Prof. Eligiusz Wajnryb, Ph.D., Dr. Habil. 

Doctoral thesis
19831017  Równanie Boltzmanna dla ruchu cząstki próbnej w ośrodku rozpraszającym (UW)
 731 
Habilitation thesis
2000  Efektywna lepkość zawiesin koloidalnych 
Professor
20130603  Title of professor 
Supervision of doctoral theses
1.  20111027  Kędzierski Marcin  Zastosowanie metody multipolowej do analizy oddziaływań hydrodynamicznych w cylindrycznym mikrokanale  643 
Recent publications
1.  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:
 
2.  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:
 
3.  Wajnryb E., Mizerski K.^{♦}, Shorttime selfdiffusion, collective diffusion and effective viscosity of dilute hard sphere magnetic suspensions, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, DOI: 10.1017/jfm.2016.48, Vol.791, pp.237259, 2016 Abstract: The virial corrections to shorttime self and collective diffusion coefficients as well as the effective viscosity are calculated for suspensions of hard spheres with the same radii and constant (blocked within the particle) magnetization modelled by a point dipole. Analytic, integral formulae derived from basic principles of statistical mechanics are provided for both cases – in the absence and in the presence of an external magnetic field. In the former case the diffusion and viscosity coefficients are evaluated numerically as a function of the strength of magnetic interactions between the particles and it is reported that the translational collective diffusion coefficient is significantly greater than all the other coefficients. In the presence of an external magnetic field the coefficients become anisotropic and are evaluated in the asymptotic regime of weak interparticle magnetic interactions. Keywords:colloids, lowReynoldsnumber flows, magnetic fluids Affiliations:
 
4.  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:
 
5.  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:
 
6.  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:
 
7.  Lisicki M.^{♦}, Cichocki B.^{♦}, Wajnryb E., Nearwall diﬀusion tensor of an axisymmetric colloidal particle, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.4958727, Vol.145, pp.03490418, 2016 Abstract: Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the nearwall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby noslip wall. The relative correction scales as powers of inverse wallparticle distance and its angular structure is represented by simple functions in sines and cosines of the particle’s inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translationrotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes and corrects relations known from earlier numerical and theoretical findings. Affiliations:
 
8.  Pręgowska A., Szczepański J., Wajnryb E., Temporal code versus rate code for binary Information Sources, NEUROCOMPUTING, ISSN: 09252312, DOI: 10.1016/j.neucom.2016.08.034, Vol.216, pp.756762, 2016 Abstract: Neuroscientists formulate very different hypotheses about the nature of neural coding. At one extreme, it has been argued that neurons encode information through relatively slow changes in the arrival rates of individual spikes (rate codes) and that the irregularity in the spike trains reflects the noise in the system. At the other extreme, this irregularity is the code itself (temporal codes) so that the precise timing of every spike carries additional information about the input. It is well known that in the estimation of Shannon Information Transmission Rate, the patterns and temporal structures are taken into account, while the “rate code” is already determined by the firing rate, i.e. by the spike frequency. In this paper we compare these two types of codes for binary Information Sources, which model encoded spike trains. Assuming that the information transmitted by a neuron is governed by an uncorrelated stochastic process or by a process with a memory, we compare the Information Transmission Rates carried by such spike trains with their firing rates. Here we show that a crucial role in the relation between information transmission and firing rates is played by a factor that we call the “jumping” parameter. This parameter corresponds to the probability of transitions from the nospikestate to the spikestate and vice versa. For low jumping parameter values, the quotient of information and firing rates is a monotonically decreasing function of the firing rate, and there therefore a straightforward, onetoone, relation between temporal and rate codes. However, it turns out that for large enough values of the jumping parameter this quotient is a nonmonotonic function of the firing rate and it exhibits a global maximum, so that in this case there is an optimal firing rate. Moreover, there is no onetoone relation between information and firing rates, so the temporal and rate codes differ qualitatively. This leads to the observation that the behavior of the quotient of information and firing rates for a large jumping parameter value is especially important in the context of bursting phenomena. Keywords:Information Theory, Information Source, Stochastic process, Information transmission rate, Firing rate Affiliations:
 
9.  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:
 
10.  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:
 
11.  Liu Y.^{♦}, Bławzdziewicz J.^{♦}, Cichocki B.^{♦}, Dhont J.K.G.^{♦}, Lisicki M.^{♦}, Wajnryb E., Youngf Y.N.^{♦}, Lang P.R.^{♦}, Nearwall dynamics of concentrated hardsphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations, SOFT MATTER, ISSN: 1744683X, DOI: 10.1039/c5sm01624j, Vol.11, pp.73167327, 2015 Abstract: In this article we report on a study of the nearwall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ ≈ 0.25 which provides us with a fast and noncostly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the nearwall selfdiffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that manyparticle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall. Affiliations:
 
12.  Słowicka A., Wajnryb E., EkielJeżewska M., 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:
 
13.  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:
 
14.  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:
 
15.  Pręgowska A., Szczepański J., Wajnryb E., Mutual information against correlations in binary communication channels, BMC NEUROSCIENCE, ISSN: 14712202, DOI: 10.1186/s1286801501680, Vol.16, No.32, pp.17, 2015 Abstract: Background Shannon information, Communication channel, Entropy, Mutual information, Correlation, Neuronal encoding Affiliations:
 
16.  Żuk P.J.^{♦}, Wajnryb E., Mizerski K.A.^{♦}, Szymczak P.^{♦}, Rotne–Prager–Yamakawa approximation for differentsized particles in application to macromolecular bead models, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, DOI: 10.1017/jfm.2013.668, Vol.741, pp.R5113, 2014 Abstract: The Rotne–Prager–Yamakawa (RPY) approximation is a commonly used approach to model the hydrodynamic interactions between small spherical particles suspended in a viscous fluid at a low Reynolds number. However, when the particles overlap, the RPY tensors lose their positive definiteness, which leads to numerical problems in the Brownian dynamics simulations as well as errors in calculations of the hydrodynamic properties of rigid macromolecules using bead modelling. These problems can be avoided by using regularizing corrections to the RPY tensors; so far, however, these corrections have only been derived for equalsized particles. Here we show how to generalize the RPY approach to the case of overlapping spherical particles of different radii and present the complete set of mobility matrices for such a system. In contrast to previous ad hoc approaches, our method relies on the direct integration of force densities over the sphere surfaces and thus automatically provides the correct limiting behaviour of the mobilities for the touching spheres and for a complete overlap, with one sphere immersed in the other one. This approach can then be used to calculate hydrodynamic properties of complex macromolecules using bead models with overlapping, differentsized beads, which we illustrate with an example. Keywords:complex fluids, computational methods, lowReynoldsnumber flows, mathematical foundations, suspensions Affiliations:
 
17.  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:
 
18.  Mizerski K.A.^{♦}, Wajnryb E., Żuk P.J.^{♦}, Szymczak P.^{♦}, The RotnePragerYamakawa approximation for periodic systems in a shear flow, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.4871113, Vol.140, pp.18410319, 2014 Abstract: RotnePragerYamakawa approximation is a commonly used approach to model hydrodynamic interactions between particles suspended in fluid. It takes into account all the longrange contributions to the hydrodynamic tensors, with the corrections decaying at least as fast as the inverse fourth power of the interparticle distances, and results in a positive definite mobility matrix, which is fundamental in Brownian dynamics simulations. In this communication, we show how to construct the RotnePragerYamakawa approximation for the bulk system under shear flow, which is modeled using the LeesEdwards boundary conditions. Keywords:Tensor methods, Hydrodynamics, Shear flows, Brownian dynamics, Boundary value problems Affiliations:
 
19.  Wajnryb E., Mizerski K.A.^{♦}, Żuk P.J.^{♦}, Szymczak P.^{♦}, Generalization of the RotnePragerYamakawa mobility and shear disturbance tensors, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, DOI: 10.1017/jfm.2013.402, Vol.731, pp.R3112, 2013 Abstract: The Rotne–Prager–Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation are that it includes all longrange terms (i.e. decaying as R−3 or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne–Prager–Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne–Prager–Yamakawa approximation can be generalized for other geometries and boundary conditions. Keywords:computational methods, lowReynoldsnumber flows, suspensions Affiliations:
 
20.  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:
 
21.  Arnold M.M.^{♦}, Szczepański J., Montejo N.^{♦}, Amigó J.M.^{♦}, Wajnryb E., SanchezVives M.V.^{♦}, Information content in cortical spike trains during brain state transitions, JOURNAL OF SLEEP RESEARCH, ISSN: 09621105, DOI: 10.1111/j.13652869.2012.01031.x, Vol.22, pp.1321, 2013 Abstract: Even in the absence of external stimuli there is ongoing activity in the cerebral cortex as a result of recurrent connectivity. This paper attempts to characterize one aspect of this ongoing activity by examining how the information content carried by specific neurons varies as a function of brain state. We recorded from rats chronically implanted with tetrodes in the primary visual cortex during awake and sleep periods. Electroencephalogram and spike trains were recorded during 30min periods, and 2–4 neuronal spikes were isolated per tetrode offline. All the activity included in the analysis was spontaneous, being recorded from the visual cortex in the absence of visual stimuli. The brain state was determined through a combination of behavior evaluation, electroencephalogram and electromyogram analysis. Information in the spike trains was determined by using Lempel–Ziv Complexity. Complexity was used to estimate the entropy of neural discharges and thus the information content (Amigóet al. Neural Comput., 2004, 16: 717–736). The information content in spike trains (range 4–70 bits s−1) was evaluated during different brain states and particularly during the transition periods. Transitions toward states of deeper sleep coincided with a decrease of information, while transitions to the awake state resulted in an increase in information. Changes in both directions were of the same magnitude, about 30%. Information in spike trains showed a high temporal correlation between neurons, reinforcing the idea of the impact of the brain state in the information content of spike trains. Keywords:awake, brain states, entropy, firing rate, information, sleep, spike train Affiliations:
 
22.  Bilbao A.^{♦}, Wajnryb E., Vanapalli S.A.^{♦}, Bławzdziewicz J.^{♦}, Nematode locomotion in unconfined and confined fluids, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.4816718, Vol.25, pp.081902122, 2013 Abstract: The millimeterlong soildwelling nematode Caenorhabditis elegans propels itself by producing undulations that propagate along its body and turns by assuming highly curved shapes. According to our recent study [V. Padmanabhan et al. , PLoS ONE7, e40121 (Year: 2012)10.1371/journal.pone.0040121] all these postures can be accurately described by a piecewiseharmoniccurvature model. We combine this curvaturebased description with highly accurate hydrodynamic bead models to evaluate the normalized velocity and turning angles for a worm swimming in an unconfined fluid and in a parallelwall cell. We find that the worm moves twice as fast and navigates more effectively under a strong confinement, due to the large transversetolongitudinal resistancecoefficient ratio resulting from the wallmediated farfield hydrodynamic coupling between body segments. We also note that the optimal swimming gait is similar to the gait observed for nematodes swimming in highviscosity fluids. Our bead models allow us to determine the effects of confinement and finite thickness of the body of the nematode on its locomotion. These effects are not accounted for by the classical resistiveforce and slenderbody theories. Keywords:Hydrodynamics, Land transportation, Hydrological modeling, Photonic crystals, Biological movement Affiliations:
 
23.  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:
 
24.  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:
 
25.  ZuritaGotor M.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., Layering Instability in a Confined Suspension Flow, PHYSICAL REVIEW LETTERS, ISSN: 00319007, Vol.108, pp.06830115, 2012  
26.  Janssen P.J.A.^{♦}, Barón M.D.^{♦}, Anderson P.D.^{♦}, Bławzdziewicz J.^{♦}, Loewenberg M.^{♦}, Wajnryb E., Collective dynamics of confined rigid spheres and deformable drops, SOFT MATTER, ISSN: 1744683X, DOI: 10.1039/c2sm25812a, Vol.8, pp.74957506, 2012 Abstract: The evolution of linear arrays of rigid spheres and deformable drops in a Poiseuille flow between parallel walls is investigated to determine the effect of particle deformation on the collective dynamics in confined particulate flows. We find that linear arrays of rigid spheres aligned in the flow direction exhibit a particlepairing instability and are unstable to lateral perturbations. Linear arrays of deformable drops also undergo the pairing instability but also exhibit additional dynamical features, including formation of transient triplets, cascades of pairswitching events, and the eventual formation of pairs with equal interparticle spacing. Moreover, particle deformation stabilizes drop arrays to lateral perturbations. These pairing and alignment phenomena are qualitatively explained in terms of hydrodynamic farfield dipole interactions that are insensitive to particle deformation and quadrupole interactions that are deformation induced. We suggest that quadrupole interactions may underlie the spontaneous formation of droplet strings in confined emulsions under shear Affiliations:
 
27.  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:
 
28.  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:
 
29.  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:
 
30.  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:
 
31.  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:
 
32.  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:
 
33.  Kędzierski M., Wajnryb E., Shorttime selfdiffusion coefficient of a particle in a colloidal suspension bounded by a microchannel: Virial expansions and simulation, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, Vol.135, pp.1641044, 2011  
34.  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:
 
35.  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:
 
36.  Mongruela A.^{♦}, Lecoq N.^{♦}, Wajnryb E., Cichocki B.^{♦}, Feuillebois F.^{♦}, Motion of a spherocylindrical particle in a viscous fluid in confined geometry, EUROPEAN JOURNAL OF MECHANICS BFLUIDS, ISSN: 09977546, DOI: 10.1016/j.euromechflu.2011.04.005, Vol.30, pp.405408, 2011 Abstract: The motion of a millimeter size spherocylinder particle settling in a very viscous oil in a closed container is measured by laser interferometry, with the goal to model the motion of a particle of this shape in a fluid at microscales. The container is a cylinder with vertical axis and closed at both ends by horizontal plates. The displacement of the particle along the container axis is recorded with a resolution of the order of 100 nm, that is much smaller than the particle–wall separation when in the lubrication regime. The particle friction coefficient, measured as a function of the particle–wall distance, is then used to test the theoretical predictions of an accurate hydrodynamic analysis. The Stokes flow problem is solved by using the hydromultipole method, that is in general appropriate for spheres but is extended here to a nonspherical particle by using a compound of overlapping spheres. The lateral wall effect is negligible but the two parallel horizontal end plane walls are accurately taken into account. The result of the theoretical model is in good quantitative agreement with experiment for the whole settling motion of the spherocylinder, that is for any position between the walls. Keywords:Stokes flows, Suspensions, Sedimentation Affiliations:
 
37.  Szczepański J., Arnold M.^{♦}, Wajnryb E., Amigó J.M.^{♦}, SanchezVives M.V.^{♦}, Mutual information and redundancy in spontaneous communication between cortical neurons, BIOLOGICAL CYBERNETICS, ISSN: 03401200, DOI: 10.1007/s004220110425y, Vol.104, pp.161174, 2011 Abstract: An important question in neural information processing is how neurons cooperate to transmit information. To study this question, we resort to the concept of redundancy in the information transmitted by a group of neurons and, at the same time, we introduce a novel concept for measuring cooperation between pairs of neurons called relative mutual information (RMI). Specifically, we studied these two parameters for spike trains generated by neighboring neurons from the primary visual cortex in the awake, freely moving rat. The spike trains studied here were spontaneously generated in the cortical network, in the absence of visual stimulation. Under these conditions, our analysis revealed that while the value of RMI oscillated slightly around an average value, the redundancy exhibited a behavior characterized by a higher variability. We conjecture that this combination of approximately constant RMI and greater variable redundancy makes information transmission more resistant to noise disturbances. Furthermore, the redundancy values suggest that neurons can cooperate in a flexible way during information transmission. This mostly occurs via a leading neuron with higher transmission rate or, less frequently, through the information rate of the whole group being higher than the sum of the individual information rates—in other words in a synergetic manner. The proposed method applies not only to the stationary, but also to locally stationary neural signals. Keywords:Neurons, Shannon information, Entropy, Mutual information, Redundancy, Visual cortex, Spikes train, Spontaneous activity Affiliations:
 
38.  Tokarzewski S., Wajnryb E., General inequalities for multipoint Padé approximants to a Stieltjes function expanded at real points, MATHEMATICAL INEQUALITIES AND APPLICATIONS, ISSN: 13314343, Vol.14, No.4, pp.977988, 2011 Abstract: In this paper we establish the general inequalities for diagonal and subdiagonal multipoint Pad´e approximants to a Stieltjes function f in terms of power expansion of f on the real line. The inequalities derived produce the best upper and lower bounds on f with respect to the given coefficients of Stieltjes series. As an example of applications sequences of upper and lower Pad´e bounds converging to the effective dielectric constant of a random array of spheres are evaluated. Keywords:N point Pad´e approximants, Stieltjes functions, continued fractions Affiliations:
 
39.  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:
 
40.  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:
 
41.  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:
 
42.  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:
 
43.  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:
 
44.  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:
 
45.  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:
 
46.  Cichocki B.^{♦}, Wajnryb E., Bławzdziewicz J.^{♦}, Dhont J.K.G.^{♦}, Lang P.R.^{♦}, The intensity correlation function in evanescent wave scattering, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, Vol.132, pp.074704112, 2010  
47.  Kędzierski M., Wajnryb E., Precise multipole method for calculating manybody hydrodynamic interactions in a microchannel, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, Vol.133, pp.154105111, 2010  
48.  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:
 
49.  Bławzdziewicz J.^{♦}, Goodman R.H.^{♦}, Khurana N.^{♦}, Wajnryb E., Young Y.N.^{♦}, Nonlinear hydrodynamic phenomena in Stokes flow regime, PHYSICA DNONLINEAR PHENOMENA, ISSN: 01672789, DOI: 10.1016/j.physd.2009.11.013, Vol.239, pp.12141224, 2010  
50.  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:
 
51.  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:
 
52.  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:
 
53.  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:
 
54.  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:
 
55.  Guzowski J.^{♦}, Cichocki B.^{♦}, Wajnryb E., Abade G.C.^{♦}, The shorttime selfdiffusion coefficient of a sphere in a suspension of rigid rods, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.2837296, Vol.128, pp.94502111, 2008  
56.  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:
 
57.  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:
 
58.  Bławzdziewicz J.^{♦}, Wajnryb E., Equilibrium and nonequilibrium thermodynamics of particlestabilized thin liquid films, JOURNAL OF CHEMICAL PHYSICS, ISSN: 00219606, DOI: 10.1063/1.3009558, Vol.129, pp.194509114, 2008  
59.  Nagarajan R.^{♦}, Szczepański J., Wajnryb E., Interpreting nonrandom signatures in biomedical signals with LempelZiv complexity, PHYSICA DNONLINEAR PHENOMENA, ISSN: 01672789, DOI: 10.1016/j.physd.2007.09.007, Vol.237, pp.359364, 2008 Abstract: Lempel–Ziv complexity (LZ) [J. Ziv, A. Lempel, On the complexity of finite sequences, IEEE Trans. Inform. Theory 22 (1976) 75–81] and its variants have been used widely to identify nonrandom patterns in biomedical signals obtained across distinct physiological states. Nonrandom signatures of the complexity measure can occur under nonlinear deterministic as well as nondeterministic settings. Surrogate data testing have also been encouraged in the past in conjunction with complexity estimates to make a finer distinction between various classes of processes. In this brief letter, we make two important observations (1) NonGaussian noise at the dynamical level can elude existing surrogate algorithms namely: Phaserandomized surrogates (FT) amplitudeadjusted Fourier transform (AAFT) and iterated amplitudeadjusted Fourier transform (IAAFT). Thus any inference nonlinear determinism as an explanation for the nonrandomness is incomplete (2) Decrease in complexity can be observed even across two linear processes with identical autocorrelation functions. The results are illustrated with a secondorder autoregressive process with Gaussian and nonGaussian innovations. AR(2) processes have been used widely to model several physiological phenomena, hence their choice. The results presented encou rage cautious interpretation of nonrandom signatures in experimental signals using complexity measures. Keywords:Lempel–Ziv complexity, Surrogate testing, Autoregressive process Affiliations:
 
60.  Barón M.D.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., Hydrodynamic crystals: collective dynamics of regular arrays of spherical particles in a parallelwall channel, PHYSICAL REVIEW LETTERS, ISSN: 00319007, DOI: 10.1103/PhysRevLett.100.174502, Vol.100, pp.17450214, 2008 Abstract: Simulations of over 10^3 hydrodynamically coupled solid spheres are performed to investigate collective motion of linear trains and regular square arrays of particles suspended in a fluid bounded by two parallel walls. Our novel accelerated Stokesiandynamics algorithm relies on simplifications associated with the HeleShaw asymptotic farfield form of the flow scattered by the particles. The simulations reveal propagation of particledisplacement waves, deformation, and rearrangements of a particle lattice, propagation of dislocation defects in ordered arrays, and longlasting coexistence of ordered and disordered regions. Affiliations:
 
61.  Bławzdziewicz J.^{♦}, Wajnryb E., An analysis of the farfield response to external forcing of a suspension in the Stokes flow in a parallelwall channel, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.2976306, Vol.20, pp.93303120, 2008  
62.  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:
 
63.  ZuritaGotor M.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., Swapping trajectories: a new wallinduced crossstreamline particle migration mechanism in a dilute suspension of spheres, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, Vol.592, pp.447469, 2007  
64.  ZuritaGotor M.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., Motion of a rodlike particle between parallel walls with application to suspension rheology, JOURNAL OF RHEOLOGY, ISSN: 01486055, DOI: 10.1122/1.2399084, Vol.51, pp.7197, 2007  
65.  Bhattacharya S.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., Farfield approximation for hydrodynamic interactions in parallelwall geometry, JOURNAL OF COMPUTATIONAL PHYSICS, ISSN: 00219991, DOI: 10.1016/j.jcp.2005.07.015, Vol.212, pp.718738, 2006  
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.  Bhattacharya S.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., Hydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.2195992, Vol.18, pp.533010, 2006  
68.  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:
 
69.  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:
 
70.  Bławzdziewicz J.^{♦}, Wajnryb E., Phase equilibria in stratified thin liquid films stabilized by colloidal particles, EUROPHYSICS LETTERS, ISSN: 02955075, DOI: 10.1209/epl/i2004105345, Vol.71, No.2, pp.269275, 2005  
71.  Bhattacharya S.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., Hydrodynamic interactions of spherical particles in suspension confined between two planar walls, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, DOI: 10.1017/S002211200500593, Vol.541, pp.263292, 2005  
72.  Bławzdziewicz J.^{♦}, Wajnryb E., Given J.A.^{♦}, Hubbard J.B.^{♦}, Sharp scalar and tensor bounds on the hydrodynamic friction and mobility of arbitrarily shaped bodies in Stokes flow, PHYSICS OF FLUIDS, ISSN: 10706631, DOI: 10.1063/1.1852315, Vol.17, No.3, pp.03360219, 2005  
73.  Bhattacharya S.^{♦}, Bławzdziewicz J.^{♦}, Wajnryb E., Manyparticle hydrodynamic interactions in parallelwall geometry: Cartesianrepresentation method, PHYSICA ASTATISTICAL MECHANICS AND ITS APPLICATIONS, ISSN: 03784371, DOI: 10.1016/j.physa.2005.03.031, Vol.356, pp.294340, 2005 
List of chapters in recent monographs
1. 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 
2. 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 
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.  Bławzdziewicz J.^{♦}, Wajnryb E., The swappingtrajectory effect: lattice evolution and buckling transition in wallbounded hydrodynamic crystals, Symposium on Microparticles in Stokes Flows in Honor of Francois Feuillebois 65th Birthday, 20110821/0824, Warszawa (PL), DOI: 10.1088/17426596/392/1/012008, Vol.392, pp.012008111, 2012 Abstract: We analyze novel structural transformations in perturbed periodic square monolayers of microspheres in parabolic flow between two parallel walls. We find that a perturbed monolayer is initially stabilized by the swappingtrajectory mechanism that causes the particles to fluctuate between faster and slower streamlines in such a way that particle collisions do not occur. The fluctuations slowly decay in time, and the array achieves nearly perfect rectangular order. Surprisingly, after the fluctuations have dissipated, the particle lattice undergoes a sudden buckling instability that produces coherent vertical displacements of particle rows oriented in the flow direction. The instability results in formation of a disordered phase in which particles are arranged into meandering strings, similar to the structures observed in recent experiments [2012 PNAS 109 63]. We show that the behavior of the system is controlled by the swappingtrajectory interactions at all stages of the evolution. Affiliations:
 
3.  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  
4.  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:

Conference abstracts
1.  EkielJeżewska M.L., Słowicka A.M., Wajnryb E., Dynamics of flexible fibers in shear flows, Flowing matter, 20160111/0115, Porto (PT), pp.7475, 2016  
2.  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:
 
3.  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:
 
4.  Żuk J.P.^{♦}, Wajnryb E., From rheology to molecular detail  viscosity of suspension of complex molecules, ICTAM XXIV, 24th International Congress of Theoretical and Applied Mechanics, 20160821/0826, Montréal (CA), pp.12561257, 2016 Abstract: The viscosity of solution is intrinsically connected with its composition and the properties of individual particles. For complex macromolecules there often exist coupling between the flow and the state of the molecule. The distribution of particle shapes and movements reacts to the external flow and the flow reacts to this distribution change. This coupling determines the amount of stress induced by the molecules immersed in the fluid that results in change of the viscosity. Using the RotnePrager Yamakawa approximation we show, that given molecular model, one can infer the details of the molecules based on rheology of the solution. Affiliations:
 
5.  Szczepański J., SanchezVives M.V.^{♦}, Arnold M.M.^{♦}, Montejo N.^{♦}, Paprocki B.^{♦}, Pręgowska A., Amigó J.M.^{♦}, Wajnryb E., Analyzing Neuroscience Signals using Information Theory and Complexity Shannon Communication Approach, 12th INCF, 12th INCF Workshop on Node Communication and Collaborative Neuroinformatics, 20150416/0417, Warszawa (PL), pp.132, 2015  
6.  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:
 
7.  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:
 
8.  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:
 
9.  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:
