynoldsnumber flows, Stokesian dynamics Affiliations:
 
16.  Kuei S.^{♦}, Słowicka A.M., EkielJeżewska M.L., Wajnryb E., Stone H.A.^{♦}, Dynamics and topology of a flexible chain: knots in steady shear flow, NEW JOURNAL OF PHYSICS, ISSN: 13672630, DOI: 10.1088/13672630/17/5/053009, Vol.17, pp.053009115, 2015 Abstract: We use numerical simulations of a bead–spring model chain to investigate the evolution of the conformations of long and flexible elastic fibers in a steady shear flow. In particular, for rather open initial configurations, and by varying a dimensionless elastic parameter, we identify two distinct conformational modes with different final size, shape, and orientation. Through further analysis we identify slipknots in the chain. Finally, we provide examples of initial configurations of an 'open' trefoil knot that the flow unknots and then knots again, sometimes repeating several times. Keywords:knots, low Reynolds number flows, multipole method Affiliations:
 
17.  EkielJeżewska M.L., Felderhof B.U.^{♦}, Hydrodynamic interactions between a sphere and a number of small particles, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.4904981, Vol.142, pp.01490415, 2015 Abstract: Exact expressions are derived for the pair and threebody hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds number hydrodynamics. The results follow by a combination of the solutions for flow about a sphere with noslip boundary condition derived by Stokes and Kirchhoff and the result derived by Oseen for the Green tensor of Stokes equations in the presence of a fixed sphere. Keywords:Hydrodynamics, Tensor methods, Stokes flows, Boundary value problems, Torque Affiliations:
 
18.  Słowicka A., Wajnryb E., EkielJeżewska M.L., Dynamics of flexible fibers in shear flow, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.4931598, Vol.143, pp.12490416, 2015 Abstract: Dynamics of flexible nonBrownian fibers in shear flow at lowReynoldsnumber are analyzed numerically for a wide range of the ratios A of the fiber bending force to the viscous drag force. Initially, the fibers are aligned with the flow, and later they move in the plane perpendicular to the flow vorticity. A surprisingly rich spectrum of different modes is observed when the value of A is systematically changed, with sharp transitions between coiled and straightening out modes, perioddoubling bifurcations from periodic to migrating solutions, irregular dynamics, and chaos. Keywords:Shear flows, Chaotic dynamics, Vortex dynamics, Numerical solutions, Periodic solutions Affiliations:
 
19.  SonnSegev A.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., EkielJeżewska M.L., Diamant H.^{♦}, Roichman Y.^{♦}, Structure and dynamics of a layer of sedimented particles, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.4928644, Vol.143, pp.074704114, 2015 Abstract: We investigate experimentally and theoretically thin layers of colloid particles held adjacent to a solid substrate by gravity. Epifluorescence, confocal, and holographic microscopy, combined with Monte Carlo and hydrodynamic simulations, are applied to infer the height distribution function of particles above the surface, and their diffusion coefficient parallel to it. As the particle area fraction is increased, the height distribution becomes bimodal, indicating the formation of a distinct second layer. In our theory, we treat the suspension as a series of weakly coupled quasitwodimensional layers in equilibrium with respect to particle exchange. We experimentally, numerically, and theoretically study the changing occupancies of the layers as the area fraction is increased. The decrease of the particle diffusion coefficient with concentration is found to be weakened by the layering. We demonstrate that particle polydispersity strongly affects the properties of the sedimented layer, because of particle size segregation due to gravity. Keywords:colloidal particles, gravity, horizontal wall, twodimensional layers, diffusion, height distribution function Affiliations:
 
20.  Cichocki B.^{♦}, EkielJeżewska M.L., Wajnryb E., Brownian motion of a particle with arbitrary shape, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.4921729, Vol.142, pp.21490219, 2015 Abstract: rownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the timedependent crosscorrelations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed. Keywords:Tensor methods, Brownian motion, Matrix theory, Rotational correlation time, Eigenvalues Affiliations:
 
21.  Gruca M., Bukowicki M., EkielJeżewska M.L., Periodic and quasiperiodic motions of many particles falling in a viscous fluid, PHYSICAL REVIEW E, ISSN: 15393755, DOI: 10.1103/PhysRevE.92.023026, Vol.92, pp.023026110, 2015 Abstract: The dynamics of regular clusters of many nontouching particles falling under gravity in a viscous fluid at low Reynolds number are analyzed within the pointparticle model. The evolution of two families of particle configurations is determined: two or four regular horizontal polygons (called “rings”) centered above or below each other. Two rings fall together and periodically oscillate. Four rings usually separate from each other with chaotic scattering. For hundreds of thousands of initial configurations, a map of the cluster lifetime is evaluated in which the longlasting clusters are centered around periodic solutions for the relative motions, and they are surrounded by regions of chaotic scattering in a similar way to what was observed by Janosi et al. [Phys. Rev. E. 56, 2858 (1997)] for three particles only. These findings suggest that we should consider the existence of periodic orbits as a possible physical mechanism of the existence of unstable clusters of particles falling under gravity in a viscous fluid. Keywords:Stokes equations, particle clusters, sedimentation, chaotic scattering, periodic orbits Affiliations:
 
22.  Cichocki B.^{♦}, EkielJeżewska M.L., Wajnryb E., Hydrodynamic radius approximation for spherical particles suspended in a viscous ﬂuid: Inﬂuence of particle internal structure and boundary, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.4871498, Vol.140, pp.16490217, 2014 Abstract: Systems of spherical particles moving in Stokes flow are studied for different particle internal structures and boundaries, including the Navierslip model. It is shown that their hydrodynamic interactions are well described by treating them as solid spheres of smaller hydrodynamic radii, which can be determined from measured singleparticle diffusion or intrinsic viscosity coefficients. Effective dynamics of suspensions made of such particles is quite accurately described by mobility coefficients of the solid particles with the hydrodynamic radii, averaged with the unchanged direct interactions between the particles. Keywords:hydrodynamic radius, Stokes equations Affiliations:
 
23.  EkielJeżewska M.L., Class of periodic and quasiperiodic trajectories of particles settling under gravity in a viscous fluid, PHYSICAL REVIEW E, ISSN: 15393755, DOI: 10.1103/PhysRevE.90.043007, Vol.90, pp.043007110, 2014 Abstract: We investigate regular configurations of a small number of nonBrownian particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the pointparticle approximation. A family of regular configurations is found with periodic oscillations of all the settling particles. The oscillations are shown to be robust under some outofphase rearrangements of the particles. In the presence of an additional particle above such a regular configuration, the particle periodic trajectories are horizontally repelled from the symmetry axis, and flattened vertically. The results are used to propose a mechanism of how a spherical cloud, made of a large number of particles distributed at random, evolves and destabilizes. Keywords:Stokes equations, sedimentation, particle cluster, suspension drop, periodic orbits Affiliations:
 
24.  Pasol L.^{♦}, Martin M.^{♦}, EkielJeżewska M.L., Wajnryb E., Bławzdziewicz J.^{♦}, Feuillebois F.^{♦}, Corrigendum to ‘‘Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to fieldflow fractionation and hydrodynamic chromatography’’, CHEMICAL ENGINEERING SCIENCE, ISSN: 00092509, DOI: 10.1016/j.ces.2012.12.020, Vol.90, pp.5152, 2013 Abstract: The authors report that there is a confusion in the definition of the friction factors, pffp, pccp in Pasol et al. (2011). Keywords:friction factors, Poiseuille flow, spherical particle, fieldflow fractionation, hydrodynamic chromatotography Affiliations:
 
25.  Słowicka A.M., Wajnryb E., EkielJeżewska M.L., Lateral migration of flexible fibers in Poiseuille flow between two parallel planar solid walls, EUROPEAN PHYSICAL JOURNAL E, ISSN: 12928941, DOI: 10.1140/epje/i2013130312, Vol.36, pp.112, 2013 Abstract: Dynamics of nonBrownian flexible fibers in Poiseuille flow between two parallel planar solid walls is evaluated from the Stokes equations which are solved numerically by the multipole method. Fibers migrate towards a critical distance from the wall zc, which depends significantly on the fiber length N and bending stiffness A. This effect can be used to sort fibers. Three types of accumulation are found, depending on a sheartobending parameter Γ. In the first type, stiff fibers deform only a little and accumulate close to the wall, where their tendency to drift away from the channel is balanced by the repulsive hydrodynamic interaction with the wall. In the second type, flexible fibers deform significantly and accumulate far from the wall. In both types, the fiber shapes at the accumulation positions are repeatable, while in the third type, they are very compact and nonrepeatable. The difference between the second and third accumulation types is a special case of the difference between the regular and irregular modes for the dynamics of migrating fibers. At the regular mode, far from walls, the fiber tumbling frequency satisfies Jeffery’s expression, with the local shear rate and the aspect ratio close to N. Keywords:Selforganisation, Supramolecular assemblies Affiliations:
 
26.  Cichocki B.^{♦}, EkielJeżewska M.L., Wajnryb E., Shorttime dynamics and highfrequency rheology of suspensions of spherical coreshell particles with thinshells, COLLOIDS AND SURFACES APHYSICOCHEMICAL AND ENGINEERING ASPECTS, ISSN: 09277757, DOI: 10.1016/j.colsurfa.2012.10.053, Vol.418, pp.2228, 2013 Abstract: Shorttime dynamics and highfrequency rheology for suspensions of nonoverlapping core–shell particles with thin shells were analyzed. In the thinshell limit, the singleparticle scattering coefficients were derived and shown to define a unique effective radius. This result was used to justify theoretically (in the thinshell limit) the accuracy of the annulus approximation with the inner radius equal to the effective hydrodynamic radius of the core–shell particle. The twoparticle virial expansion of the translational and rotational selfdiffusion, sedimentation and viscosity was performed. The virial coefficients were evaluated and shown to be accurately approximated by the effective annulus model, in contrast to the imprecise effective hard sphere model. Keywords:Stokes equations, Core–shell particles, Permeable medium Affiliations:
 
27.  EkielJeżewska M.L., Nasi dziadkowie jako uczniowie i nauczyciele, Rocznik Mińskomazowiecki, ISSN: 1232633X, Vol.21, pp.245258, 2013 Abstract: Każdy z nas ma własne wspomnienia szkolne, a także słyszał opowieści o nauce rodziców i dziadków. Wyselekcjonujmy z nich takie, które dotyczą ważnych elementów kształcenia i pokażmy innym. Porozmawiajmy o tym, na czym polega takie uczenie się, jakiego potrzebujemy i za jakim tęsknimy. Przykładem może służyć rozmowa, która zaczęła się od pokazania osobistych pamiątek szkolnych kilku rodzin z regionu Mińska Mazowieckiego i przywołania wspomnień związanych z najlepszymi tradycjami i historią polskiej edukacji w I połowie XX wieku. Eksponaty te od 22 listopada 2012 do 10 marca 2013 r. można było zobaczyć w Muzeum Ziemi Mińskiej na wystawie „Nasi dziadkowie jako uczniowie i nauczyciele”. Artykuł opowiada o tej wystawie i relacjonuje niektóre zebrane przy tej okazji wspomnienia. Keywords:nauka, edukacja, tradycje Affiliations:
 
28.  Abade G.C.^{♦}, Cichocki B.^{♦}, EkielJeżewska M.L., Naegele G.^{♦}, Wajnryb E., Diffusion, sedimentation, and rheology of concentrated suspensions of coreshell particles, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3689322, Vol.136, pp.104902116, 2012 Abstract: Shorttime dynamic properties of concentrated suspensions of colloidal coreshell particles are studied using a precise force multipole method which accounts for manyparticle hydrodynamic interactions. A coreshell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ−1. The solvent flow inside the permeable shell is described by the BrinkmanDebyeBueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact nonhydrodynamically by a hardsphere nooverlap potential of radius b. Numerical results are presented for the highfrequency shear viscosity, η∞, sedimentation coefficient, K, and the shorttime translational and rotational selfdiffusion coefficients, D t and D r . The simulation results cover the full threeparametric fluidphase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Manyparticle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the coreshell systems can be approximated neither by noshell nor by nocore models. However, one of our findings is that for κ(b − a) ≳ 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration. Keywords:coreshell particles, suspension, diffusion, sedimentation, effective viscosity Affiliations:
 
29.  Cichocki B.^{♦}, EkielJeżewska M.L., Wajnryb E., Communication: Translational Brownian motion for particles of arbitrary shape, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3689842, Vol.136, pp.07110214, 2012 Abstract: A single Brownian particle of arbitrary shape is considered. The timedependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the longtime limit, the slope of W(t) is determined uniquely by the trace of the translationaltranslational mobility matrix μtt evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the longtime limit. Keywords:translational and rotational Brownian motion, mean square displacement, particle of arbitrary shape, mobility center Affiliations:
 
30.  Słowicka A.M., EkielJeżewska M.L., Sadlej K., Wajnryb E., Dynamics of fibers in a wide microchannel, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3678852, Vol.136, pp.04490418, 2012 Abstract: Dynamics of single flexible nonBrownian fibers, tumbling in a Poiseuille flow between two parallel solid plane walls, is studied with the use of the HYDROMULTIPOLE numerical code, based on the multipole expansion of the Stokes equations, corrected for lubrication. Fibers, which are closer to a wall, more flexible (less stiff) or longer, deform more significantly and, for a wide range of the system parameters, they faster migrate towards the middle plane of the channel. For the considered systems, fiber velocity along the flow is only slightly smaller than (and can be well approximated by) the Poseuille flow velocity at the same position. In this way, the history of a fiber migration across the channel is sufficient to determine with a high accuracy its displacement along the flow. Keywords:Stokes equations, flexible fiber, Poiseuille flow, solid walls Affiliations:
 
31.  Adamczyk Z.^{♦}, Cichocki B.^{♦}, EkielJeżewska M.L., Słowicka A., Wajnryb E., Wasilewska M.^{♦}, Fibrinogen conformations and charge in electrolyte solutions derived from DLS and dynamic viscosity measurements, JOURNAL OF COLLOID AND INTERFACE SCIENCE, ISSN: 00219797, DOI: 10.1016/j.jcis.2012.07.010, Vol.385, pp.244257, 2012 Abstract: Hydrodynamic properties of fibrinogen molecules were theoretically calculated. Their shape was approximated by the bead model, considering the presence of flexible side chains of various length and orientation relative to the main body of the molecule. Using the bead model, and the precise manymultipole method of solving the Stokes equations, the mobility coefficients for the fibrinogen molecule were calculated for arbitrary orientations of the arms whose length was varied between 12 and 18 nm. Orientation averaged hydrodynamic radii and intrinsic viscosities were also calculated by considering interactions between the side arms and the core of the fibrinogen molecule. Whereas the hydrodynamic radii changed little with the interaction magnitude, the intrinsic viscosity exhibited considerable variation from 30 to 60 for attractive and repulsive interactions, respectively. These theoretical results were used for the interpretation of experimental data derived from sedimentation and diffusion coefficient measurements as well as dynamic viscosity measurements. Optimum dimensions of the fibrinogen molecule derived in this way were the following: the contour length 84.7 nm, the side arm length 18 nm, and the total volume 470 nm3, which gives 16% hydration (by volume). Our calculations enabled one to distinguish various conformational states of the fibrinogen molecule, especially the expanded conformation, prevailing for pH < 4 and lower ionic strength, characterized by high intrinsic viscosity of 50 and the hydrodynamic radius of 10.6 nm. On the other hand, for the physiological condition, that is, pH = 7.4 and the ionic strength of 0.15 M NaCl, the semicollapsed conformation dominates. It is characterized by the average angle equal to = 55, intrinsic viscosity of 35, and the hydrodynamic radius of 10 nm. Additionally, the interaction energy between the arms and the body of the molecule was predicted to be 4 kT units, confirming that they are oppositely charged than the central nodule. Results obtained in our work confirm an essential role of the side chains responsible for a highly anisotropic charge distribution in the fibrinogen molecule. These finding can be exploited to explain anomalous adsorption of fibrinogen on various surfaces. Keywords:Bead model of fibrinogen, Charge distribution over fibrinogen, Conformations of fibrinogen molecule, Fibrinogen molecule conformations, Hydrodynamic radius of fibrinogen, Viscosity of fibrinogen solutions Affiliations:
 
32.  EkielJeżewska M.L., System kształcenia Komisji Edukacji Narodowej, Rozprawy z dziejów oświaty, ISSN: 00804754, Vol.XLIX, pp.55110, 2012 Abstract: In a successfully developing system, goal, principles and processes are coupled with each other and with a continuous increase of knowledge. Analyzing these relations, Wilson, Barsky and Daviss proposed universal criteria to assess progress of systemic changes. These criteria can be applied to development of a modern technology or science, as well as to education reforms. The goal of this work is to apply these criteria to analyze effectiveness of the schooling system created by the Polish Commission of the National Education (KEN). We have shown how the overarching goal of education – economical and political development of Poland – was consistent with the KEN basic principles: common goals, freedom and autonomy, ownership of accumulated knowledge. We have demonstrated how KEN kept alive six processes inherent to successful system reforms: knowledge accumulation, sustained professional development within a recognized hierarchy of practitioner’s expertise and transmission of this expertise to others, design of complex entities, improvement of quality, diffusion of innovations, and redesign. In this way, we have provided an example how a similar assessment can be performed for modern educational initiatives, programs, systems and reforms, in contrast to common evaluation of individual teachers and students. Following the best Polish educational tradition, we have reminded that, nowadays, we need to rethink what does it mean to learn and teach productively, and what should be the overarching goal of schooling in the society of the XXI century. Keywords:Komisja Edukacji Narodowej, reforma edukacji, procesy charakteryzujące rozwój systemu, sprzężecie celu, procesów, zasad i wiedzy w skutecznym systemie Affiliations:
 
33.  Pasol L.^{♦}, Martin M.^{♦}, EkielJeżewska M.L., Wajnryb E., Bławzdziewicz J.^{♦}, Feuillebois F.^{♦}, Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to fieldflow fractionation and hydrodynamic chromatography, CHEMICAL ENGINEERING SCIENCE, ISSN: 00092509, DOI: 10.1016/j.ces.2011.05.033, Vol.66, pp.40784089, 2011 Abstract: The motion of a solid spherical particle entrained in a Poiseuille flow between parallel plane walls has various applications to separation methods, like fieldflow fractionation and hydrodynamic chromatography. Various handy formulae are presented here to describe the particle motion, with these applications in mind. Based on the assumption of a low Reynolds number, the multipole expansion method coupled to a Cartesian representation is applied to provide accurate results for various friction factors in the motion of a solid spherical particle embedded in a viscous fluid between parallel planes. Accurate results for the velocity of a freely moving solid spherical particle are then obtained. These data are fitted so as to obtain handy formulae, providing e.g. the velocity of the freely moving sphere with a 1% error. For cases where the interaction with a single wall is sufficient, simpler fitting formulae are proposed, based on earlier results using the bispherical coordinates method. It appears that the formulae considering only the interaction with a nearest wall are applicable for a surprisingly wide range of particle positions and channel widths. As an example of application, it is shown how in hydrodynamic chromatography earlier models ignoring the particlewall hydrodynamic interactions fail to predict the proper choice of channel width for a selective separation. The presented formulae may also be used for modeling the transport of macromolecular or colloidal objects in microfluidic systems. Keywords:Creeping flow, Particle, Suspension, Interaction with walls, Separations, Selectivity Affiliations:
 
34.  Abade G.C.^{♦}, Cichocki B.^{♦}, EkielJeżewska M.L., Nägele G.^{♦}, Wajnryb E., Rotational and translational selfdiffusion in concentrated suspensions of permeable particles, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3604813, Vol.134, pp.24490317, 2011 Abstract: In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of shorttime dynamic properties were calculated, except for the rotational selfdiffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational selfdiffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45% and for a wide range of permeability values. From the simulation results and earlier results for the firstorder virial coefficient, we find that the rotational selfdiffusion coefficient of permeable spheres can be scaled to the corresponding coefficient of impermeable particles of the same size. We also show that a similar scaling applies to the translational selfdiffusion coefficient considered earlier. From the scaling relations, accurate analytic approximations for the rotational and translational selfdiffusion coefficients in concentrated systems are obtained, useful to the experimental analysis of permeableparticle diffusion. The simulation results for rotational diffusion of permeable particles are used to show that a generalized StokesEinsteinDebye relation between rotational selfdiffusion coefficient and highfrequency viscosity is not satisfied. Keywords:selfdiffusion, permeable particles, concentrated suspensions Affiliations:
 
35.  EkielJeżewska M.L., Wajnryb E., Lifetime of a cluster of spheres settling under gravity in Stokes flow, PHYSICAL REVIEW E, ISSN: 15393755, DOI: 10.1103/PhysRevE.83.067301, Vol.83, pp.06730114, 2011 Abstract: The evolution of a cluster of three identical nontouching spheres settling in a vertical plane due to gravity in Stokes flow has been evaluated numerically for a twoparameter family of initial configurations, with the sphere centers close to each other and located on a horizontal line. A condition has been specified which relates the cluster lifetime to its geometry. The cluster lifetime and the label of the sphere left behind are very sensitive to initial conditions, as within the pointparticle approximation of Janosi et al. [Phys. Rev. E 56, 2858 (1997)]. The finding is that an increase of the sphere radii always reduces the range of initial conditions leading to chaotic scattering. The hydrodynamic interactions between close spheres stabilize the cluster. Keywords:Stokes flow, particles settling under gravity, hydrodynamic interactions, chaotic scattering, cluster lifetime Affiliations:
 
36.  Myłyk A., Meile W.^{♦}, Brenn G.^{♦}, EkielJeżewska M.L., Breakup of suspension drops settling under gravity in a viscous fluid close to a vertical wall, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.3600660, Vol.23, pp.063302114, 2011 Abstract: The evolution of suspension drops sedimenting under gravity in a viscous fluid close to a vertical wall was studied experimentally and numerically with the use of the pointforce model, in the Stokes flow regime. The fluid inside and outside the drop was identical. The initial distribution of the suspended solid heavy particles was uniform inside a spherical volume. In the experiments and in the simulations, the suspension drops evolved qualitatively in the same way as in an unbounded fluid. However, it was observed, both experimentally and numerically, that, on the average, the destabilization time T and the distance L traveled by the drop until breakup were smaller for a closer distance h of the drop center from the wall, with approximately linear dependence of T and L on D/h, for h larger or comparable to the drop diameter D. Destabilization times and lengths of individual drops with different random configurations of the particles were shown to differ significantly from each other, owing to the chaotic nature of the particle dynamics. Keywords:suspension drop, Stokes flow, pointparticle model, experiment, destabilization time Affiliations:
 
37.  Cichocki B.^{♦}, EkielJeżewska M.L., Nägele G.^{♦}, Wajnryb E., Firstorder virial expansion of shorttime diffusion and sedimentation coefficients of permeable particles suspensions, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.3626196, Vol.23, pp.08330318, 2011 Abstract: For suspensions of permeable particles, the shorttime translational and rotational selfdiffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a uniformly permeable sphere of a given permeability, with the internal solvent flow described by the DebyeBuecheBrinkman equation. The particles are assumed to interact nonhydrodynamically by their excluded volumes. The virial expansion of the transport properties in powers of the volume fraction is performed up to the twoparticle level. The firstorder virial coefficients corresponding to twobody hydrodynamic interactions are evaluated with very high accuracy by the series expansion in inverse powers of the interparticle distance. Results are obtained and discussed for a wide range of the ratio, x, of the particle radius to the hydrodynamic screening length inside a permeable sphere. It is shown that for x≥10, the virial coefficients of the transport properties are wellapproximated by the hydrodynamic radius (annulus) model developed by us earlier for the effective viscosity of porousparticle suspensions. Keywords:Stokes equations, hydrodynamic interactions, diffusion, sedimentation, permeable particles, suspesnion, virial expansion Affiliations:
 
38.  Adamczyk Z.^{♦}, Sadlej K., Wajnryb E., Nattich M.^{♦}, EkielJeżewska M.L., Bławzdziewicz J.^{♦}, Streaming potential studies of colloidal, polyelectrolyte and protein deposition, ADVANCES IN COLLOID AND INTERFACE SCIENCE, ISSN: 00018686, DOI: 10.1016/j.cis.2009.09.004, Vol.153, pp.129, 2010 Abstract: Recent developments in the electrokinetic determination of particle, protein and polyelectrolyte monolayers at solid/electrolyte interfaces, are reviewed. Illustrative theoretical results characterizing particle transport to interfaces are presented, especially analytical formulae for the limiting flux under various deposition regimes and expressions for diffusion coefficients of various particle shapes. Then, blocking effects appearing for higher surface coverage of particles are characterized in terms of the random sequential adsorption model. These theoretical predictions are used for interpretation of experimental results obtained for colloid particles and proteins under convection and diffusion transport conditions. The kinetics of particle deposition and the structure of monolayers are analyzed quantitatively in terms of the generalized random sequential adsorption (RSA) model, considering the coupling of the bulk and surface transport steps. Experimental results are also discussed, showing the dependence of the jamming coverage of monolayers on the ionic strength of particle suspensions. In the next section, theoretical and experimental results pertaining to electrokinetics of particle covered surfaces are presented. Theoretical models are discussed, enabling a quantitative evaluation of the streaming current and the streaming potential as a function of particle coverage and their surface properties (zeta potential). Experimental data related to electrokinetic characteristics of particle monolayers, mostly streaming potential measurements, are presented and interpreted in terms of the above theoretical approaches. These results, obtained for model systems of monodisperse colloid particles are used as reference data for discussion of experiments performed for polyelectrolyte and protein covered surfaces. The utility of the electrokinetic measurements for a precise, in situ determination of particle and protein monolayers at various interfaces is pointed out. Keywords:Colloid deposition, Nanoparticle deposition, Particle covered surfaces, Polyelectrolyte deposition, Protein deposition, Streaming potential of covered surfaces Affiliations:
 
39.  Sadlej K., Wajnryb E., EkielJeżewska M.L., Lamparska D., Kowalewski T.A., Dynamics of nanofibres conveyed by low Reynolds number flow in a microchannel, INTERNATIONAL JOURNAL OF HEAT AND FLUID FLOW, ISSN: 0142727X, DOI: 10.1016/j.ijheatfluidflow.2010.02.021, Vol.31, No.6, pp.9961004, 2010 Abstract: In this paper we aim to create an experimental and numerical model of nano and micro filaments suspended in a confined Poiseuille flow. The experimental data obtained for short nanofibres will help to elucidate fundamental questions concerning mobility and deformation of biological macromolecules due to hydrodynamic stresses from the surrounding fluid motion. Nanofibres used in the experiments are obtained by electrospinning polymer solutions. Their typical dimensions are 100–1000 μm (length) and 0.1–1 μm (diameter). The nanofibre dynamics is followed experimentally under a fluorescence microscope. A precise multipole expansion method of solving the Stokes equations, and its numerical implementation are used to construct a beadspring model of a filament moving in a Poiseuille flow between two infinite parallel walls. Simulations show typical behaviour of elongated macromolecules. Depending on the parameters, folding and unfolding sequences of a flexible filament are observed, or a rotational and translation motion of a shapepreserving filament. An important result of our experiments is that nanofibres do not significantly change their shape while interacting with a microflow. It appeared that their rotational motion is better reproduced by the shapepreserving Stokesian bead model with all pairs of beads connected by springs, omitting explicit bending forces. Keywords:Nanofibres suspension, Microchannels, Filament dynamics, Stokesian dynamics, Multipole expansion Affiliations:
 
40.  Abade G.C.^{♦}, Cichocki B.^{♦}, EkielJeżewska M.L., Nägele G.^{♦}, Wajnryb E., Shorttime dynamics of permeable particles in concentrated suspensions, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3274663, Vol.132, pp.014503117, 2010 Abstract: We study shorttime diffusion properties of colloidal suspensions of neutral permeable particles. An individual particle is modeled as a solventpermeable sphere of interaction radius a and uniform permeability k, with the fluid flow inside the particle described by the Debye–Bueche–Brinkman equation, and outside by the Stokes equation. Using a precise multipole method and the corresponding numerical code HYDROMULTIPOLE that account for higherorder hydrodynamic multipole moments, numerical results are presented for the hydrodynamic function, H(q), the shorttime selfdiffusion coefficient, Ds, the sedimentation coefficient K, the collective diffusion coefficient, Dc, and the principal peak value H(qm), associated with the shorttime cage diffusion coefficient, as functions of porosity and volume fraction. Our results cover the full fluid phase regime. Generic features of the permeable sphere model are discussed. An approximate method by Pusey to determine Ds is shown to agree well with our accurate results. It is found that for a given volume fraction, the wavenumber dependence of a reduced hydrodynamic function can be estimated by a single master curve, independent of the particle permeability, given by the hardsphere model. The reduced form is obtained by an appropriate shift and rescaling of H(q), parametrized by the selfdiffusion and sedimentation coefficients. To improve precision, another reduced hydrodynamic function, hm(q), is also constructed, now with the selfdiffusion coefficient and the peak value, H(qm), of the hydrodynamic function as the parameters. For wavenumbers qa > 2, this function is permeability independent to an excellent accuracy. The hydrodynamic function of permeable particles is thus well represented in its qdependence by a permeabilityindependent master curve, and three coefficients, Ds, K, and H(qm), that do depend on the permeability. The master curve and its coefficients are evaluated as functions of concentration and permeability. Keywords:Stokes equations, hydrodynamic interactions, selfdiffusion, sedimentation, permeable particles, suspension Affiliations:
 
41.  Sadlej K., Wajnryb E., EkielJeżewska M.L., Hydrodynamic interactions suppress deformation of suspension drops in Poiseuille ﬂow, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, Vol.133, pp.054901110, 2010 Abstract: Evolution of a suspensiondrop entrained by Poiseuille flow is studied numerically at a low Reynolds number. A suspensiondrop is modeled by a cloud of many nontouching particles, initially randomly distributed inside a spherical volume of a viscous fluid which is identical to the host fluid outside the drop. Evolution of particle positions and velocities is evaluated by the accurate multipole method corrected for lubrication, implemented in the HYDROMULTIPOLE numerical code. Deformation of the drop is shown to be smaller for a larger volume fraction. At high concentrations, hydrodynamic interactions between close particles significantly decrease elongation of the suspensiondrop along the flow in comparison to the corresponding elongation of the purefluid drop. Owing to hydrodynamic interactions, the particles inside a densesuspension drop tend to stay for a long time together in the central part of the drop; later on, small clusters occasionally separate out from the drop, and are stabilized by quasiperiodic orbits of the constituent nontouching particles. Both effects significantly reduce the drop spreading along the flow. At large volume fractions, suspensiondrops destabilize by fragmentation, and at low volume fractions, by dispersing into single particles. Keywords:Stokes equations, Poiseuille flow, suspension drop, hydrodynamic interactions Affiliations:
 
42.  Abade G.C.^{♦}, Cichocki B.^{♦}, EkielJeżewska M.L., Nägele G.^{♦}, Wajnryb E., Highfrequency viscosity of concentrated porous particles suspensions, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3474804, Vol.133, pp.08490619, 2010 Abstract: We determine the highfrequency limiting shear viscosity in colloidal suspensions of rigid, uniformly porous spheres of radius a as a function of volume fraction and inverse porosity parameter x. Our study covers the complete fluidstate regime. The flow inside the spheres is modeled by the Debye–Bueche–Brinkman equation using the boundary condition that fluid velocity and stress change continuously across the sphere surfaces. The manysphere hydrodynamic interactions in concentrated systems are fully accounted for by a precise hydrodynamic multipole method encoded in our HYDROMULTIPOLE program extended to porous particles. A truncated virial expansion is used to derive an accurate and easytouse generalized Saitô formula for. The simulation data are used to test the performance of two simplifying effective particle models. The first model describes the effective particle as a nonporous sphere characterized by a single effective radius dependent on x. In the more refined second model, the porous spheres are modeled as spherical annulus particles with an inner hydrodynamic radius as a function of x, defining the nonporous dry core and characterizing hydrodynamic interactions, and an outer excluded volume radius a characterizing the unchanged direct interactions. Only the second model is in a satisfactory agreement with the simulation data. Keywords:Stokes flow, permeable particles, effective viscosity, lubrication, concentrated suspensions Affiliations:
 
43.  Bławzdziewicz J.^{♦}, EkielJeżewska M.L., Wajnryb E., Motion of a spherical particle near a planar fluidfluid interface: The effect of surface incompressibility, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3475197, Vol.133, No.11, pp.114702112, 2010 Abstract: Hydrodynamic coupling of a spherical particle to an undeformable planar fluidfluidinterface under creepingflow conditions is discussed. The interface can be either surfactantfree or covered with an incompressible surfactant monolayer. In the incompressible surfactant limit, a uniform surfactant concentration is maintained by Marangoni stresses associated with infinitesimal surfactant redistribution. Our detailed numerical calculations show that the effect of surface incompressibility on lateral particle motion is accurately accounted for by the first reflection of the flow from the interface. For small particleinterface distances, the remaining contributions are significant, but they are weakly affected by the surface incompressibility. We show that for small particlewall gaps, the transverse and lateral particle resistance coefficients can be rescaled onto corresponding universal master curves. The scaling functions depend on a scaling variable that combines the particlewall gap with the viscosity ratio between fluids on both sides of the interface. A logarithmic dependence of the contact value of the lateral resistance function on the viscosity ratio is derived. Accurate numerical calculations are performed using our Cartesianrepresentation method. Keywords:Viscosity, Friction, Lubrication, Liquid liquid interfaces, Surfactants Affiliations:
 
44.  Bławzdziewicz J.^{♦}, EkielJeżewska M.L., Wajnryb E., Hydrodynamic coupling of spherical particles to a planar fluidfluid interface: Theoretical analysis, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3475217, Vol.133, pp.114703111, 2010 Abstract: We have developed a new technique based on our Cartesianrepresentation method to describe hydrodynamic interactions of a spherical particle with an undeformable planar fluidfluid interface under creepingflow conditions. The interface can be either surfactantfree or covered with an incompressible surfactant monolayer. We consider the effect of surface incompressibility and surface viscosity on particle motion. The new algorithm allows to calculate particle mobility coefficients for hydrodynamically coupled particles, moving either on the same or on the opposite sides of the interface. Keywords:Stokes equations, hydrodynamic interactions, fluidfluid interface, surfactant Affiliations:
 
45.  Abade G.C.^{♦}, Cichocki B.^{♦}, EkielJeżewska M.L., Nägele G.^{♦}, Wajnryb E., Highfrequency viscosity and generalized Stokes–Einstein relations in dense suspensions of porous particles, JOURNAL OF PHYSICSCONDENSED MATTER, ISSN: 09538984, DOI: 10.1088/09538984/22/32/322101, Vol.22, pp.32210116, 2010 Abstract: We study the highfrequency limiting shear viscosity, η∞, of colloidal suspensions of uncharged porous particles. An individual particle is modeled as a uniformly porous sphere with the internal solvent flow described by the Debye–Bueche–Brinkman equation. A precise hydrodynamic multipole method with a full account of manyparticle hydrodynamic interactions encoded in the HYDROMULTIPOLE program extended to porous particles, is used to calculate η∞ as a function of porosity and concentration. The secondorder virial expansion for η∞ is derived, and its range of applicability assessed. The simulation results are used to test the validity of generalized Stokes–Einstein relations between η∞ and various shorttime diffusion coefficients, and to quantify the accuracy of a simplifying cell model calculation of η∞. An easytouse generalized Saitˆo formula for η∞ is presented which provides a good description of its porosity and concentration dependence. Keywords:Stokes flow, hydrodynamic interactions, permeable particles, dense suspensions, effective viscosity Affiliations:
 
46.  Abade G.C.^{♦}, Cichocki B.^{♦}, EkielJeżewska M.L., Nägele G.^{♦}, Wajnryb E., Dynamics of permeable particles in concentrated suspensions, PHYSICAL REVIEW E, ISSN: 15393755, DOI: 10.1103/PhysRevE.81.020404, Vol.81, pp.02040414, 2010 Abstract: We calculate shorttime diffusion properties of suspensions of porous colloidal particles as a function of their permeability, for the full fluidphase concentration range. The particles are modeled as spheres of uniform permeability with excluded volume interactions. Using a precise multipole method encoded in the HYDROMULTIPOLE program, results are presented for the hydrodynamic function, H(q), sedimentation coefficient, and selfdiffusion coefficients with a full account of manybody hydrodynamic interactions. While selfdiffusion and sedimentation are strongly permeability dependent, the wavenumber dependence of the hydrodynamic function can be reduced by appropriate shifting and scaling, to a single master curve, independent of permeability. Generic features of the permeable sphere model are discussed. Keywords:Stokes equations, hydrodynamic interactions, permeable particles, concentrated suspensions, selfdiffusion, hydrodynamic function, collective diffusion Affiliations:
 
47.  Myłyk A., EkielJeżewska M.L., How walls influence destabilization of a suspension drop settling under gravity in a viscous fluid?, COLLOIDS AND SURFACES APHYSICOCHEMICAL AND ENGINEERING ASPECTS, ISSN: 09277757, DOI: 10.1016/j.colsurfa.2010.01.013, Vol.365, pp.109111, 2010 Abstract: An experiment was performed to test the influence of walls on destabilization of a suspension drop settling under gravity in a viscous fluid in the low Reynolds number regime. The averaged distance the drop settled until destabilization was determined. In was found that in the presence of one or two parallel vertical walls close by, the destabilization length is shorter than in an unbounded fluid. Keywords:Low Reynolds number flow, Destabilization of suspension drop Affiliations:
 
48.  Adamczyk Z.^{♦}, Sadlej K., Wajnryb E., EkielJeżewska M.L., Warszyński P.^{♦}, Hydrodynamic radii and diffusion coefficients of particle aggregates derived from the bead model, JOURNAL OF COLLOID AND INTERFACE SCIENCE, ISSN: 00219797, DOI: 10.1016/j.jcis.2010.03.066, Vol.347, pp.192201, 2010 Abstract: The multiple expansion method was applied for calculating friction tensors and hydrodynamic radii RH of rigid molecules of various shape, composed of ns equal sized, touching spheres. The maximum value of ns studied was 450, which covers most situations met in practice. Calculations were performed for linear chains, halfcircles, circles (cyclic molecules) and Sshaped aggregates. It was shown that our results agreed with previous theoretical data obtained for linear chains and cyclic aggregates, for ns < 100. For larger ns, studied exclusively in our work, interpolating analytical expressions were formulated for the hydrodynamic radii RH. These expressions, involving logarithmic function of the aspect ratio parameter (length to width ratio of the macromolecules), are the main finding of our work. Using these expressions, the ratio of the hydrodynamic radius of cyclictolinear aggregate qf was calculated, which is a parameter of vital significance. It was determined that qf attained values close to 0.95 for ns ∼450. This suggests that the previous analytical results derived by Tchen [19], in the slender body limit, who predicted that qf → 12/11 = 1.09, are not applicable for ns < 450. Using the RH values, the average translation diffusion coefficients and the sedimentation coefficients for these aggregate shapes were calculated. It was shown that our theoretical results are in good agreement with experimental data obtained for polyelectrolytes and for DNA fragments of various molecular mass. It was concluded that our results can be effectively used to determine the shape of macromolecules, in particular to discriminate between linear and cyclic DNA configurations. Keywords:Aggregates of particles of various shapes, Bead model of particle aggregates, Diffusion coefficients of particle aggregates, DNA bead model of, DNA fragment hydrodynamic radii, Hydrodynamic radius of aggregates, Linear chain aggregates, Sedimentation coefficients of aggregates and macromolecules Affiliations:
 
49.  Cichocki B.^{♦}, EkielJeżewska M.L., Green tensors for Debye–Büche–Brinkman equations generalized for axisymmetric medium, JOURNAL OF MATHEMATICAL PHYSICS, ISSN: 00222488, DOI: 10.1063/1.3498686, Vol.51, pp.103101112, 2010 Abstract: A fluid flow through a nonisotropic porous medium with an axial symmetry is considered. The Green tensors for the corresponding nonisotropic Debye–Büche–Brinkman equations are calculated in terms of single integrals. Shortdistance and farfield limiting behavior is discussed. The exact solution for the Green tensors is found explicitly in the limiting case of an infinite shielding length along the symmetry axis of the system. Keywords:Tensor methods, Porous media, Fluid equations, Integral equations, Exact solutions Affiliations:
 
50.  Feuillebois F.^{♦}, EkielJeżewska M.L., Suspensions de particules et interactions hydrodynamiques dans fun luide visqueux, Annales / Centre Scientifique de l'Académie Polonaise des Sciences, Vol.12, pp.4461, 2010 Abstract: Un groupe polonais (dont les responsables ont été B. Cichocki durant la période 19961997 et M. L. EkielJeżewska depuis 1998 jusqu’à ce jour, en 2010) et un groupe français (dont le responsable est F. Feuillebois) collaborent depuis 1996 dans le cadre des échanges entre le CNRS (Laboratoires PMMH jusqu’à fin 2009, puis maintenant LIMSI) et l’Académie des Sciences de Pologne (IPPT PAN). Le domaine d’étude de cette collaboration en Mécanique des Fluides concerne les suspensions de particules dans des fluides visqueux et en particulier les interactions hydrodynamiques dans les suspensions. Keywords:suspensions, hydrodynamic interactions, viscous fluids, microscale Affiliations:
 
51.  EkielJeżewska M.L., Odnalezione akta Biblioteki Powiatowego Oddziału ZNP w Mińsku Mazowieckim, Rocznik Mińskomazowiecki, ISSN: 1232633X, Vol.18, pp.124135, 2010 Abstract: Na podstawie archiwaliów dotyczących oświaty i życia społecznego w powiecie mińskim odnalezionych w mieszkaniu nauczycieli Janiny i Józefa Sylwestrowiczów opowiedziana zostaje ciekawa historia Biblioteki Oddziału Powiatowego Związku Nauczycielstwa Polskiego w Mińsku Mazowieckim w okresie od lat trzydziestych po pięćdziesiąte. Opowieść ta ilustruje, jak ważną rolę może mieć udostępnienie nowych, nieznanych dotąd i nie opracowanych dokumentów w ramach nowej stałej wystawy w Muzeum Ziemi Mińskiej. Otóż analiza materiałów źródłowych przez młodzież szkolną i pedagogów w ramach warsztatów edukacyjnych wykorzystujących te zbiory może przyczynić się do głębszego poznania historii regionu, a zarazem stworzenia nowych atrakcyjnych form kształcenia. Keywords:biblioteka nauczycielska, muzeum, edukacja Affiliations:
 
52.  EkielJeżewska M.L., Zabytkowe kuchnie i łazienki w Mińsku Mazowieckim i Paryżu, Rocznik Mińskomazowiecki, ISSN: 1232633X, Vol.18, pp.187255260, 2010 Abstract: W artykule na fotografiach pokazujemy fragment tworzonej właśnie w Muzeum Ziemi Mińskiej nowej wystawy stałej, a mianowicie skromnie wyposażoną kuchnię i łazienkę polskiego mieszkania nauczycieli w okresie międzywojennym, a obok analogiczne wnętrza stanowiące ekspozycję stałą Muzeum Nissim de Camondo w Paryżu. edukacja, oszczędność, tradycje i wartości II RP Affiliations:
 
53.  EkielJeżewska M.L., W Muzeum Ziemi Mińskiej ożyją przedwojenne tradycje polskich nauczycieli, Rocznik Mińskomazowiecki, ISSN: 1232633X, Vol.18, pp.190196, 261262, 2010 Abstract: Wielowątkowa kolekcja oświatowa Sylwestrowiczów jest zalążkiem, który stwarza szansę na pokazanie w Muzeum Ziemi Mińskiej szerokim kręgom zainteresowanych, na czym polegało życie i praca przedwojennych polskich nauczycieli. Na nowej stałej wystawie można tu będzie usłyszeć barwną opowieść, ilustrowaną prawdziwymi rekwizytami tej właśnie rodziny, ich zdjęciami i dokumentami, odwiedzić pokoje, z których ,,jakby przed chwilą wyszli'' dawni mieszkańcy, posłuchać wspomnień z tamtych lat. A studentów i pedagogów z pewnością zaciekawi wzięcie udziału w lekcji szkolnej i poeksperymentowanie zgodnie z treścią podręcznika czy zapisków nauczyciela, a także zapoznanie się na podstawie dokumentacji z przebiegiem kursów pedagogicznych i rolą bibliotek1 oraz przestudiowanie przedwojennych dokumentów. Keywords:Nauka, edukacja, muzeum, tradycja, pedagog Affiliations:
 
54.  Sadlej K., Wajnryb E., Bławzdziewicz J.^{♦}, EkielJeżewska M.L., Adamczyk Z.^{♦}, Streaming current and streaming potential for particle covered surfaces: Virial expansion and simulations, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3103545, Vol.130, pp.144706111, 2009 Abstract: Streaming potential changes induced by deposition of particles at solid/liquid interfaces are considered theoretically. The solution is obtained in terms of a virial expansion of the streaming potential up to the third order of the surface coverage of particles, assumed to be distributed according to the hard sphere equilibrium distribution function. Theoretical methods, including the idea of cluster expansion, are adopted from statistical physics. In the cluster expansion, twobody and threebody hydrodynamic interactions are evaluated with a high precision using the multipole method. The multipole expansion algorithm is also used to perform numerical simulations of the streaming potential, valid for the entire surface coverage range met in practice. Results of our calculations are in good agreement with the experimental data for spherical latex particles adsorbed on a mica surface. Keywords:Streaming current, streaming potential, particlecovered wall, Stokes equations, hydrodynamic interactions, multiple expansion, viral exapnsion Affiliations:
 
55.  Cichocki B.^{♦}, EkielJeżewska M.L., Selfdiffusion of a sphere in an effective medium of rods, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3146786, Vol.130, pp.21490216, 2009 Abstract: Selfdiffusion of a sphere in a network of rods is analyzed theoretically.Hydrodynamic interactions are taken into account according to the model of Dhont et al. [J. Chem. Phys.122, 044905 (2005); Dhont et al., J. Chem. Phys.124, 044907 (2006); Dhont et al., J. Chem. Phys.126, 214501 (2007)] based on the Debye–Bueche–Brinkman equation. The hydrodynamic screening length of the effective medium is assumed to be much larger than the sphere radius and the rod thickness. The selfdiffusion coefficient, given by Dhont et al. in terms of fourdimensional integrals, is in this work expressed in terms of a single integral only and therefore evaluated numerically with a high precision. Moreover, simple expressions for the selfdiffusion coefficient are derived and shown to be independent of the rod length. They can be useful for experimental verification of the model. Keywords:Hydrodynamics, Friction, Hydrological modeling, Self diffusion, Tensor methods Affiliations:
 
56.  EkielJeżewska M.L., Wajnryb E., Hydrodynamic orienting of asymmetric microobjects under gravity, JOURNAL OF PHYSICSCONDENSED MATTER, ISSN: 09538984, DOI: 10.1088/09538984/21/20/204102, Vol.21, No.20, pp.20410218, 2009 Abstract: It is shown that nonsymmetric microobjects orient while settling under gravity in a viscous fluid. To analyze this process, a simple shape is chosen: a nondeformable 'chain'. The chain consists of two straight arms, made of touching solid spheres. In the absence of external torques, the spheres are free to spin along the arms. The motion of the chain is evaluated by solving the Stokes equations with the use of the multipole method. It is demonstrated that the spinning beads speed up sedimentation by a small amount and increase the orientation rate significantly in comparison to the corresponding rigid chain. It is shown that chains orient towards the Vshaped stable stationary configuration. In contrast, rods and starshaped microobjects do not rotate. The hydrodynamic orienting is relevant for efficient swimming of nonsymmetric microobjects and for sedimenting suspensions. Keywords:Stokes flow, hydrodynamic interactions, particles settling under gravity, hydrodynamic orientinfg Affiliations:
 
57.  Alabrudziński S.^{♦}, EkielJeżewska M.L., ChehataGomez D.^{♦}, Kowalewski T.A., Particle clusters settling under gravity in a viscous fluid, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.3168615, Vol.21, No.7, pp.7330218, 2009 Abstract: Clusters made of a small number of close solid spherical particles at a random configuration, sedimenting through a viscous fluid at small Reynolds number, were experimentally investigated at a shorttime scale. The cluster settling velocities were measured and shown to be well approximated by the ensembleaveraged formula derived earlier for the uniform distribution of the point particles inside a spherical volume. It was emphasized that the “effective radius” of this volume in general should be smaller than the actual radius of a cluster made of the spheres, and the relation between both radii was determined. The formula was also shown to account well for the gravitational settling of rigid conglomerates, measured and computed elsewhere. Keywords:cluster of sendimenting particles, small Reynolds number Affiliations:
 
58.  EkielJeżewska M.L., Wajnryb E., Precise multipole method for calculating hydrodynamic interactions between spherical particles in the Stokes flow, Theoretical Methods for Micro Scale Viscous Flows, ISBN: 9788178954004, pp.127172, 2009 Abstract: An efficient procedure with a controlled high accuracy, the sphericalmultipole method, is presented, adequate for evaluating Stokesian dynamics of nondeformable spherical particles suspended in a fluid, or hydrodynamic resistance of moving or motionless systems of such particles under lowReynoldsnumber flows. We present a few examples of specific applicatins of this method. In this procedure, the relative motion of particles is corrected for lubrication, to achieve fast convergence with the multipole order of the truncation. The main advantage of this algorithm is that it is possible to perform computations with a very high multipole order of the truncation, controlling the accuracy. Moreover, the method is applicable to systems of various types of the particles in a fluid bounded by one or two parallel flat interfaces. Keywords:Stokes equations, hydrodynamic interactions, multipole expansion Affiliations:
 
59.  EkielJeżewska M.L., Sadlej K., Wajnryb E., Friction of rodlike particles adsorbed to a planar surface in a shear flow, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.2957492, Vol.129, pp.4110414, 2008 Abstract: A planar hard surface covered with elongated stiff rodlike particles in shear flow is considered in the lowReynoldsnumber regime assuming low particle surface coverage. The particles are modeled as straight chains of spherical beads. Multipole expansion of the Stokes equations (the accurate HYDROMULTIPOLE algorithm) is applied to evaluate the hydrodynamic force exerted by the fluid on the rodlike particles, depending on their shape, i.e., on the number of beads and their orientation with respect to the wall and to the ambient shear flow. Keywords:Stokes flow, hydrodynamic interactions, rigid rod, solid wall, hydrodynamic friction Affiliations:
 
60.  EkielJeżewska M.L., Wajnryb E., Bławzdziewicz J.^{♦}, Feuillebois F.^{♦}, Lubrication approximation for microparticles moving along parallel walls, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3009251, Vol.129, pp.18110214, 2008 Abstract: Lubrication expressions for the friction coefficients of a spherical particle moving in a fluid between and along two parallel solid walls are explicitly evaluated in the lowReynoldsnumber regime. They are used to determine lubrication expression for the particle free motion under an ambient Poiseuille flow. The range of validity and the accuracy of the lubrication approximation are determined by comparing with the corresponding results of the accurate multipole procedure. The results are applicable for thin, wide, and long microchannels, or quasitwodimensional systems. Keywords:Lubrication, Friction, Poiseuille flow, Particle velocity, Fluid equations Affiliations:
 
61.  EkielJeżewska M.L., Gubiec T.^{♦}, Szymczak P.^{♦}, Stokesian dynamics of close particles, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.2930881, Vol.20, pp.63102110, 2008 Abstract: Stokesian dynamics simulations of close particles are reported, taking into account lubrication forces and manybody hydrodynamic interactions between spheres. A periodic trajectory of three particles maintaining a permanent proximity to each other has been found and analyzed. This solution is used as a benchmark to study the accuracy and stability of various numerical integration schemes. In particular, different methods of preventing unphysical overlaps of the particles are considered and potential artifacts discussed. Keywords:Kinematics, Renormalization, Surface dynamics, Lubrication, Hydrodynamics Affiliations:
 
62.  Myłyk A., EkielJeżewska M.L., Odwracalność mikroprzepływów, POSTĘPY FIZYKI, ISSN: 00325430, Vol.59, No.6, pp.238243, 2008 Abstract: In daily life, at the macroscopic scale, inertia of water flows is commonly experienced and applied. However, for microobjects moving in water environment, inertia is negligible. That is why sometimes the processes observed at the microscale are in contradiction with our intuition. The examples of such amazing effects can be seen on the famous G.I. Taylor’s movie. The aim of this paper is to analyze the most spectacular of the demonstrations presented there: apparently mixed fluid recovers its initial inhomogeneous structure when the direction of the mixing is reversed. Keywords:Lepki płyn, odwracalność mikroprzepływów, bezwładność Affiliations:
 
63.  Alabrudziński S.^{♦}, Kowalewski T.A., EkielJeżewska M.L., Suchecki W.^{♦}, Metoda pomiaru ruchu malej grupy czastek opadajacej w cieczy, Wybrane zagadnienia przepływów i wymiany ciepła, pp.5985, 2008 Abstract: Praca zawiera opis badań zjawiska opadania cząstek kulistych w cieczy o dużej lepkości, a w szczególności wzajemnych oddzaiływań między poszczególnymi, opadającymi razem cząstkami. Opisano stanowisko badawcze, sposób przeprowadzenia pomiarów oraz przedstawiono wybrane wyniki badań. Keywords:gliceryna, kilka cząsteki szklanych, eksperyment, trajektorie cząstek, dynamika Affiliations:
 
64.  Cichocki B.^{♦}, EkielJeżewska M.L., Wajnryb E., Hydrodynamic interactions between spheres in a viscous fluid with a flat free surface or hard wall, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.2724815, Vol.126, pp.184704184707, 2007 Abstract: Hydrodynamic interactions between spheres immersed in a lowReynoldsnumber fluid flow close to a flat free surface or hard wall are investigated. The spheres may have different or equal radii, and may be separated from the boundary or at contact with the free surface. A simple and useful expression is derived for the propagator (Green operator) connecting centers of two spheres. In the derivation, the method of images and the displacement theorems are used. Symmetry of the displacement operators is explicitly shown. The significance of these results in efficient Stokesian and Brownian dynamics simulations is outlined. An example of an application is shown. Keywords:Free surface, Hydrodynamics, Friction, Fluid flows, Mirrors Affiliations:
 
65.  Dudyński M.T.^{♦}, EkielJeżewska M.L., The relativistic Boltzmann equation  mathematical and physical aspects, JOURNAL OF TECHNICAL PHYSICS, ISSN: 03248313, Vol.48, No.6, pp.3947, 2007 Abstract: Mathematical structure of the linearized Boltzmann equation is outlined. Physical interpretation of the assumed relativistic crosssections is discussed. Keywords:relativistic Boltzmann equation, relativistic crosssection Affiliations:
 
66.  EkielJeżewska M.L., Wajnryb E., Equilibria for the relative motion of three heavy spheres in Stokes fluid flow, PHYSICAL REVIEW E, ISSN: 15393755, DOI: 10.1103/PhysRevE.73.046309, Vol.E 73, pp.463090, 2006 Abstract: Dynamics of three identical solid spheres falling under gravity in lowReynoldsnumber fluid flow is investigated. Stationary solutions are found. Their stability is discussed. Phase portraits for two types of symmetric motions are calculated. Keywords:Stokes equations, hydrodynamic interactions, particles settling under gravity Affiliations:
 
67.  EkielJeżewska M.L., Metzger B.^{♦}, Guazzelli E.^{♦}, Spherical cloud of point particles falling in a viscous fluid, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.2186692, Vol.18, pp.381040, 2006 Abstract: Statistical mechanics is applied to calculate ensembleaveraged particle and fluid velocity fields of a spherical cloud of point particles sedimenting at a low Reynolds number. The analogy with the fall of a liquid drop in another lighter fluid is discussed. Keywords:Fluid drops, Tensor methods, Fluid equations, Hydrodynamics, Reynolds stress modeling Affiliations:
 
68.  EkielJeżewska M.L., Felderhof B.U.^{♦}, Clusters of particles falling in a viscous fluid with periodic boundary conditions, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.2396910, Vol.18, pp.1215020, 2006 Abstract: Exemplary dynamics of three point particles falling under gravity in Stokes flow with periodic boundary conditions is presented in a movie. Stable and unstable solutions of the equations of Stokesian dynamics are explicitly shown for two initial configurations: equilateral triangles with side lengths close to a critical size. Keywords:Kinematics, Suspensions, Boundary value problems, Viscosity, Anisotropy Affiliations:
 
69.  EkielJeżewska M.L., Wajnryb E., Accuracy of the multipole expansion applied to a sphere in a creeping flow parallel to a wall, QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, ISSN: 00335614, DOI: 10.1093/qjmam/hbl016, Vol.59, pp.563585, 2006 Abstract: An example system is studied to discuss precision of the multipole expansion, applied to determine forces exerted on particles by a viscous lowReynoldsnumber fluid flow. A single sphere in an ambient flow (pure shear, quadratic, and modulated shear) parallel to a close plane wall is considered. Forces and torques exerted by the ambient flow on a motionless sphere are evaluated. Their precision is determined and related to a multipole order of the truncation. Similar analysis is performed for a moving sphere with no ambient flow and for a freely moving sphere. Relative motion of the sphere with respect to the wall gives rise to strong lubrication interactions. It is analysed how these interactions affect accuracy of the pure multipole expansion, and what are the smallest distances where it becomes insufficient. An alternative precise method is applied, in which lubrication expressions are subtracted from the hydrodynamic forces and torques, and the residue is evaluated as a fastconvergent series of inverse powers of the distance between the sphere centre and the wall. The accuracy of this procedure is carefully analysed. Keywords:Stokes flow, lubrication, multipole method Affiliations:
 
70.  EkielJeżewska M.L., Wajnryb E., Threeparticle motion under gravity in Stokes flow: an equilibrium for spheres in contrast to “an endofworld” for point particles, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.58, No.45, pp.489494, 2006 Abstract: Evolution of three identical solid spheres falling under gravity in a lowReynolds number flow is investigated for a symmetric initial configuration. Three spheres aligned horizontally at equal distances evolve towards an equilibrium relative configuration while the point particles collapse onto a single point in a finite time. Keywords:Stokes equations, hydrodynamic interactions, particles settling under gravity Affiliations:
 
71.  EkielJeżewska M.L., Felderhof B.U.^{♦}, Periodic sedimentation of three particles in periodic boundary conditions, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.2008827, Vol.17, pp.931020, 2005 Abstract: Solutions of the equations of Stokesian dynamics for point particles are found for periodic boundary conditions with three particles per unit cell of a simple cubic lattice. Two particles per cell move with equal velocity, but three particles per cell usually lead to irregular motion. For a class of initial conditions with special symmetry motions are found that are periodic in time as well as in space. It is shown that there is a range of stability in which the motions are robust under perturbation. Keywords:Tensor methods, Boundary value problems, Eigenvalues, Periodic solutions, Equations of motion Affiliations:

List of chapters in recent monographs
1. 515  EkielJeżewska M.L., 100 lat Związku Nauczycielstwa Polskiego na terenie powiatu mińskiego 19162016, rozdział: O Powiatowej Bibliotece Nauczycielskiej ZNP w Mińsku Mazowieckim w latach 193151, Zarząd Oddziału ZNP w Mińsku Mazowieckim, pp.154169, 2016  
2. 339  EkielJeżewska M.L., Advances in Science, Technology, Higher Education and Society in the Conceptual Age: STHESCA, rozdział: The system of learning and teaching organized by the Polish Commission of the National Education (177394), AHFE Conference in US, pp.3140, 2014  
3. 340  EkielJeżewska M.L., Human Factors of a Global Society; A system of systems perspective, rozdział: Experimenting with Teaching Contexts, CRC Press Taylor & Francis Group, 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 334872742, 79, pp.895905, 2014  
4. 305  Cichocki B.^{♦}, EkielJeżewska M.L., Naegele G.^{♦}, Wajnryb E., Drops and Bubbles in Contact with Solid Surface, rozdział: Hydrodynamic Interactions Between Solid Particles at a FluidGas Interface, Ferrari M., Liggieri L., Miller R., CRC Press, Leiden, pp.93104, 2012  
5. 375  EkielJeżewska M.L., Wajnryb E., Theoretical Methods for Micro Scale Viscous Flows, rozdział: Precise multipole method for calculating hydrodynamic interactions between spherical particles in the Stokes flow, Transworld Research Network, François Feuillebois and Antoine Sellier (Eds.), pp.127172, 2009  
6. 241  Alabrudziński S.^{♦}, EkielJeżewska M.L., Suchecki W.^{♦}, Kowalewski T.A., Wybrane zagadnienia przepływu płynów i wymiany ciepła, rozdział: Metoda pomiaru ruchu malej grupy cząstek opadającej w cieczy, Oficyna Wydawnicza Politechniki Warszawskiej (Warszawa), Suchecki W. (Eds.), pp.5985, 2008  
7. 331  Alabrudziński S.^{♦}, EkielJeżewska M.L., Kowalewski T.A., Urbaniec K.^{♦}, Wybrane zagadnienia mechaniki w budowie urządzeń technicznych, rozdział: Badania eksperymentalne i interpretacja teoretyczna oddziaływań hydrodynamicznych grupy czastek kulistych opadajacych w lepkiej cieczy, Instytut Inżynierii Materiałowej Politechniki Warszawskiej, pp.721, 2008 
Editor of monographs
1. 298  EkielJeżewska M.L., Microparticles in Stokes Flows: Symposium in Honor of François Feuillebois' 65th Birthday, 2124 August 2011, Warsaw, Poland, JOURNAL OF PHYSICS: CONFERENCE SERIES, 392, 2012, IOP SCIENCE, pp.1176, 2012 
Conference papers
1.  Cichocki B.^{♦}, EkielJeżewska M.L., Wajnryb E., Intrinsic viscosity for Brownian particles of arbitrary shape, Symposium on Microparticles in Stokes Flows in Honor of Francois Feuillebois 65th Birthday, 20110821/0824, Warszawa (PL), DOI: 10.1088/17426596/392/1/012004, Vol.392, pp.01200417, 2012 Abstract: General expressions for the frequencydependent Brownian contribution to the intrinsic viscosity of arbitraryshaped particles have been derived from the Smoluchowski equation. Keywords:intrinsic viscosity, Brownian motion, particle of arbitrary shape Affiliations:
 
2.  Sadlej K., Wajnryb E., EkielJeżewska M.L., Kowalewski T.A., Dynamics of nanofibres conveyed by low Reynolds number flow in a microchannel, ExHFT7, 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, 20090628/0703, Kraków (PL), pp.237244, 2009  
3.  Sadlej K., EkielJeżewska M.L., Wajnryb E., Hydrodynamic friction of polymer absorbed on a planar surface, ICTAM XXII, 22nd International Congress of Theoretical and Applied Mechanics, 20080825/0829, Adelaide (AU), 2008 Abstract: A rigid polymer model consisting of two identical spherical particles, irreversibly adsorbed on a planar channel wall is considered. The linear dimensions of the polymer are assumed to be small enough to validate an expansion of the flow inside the channel to linear terms only. The polymer is therefore effectively immersed in a shearing flow. Total hydrodynamic force acting on the polymer is calculated. The dependence of that force on the polymers orientation is derived taking into account symmetries of the system. Large differences in the force are found for different polymer orientations. Applications of these results are sketched. Keywords:Stokes equations, hydrodynamic interactions, hydrodynamic friction, rigid rod, plane wall Affiliations:
 
4.  EkielJeżewska M.L., Periodic orbits of Stokesian dynamics, ICTAM XXII, 22nd International Congress of Theoretical and Applied Mechanics, 20080825/0829, Adelaide (AU), 2008 Abstract: A family of periodic in time solutions of the Stokesian dynamics has been found numerically for three identical spherical particles settling under gravity in a vertical plane. The particles stay close to each other and hydrodynamic interaction between their surfaces is essential to detect the oscillations, which have not been found in the pointparticle simulations. The periodic orbits are responsible for 'chaotic scattering' of the particles, which come and stay for some time sufficiently close to these orbits before 'escaping'. The existence of such periodic solutions is of fundamental importance for understanding evolution of manyparticle systems, and also as a benchmark for testing numerical procedures used to evaluate the Stokesian dynamics. Keywords:Stokes equations, hydrodynamic interactions, particles settling under gravity, periodic orbits Affiliations:

Conference abstracts
1.  EkielJeżewska M.L., Bukowicki M., Sedimenting elastic trumbbells, From active matter to complex fluids, 20180108/0110, Nicea (FR), pp.15, 2018  
2.  Trombley C., EkielJeżewska M.L., Stationary states of charged particles settling under gravity in a viscous fluid, From active matter to complex fluids, 20180108/0110, Nicea (FR), pp.24, 2018  
3.  Bukowicki M., EkielJeżewska M.L., Effect of bending on sedimentation of two deformable microparticles, Bulletin of the American Physical Society, ISSN: 00030503, Vol.63, No.13, pp.81, 2018  
4.  Bławzdziewicz J.^{♦}, Adamczyk Z.^{♦}, EkielJeżewska M.L., Streaming current for interfaces covered by clustered particle monolayers, Bulletin of the American Physical Society, ISSN: 00030503, Vol.63, No.13, pp.118119, 2018  
5.  EkielJeżewska M.L., Gruca M., Bukowicki M., Particles sedimenting in a permeable medium, Bulletin of the American Physical Society, ISSN: 00030503, Vol.63, No.13, pp.368, 2018  
6.  Szymczak P.^{♦}, GruzielSłomka M., Kondratiuk P.^{♦}, EkielJeżewska M.L., Sedimentation of elastic loops in a viscous fluid, Bulletin of the American Physical Society, ISSN: 00030503, Vol.63, No.13, pp.368, 2018  
7.  EkielJeżewska M.L., Cichocki B.^{♦}, Wajnryb E., Translational and rotational Brownian motion of particles of complex shapes, 30th Marian Smoluchowski Symposium on Statistical Physics, 20170903/0908, Kraków (PL), pp.12, 2017  
8.  EkielJeżewska M.L., Cichocki B.^{♦}, Wajnryb E., Brownian motion of colloidal particles with arbitrary shapes, Dynamics of Interfaces in Complex Fluids and Complex Flows, 20170228/0303, Erlangen (DE), pp.2021, 2017  
9.  Farutin A., Piasecki T., Słowicka A.M., Misbah C., Wajnryb E., EkielJeżewska M.L., Accumulation of vesicles and flexible fibers in unbounded Poiseuille flow, FLOWING MATTER 2017, 20170123/0127, Porto (PT), pp.37, 2017  
10.  EkielJeżewska M.L., Bukowicki M., Hydrodynamic and elastic interactions of sedimenting flexible fibers, Bulletin of the American Physical Society, ISSN: 00030503, Vol.62, No.14, pp.221, 2017  
11.  Słowicka A.M., Stone H.A.^{♦}, EkielJeżewska M.L., Periodic motions of flexible fibers in shear flow, Bulletin of the American Physical Society, ISSN: 00030503, Vol.62, No.14, pp.221, 2017  
12.  Bukowicki M., EkielJeżewska M.L., Symmetric pair of elongated particles settling at low Reynolds number regime, Bulletin of the American Physical Society, ISSN: 00030503, Vol.62, No.14, pp.250, 2017  
13.  Gruziel M., Thyagarajan K.^{♦}, Dietler G.^{♦}, Szymczak P.^{♦}, EkielJeżewska M.L., Dynamics of knotted flexible loops settling under a constant force in a viscous fluid, Bulletin of the American Physical Society, ISSN: 00030503, Vol.62, No.14, pp.81, 2017  
14.  Trombley C., EkielJeżewska M.L., Stable Systems of Charged Sedimenting Particles, Bulletin of the American Physical Society, ISSN: 00030503, Vol.62, No.14, pp.575, 2017  
15.  Bławzdziewicz J.^{♦}, Adamczyk Z.^{♦}, EkielJeżewska M.L., Streaming current for particlecovered surfaces: simulations and experiments, Bulletin of the American Physical Society, ISSN: 00030503, Vol.62, No.14, pp.424, 2017  
16.  EkielJeżewska M.L., Słowicka A.M., Wajnryb E., Dynamics of flexible fibers in shear flows, Flowing matter, 20160111/0115, Porto (PT), pp.7475, 2016  
17.  Słowicka A.M., Stone H.A.^{♦}, Wajnryb E., EkielJeżewska M.L., Three modes of the dynamics of flexible fibers in shear flow, ICTAM XXIV, 24th International Congress of Theoretical and Applied Mechanics, 20160821/0826, Montréal (CA), pp.11421143, 2016 Abstract: Dynamics of a single nonBrownian flexible fiber in shear flow at low Reynolds number is investigated numerically. Initially, the fiber is straight and at the equilibrium. For different initial orientations and values of bending stiffness, three generic scenarios are observed: the fiber tends to: align along the vorticity direction, tumble within the plane perpendicular to vorticity, or perform a periodic motion superposed with translation along the flow. Keywords:Stokes equations, flexible fibers, shear flow Affiliations:
 
18.  Farutin A.^{♦}, Piasecki T., Słowicka A.M., Misbah C.^{♦}, Wajnryb E., EkielJeżewska M.L., Migration of vesicles and flexible fibers in poiseuille flow, ICTAM XXIV, 24th International Congress of Theoretical and Applied Mechanics, 20160821/0826, Montréal (CA), pp.13441345, 2016 Abstract: Dynamics of flexible fibers and vesicles in unbounded planar Poiseuille flow at the lowReynoldsnumber are shown to exhibit similar basic features, when their equilibrium (moderate) aspect ratio is the same and vesicle viscosity contrast is relatively high. The lateral migration and accumulation of these two types of flexible objects are analyzed numerically. Keywords:Stokes equations, vesicles, flexible fibers Affiliations:
 
19.  Gruca M., Bukowicki M., EkielJeżewska M.L., Chaotic Scattering and Periodic Dynamics of Regular Clusters of Particles Sedimenting in a Viscous Fluid, 6th International Symposium on Bifurcations and Instabilities in Fluid Dynamics, 20150715/0717, Paryż (FR), pp.48, 2015 Abstract: Dynamics of a cluster of nonBrownian particles falling under gravity in a viscous fluid at lowReynoldsnumer regime has been extensively studied in the literature both for small and large number of particles and oscillating motions have been discovered. In this work we investigate dynamics of clusters of many nonBrownian particles in regular configurations settling under gravity in a viscous fluid. The point particle approximation is applied for the hydrodynamic interactions. We find out that a wide range of regular initial configurations of many particles leads to very long lifetime of the cluster with periodic and quasiperiodic relative motions of particles. We vary the relative distance between the particles and observe how does it affect the dynamics. Several types of periodic and quasiperiodic solutions are discovered. For broad range of initial configurations we show that a slight change of initial conditions has a large influence on the system lifetime – we observe chaotic scattering. Keywords:complex fluids, Stokesian dynamics, lowReynoldsnumber regime Affiliations:
 
20.  Słowicka A.M., Wajnryb E., EkielJeżewska M.L., Flexible Fibers in Shear Flow, 6th International Symposium on Bifurcations and Instabilities in Fluid Dynamics, 20150715/0717, Paryż (FR), pp.61, 2015 Abstract: Modes of the dynamics of flexible fibers in shear flow in a plane perpendicular to vorticity are analyzed numerically. Stokes equations, flexible fibers, shear flow Affiliations:
 
21.  EkielJeżewska M.L., Bukowicki M., Gruca M., Hydrodynamic repulsion of elastic dumbbells, Bulletin of the American Physical Society, ISSN: 00030503, Vol.60, No.21, pp.1, 2015 Abstract: Dynamics of two identical elastic dumbbells, settling under gravity in a viscous fluid at low Reynolds number are analyzed within the pointparticle model. Initially, the dumbbells are vertical, their centers are aligned horizontally, and the springs which connect the dumbbell's beads are at the equilibrium. The motion of the beads is determined numerically with the use of the RungeKutta method. After an initial relaxation phase, the system converges to a universal timedependent solution. The elastic dumbbells tumble while falling, but their relative motion is not periodic (as in case of rigid dumbbells or pairs of separated beads). The elastic constraints break the timereversal symmetry of the motion. As the result, the horizontal distance between the dumbbells slowly increases  they are hydrodynamically repelled from each other. This effect can be very large even though the elastic forces are always much smaller than gravity. [For the details, see M. Bukowicki, M. Gruca, M. L. EkielJezewska, J. Fluid Mech. 767, p. 95 (2015).] Stokes equations, dumbbells, pointparticle model, hydrodynamic repulsion Affiliations:
 
22.  Gruca M., Bukowicki M., EkielJeżewska M.L., Periodic and quasiperiodic motions of many particles falling under gravity in a viscous fluid, Jülich Soft Matter Days, 20141111/1114, Jülich (DE), pp.102, 2014 Abstract: We investigate the dynamics of many particles settling under gravity in a viscous fluid within a Stokes flow regime. We consider two families with a very wide range of regular initial configurations of many pointparticles which lead to periodic and quasiperiodic motion. We vary the relative distance between the particles and observe how does it affect the dynamics. We observe the oscillations under some outofphase rearrangements of the particles and obtain several types of periodic motions for specified range of initial conditions. We also see a large influence of initial conditions on the cluster lifetime. Keywords:complex fluid, lowReynoldsnumber regime Affiliations:
 
23.  Bukowicki M., Gruca M., EkielJeżewska M.L., Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion, Jülich Soft Matter Days, 20141111/1114, Jülich (DE), pp.99, 2014 Abstract: Periodic motion of several particles falling under gravity in a viscous fluid was theoretically and experimentally observed in a range of systems, including some fourparticle configurations or a pair of rigid rods. In addition to its fundamental significance, such a motion is considered as important to understand general features of sedimenting random swarms, and suspensions. In this work, we consider a symmetric system of two elastic fibres, modeled as elastic dumbbells, sedimenting in a vertical plane. We focus on the problem how the elasticity (which breaks timereversal symmetry of the motion) affects the system's dynamics. The point particle model is used. We observe oscillating, but nonperiodic motion of the elastic particles. Independently of the value of the spring constant, the hydrodynamic repulsion appears between the dumbbells. The trajectory shift is slower when k tends to 0 or to infinity – in these limiting cases we recover the periodic dynamics reported in the literature. For a given finite but nonzero spring constant we observe existence of a universal timedependent trajectory to which the system converge. Keywords:Stokesian dynamics, elastic dumbbells, hydrodynamics repulsion Affiliations:
 
24.  Słowicka A.M., Wajnryb E., EkielJeżewska M.L., Migration of flexible fibers entrained by Poiseuille flow in microchannel, ICTAM XXIII, 23rd International Congress of Theoretical and Applied Mechanics, 20120819/0824, Beijing (CN), pp.12, 2012 Abstract: In this work, we consider a single nonBrownian mobile and flexible fiber immersed in Poiseuille flow in a channel consisting of two parallel infinite walls. The dynamics of the fiber is evaluated numerically from the Stokes equations by a multipole code HYDROMULTIPOLE. Investigating the fiber dynamics we found out that fibers migrate to a critical position across the channel. The distance between the wall and a limiting position depends on the fiber elongation and flexibility. For more stiff fibers the critical position results from the interplay between their tendency to drift away from the channel and the repulsive hydrodynamic interaction with the wall. For less stiff fibers the limiting position is not influenced by the presence of the wall. Differences between the critical position for different fibers can be used in the process of microfibers separation by the flow. Keywords:Stokes equations, hydrodynamic interactions, Poiseuille flow, flecible fiber Affiliations:
 
25.  EkielJeżewska M.L., Myłyk A., Evolution of suspension drops settling under gravity in a viscous fluid near a vertical wall, ICTAM XXIII, 23rd International Congress of Theoretical and Applied Mechanics, 20120819/0824, Beijing (CN), pp.12, 2012 Abstract: Using the pointforce model, we analyze how evolution of a suspension drop settling under gravity in a viscous fluid is influenced by the presence of a vertical wall near by. In particular, we show that a close drop moves away from the wall while settling along. Keywords:Stokes equations, suspension drop, sedimentaiton, vertical wall, point particles, hydrodynamic interactions Affiliations:
 
26.  Słowicka A.M., Wajnryb E., EkielJeżewska M.L., Migration of microfibers entrained by Poiseuille flow in microchannel, III National Conference of Nano and Micromechanics, 20120704/0706, Warszawa (PL), pp.7172, 2012 Keywords: Stokes equations, Poiseuille flow, flexible fibers, migration Affiliations:
 
27.  Abade G.C.^{♦}, Cichocki B.^{♦}, EkielJeżewska M.L., Nagele G.^{♦}, Wajnryb E., Diffusion, sedimentation, and rheology of concentrated suspensions of coreshell particles, III National Conference of Nano and Micromechanics, 20120704/0706, Warszawa (PL), pp.7980, 2012 Abstract: Shorttime dynamic properties of concentrated suspensions of colloidal coreshell particles have been recently studied [1] using a precise force multipole method which accounts for manyparticle hydrodynamic interactions (HIs). A coreshell particle is composed of a rigid, spherical dry core of radius a surrounded by an uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ1. The solvent flow inside the permeable shell is described by the BrinkmanDebyeBueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact nonhydrodynamically by a hardsphere nooverlap potential of radius b. Numerical results are presented for the highfrequency shear viscosity, sedimentation coefficient and the shorttime translational and rotational selfdiffusion coefficients. The simulation results cover the full threeparametric fluidphase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Manyparticle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Keywords:Stokes equations, BrinkmanDebyeBueche equations, permeable particles, translational and rotational selfdiffusion, sedimentation, effective viscosity Affiliations:
 
28.  Myłyk A., EkielJeżewska M.L., Dynamika układów wielocząstkowych opadających grawitacyjnie w lepkim płynie w pobliżu płaskiej pionowej ściany, III National Conference of Nano and Micromechanics, 20120704/0706, Warszawa (PL), pp.87, 2012 Abstract: W niniejszej prezentacji zostanie pokazany wpływ płaskiej pionowej ściany na ewolucję kropli zawiesiny opadającej pod wpływem siły grawitacyjnej w lepkim płynie dla liczb Reynoldsa znacznie mniejszych od jedności. Płyn wewnątrz i na zewnątrz opadającej kropli był identyczny, a cząstki początkowo były przypadkowo rozmieszczone wewnątrz sferycznej objętości. Przeanalizowana zostanie ewolucja opadającej kropli złożonej z cząstek. Krople podczas opadania ,,gubiły'' cząstki, które jako wolniejsze pozostawały z tyłu, tworząc ponad kroplą ,,ogon'', powoli się spłaszczały i rozszerzały, a potem nagle dzieliły na dwa lub więcej fragmentów. Średnia odległość przebyta przez opadającą kroplę zawiesiny aż do rozpadu jest tym któtsza, im mniejsza jest odległość h od środka ściainy. Badanie ewolucji kropli wykonane zostało za pomocą modelu cząstek punktowych w oparciu o funkcje Greena dla równań Stokesa. Keywords:liczba Reynoldsa, model cząstek punktowych, równania Stokesa Affiliations:
