Partner: Jerzy Bławzdziewicz

Texas Tech University (US)

Recent publications
1.Feuillebois F., Ekiel-Jeżewska M.L., Wajnryb E., Sellier A., Bławzdziewicz J., High-frequency effective viscosity of a dilute suspension of particles in Poiseuille flow between parallel walls, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2016.378, Vol.800, pp.111-139, 2016
Abstract:

It is shown that the formal expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in Poiseuille flow contains a novel quadrupole term, besides the expected stresslet. This term becomes important for a very confined geometry. For a high-frequency 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 N-bead 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:

low-Reynolds-number flows

Affiliations:
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Sellier A.-École Polytechnique (FR)
Bławzdziewicz J.-Texas Tech University (US)
2.Feuillebois F., Ekiel-Jeżewska M.L., Wajnryb E., Sellier A., Bławzdziewicz J., High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2014.690, Vol.764, pp.133-147, 2015
Abstract:

A general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to N-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. 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 ‘semi-confined’ 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, low-Reynolds-number flows, suspensions

Affiliations:
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Sellier A.-École Polytechnique (FR)
Bławzdziewicz J.-Texas Tech University (US)
3.Liu Y., Bławzdziewicz J., Cichocki B., Dhont J.K.G., Lisicki M., Wajnryb E., Youngf Y.N., Lang P.R., Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations, SOFT MATTER, ISSN: 1744-683X, DOI: 10.1039/c5sm01624j, Vol.11, pp.7316-7327, 2015
Abstract:

In this article we report on a study of the near-wall 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 non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle 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:
Liu Y.-Forschugszentrum Jülich, Institute of Complex Systems (DE)
Bławzdziewicz J.-Texas Tech University (US)
Cichocki B.-University of Warsaw (PL)
Dhont J.K.G.-Forschugszentrum Jülich, Institute of Complex Systems (DE)
Lisicki M.-other affiliation
Wajnryb E.-IPPT PAN
Youngf Y.N.-New Jersey Institute of Technology (US)
Lang P.R.-Forschugszentrum Jülich, Institute of Complex Systems (DE)
4.Sonn-Segev A., Bławzdziewicz J., Wajnryb E., Ekiel-Jeżewska M.L., Diamant H., Roichman Y., Structure and dynamics of a layer of sedimented particles, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.4928644, Vol.143, pp.074704-1-14, 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 quasi-two-dimensional 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, two-dimensional layers, diffusion, height distribution function

Affiliations:
Sonn-Segev A.-Tel Aviv University (IL)
Bławzdziewicz J.-Texas Tech University (US)
Wajnryb E.-IPPT PAN
Ekiel-Jeżewska M.L.-IPPT PAN
Diamant H.-Tel Aviv University (IL)
Roichman Y.-Tel Aviv University (IL)
5.Pasol L., Martin M., Ekiel-Jeżewska M.L., Wajnryb E., Bławzdziewicz J., Feuillebois F., Corrigendum to ‘‘Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography’’, CHEMICAL ENGINEERING SCIENCE, ISSN: 0009-2509, DOI: 10.1016/j.ces.2012.12.020, Vol.90, pp.51-52, 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, field-flow fractionation, hydrodynamic chromatotography

Affiliations:
Pasol L.-Université Pierre et Marie Curie (FR)
Martin M.-CNRS (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Bławzdziewicz J.-Texas Tech University (US)
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
6.Bilbao A., Wajnryb E., Vanapalli S.A., Bławzdziewicz J., Nematode locomotion in unconfined and confined fluids, PHYSICS OF FLUIDS, ISSN: 1070-6631, DOI: 10.1063/1.4816718, Vol.25, pp.081902-1-22, 2013
Abstract:

The millimeter-long soil-dwelling 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 piecewise-harmonic-curvature model. We combine this curvature-based 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 parallel-wall cell. We find that the worm moves twice as fast and navigates more effectively under a strong confinement, due to the large transverse-to-longitudinal resistance-coefficient ratio resulting from the wall-mediated far-field hydrodynamic coupling between body segments. We also note that the optimal swimming gait is similar to the gait observed for nematodes swimming in high-viscosity 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 resistive-force and slender-body theories.

Keywords:

Hydrodynamics, Land transportation, Hydrological modeling, Photonic crystals, Biological movement

Affiliations:
Bilbao A.-Texas Tech University (US)
Wajnryb E.-IPPT PAN
Vanapalli S.A.-Texas Tech University (US)
Bławzdziewicz J.-Texas Tech University (US)
7.Zurita-Gotor M., Bławzdziewicz J., Wajnryb E., Layering Instability in a Confined Suspension Flow, PHYSICAL REVIEW LETTERS, ISSN: 0031-9007, Vol.108, pp.068301-1-5, 2012
8.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: 1744-683X, DOI: 10.1039/c2sm25812a, Vol.8, pp.7495-7506, 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 particle-pairing 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 pair-switching 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 far-field 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:
Janssen P.J.A.-Eindhoven University of Technology (NL)
Barón M.D.-Princeton University (US)
Anderson P.D.-Eindhoven University of Technology (NL)
Bławzdziewicz J.-Texas Tech University (US)
Loewenberg M.-Yale University (US)
Wajnryb E.-IPPT PAN
9.Pasol L., Martin M., Ekiel-Jeżewska M.L., Wajnryb E., Bławzdziewicz J., Feuillebois F., Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography, CHEMICAL ENGINEERING SCIENCE, ISSN: 0009-2509, DOI: 10.1016/j.ces.2011.05.033, Vol.66, pp.4078-4089, 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 field-flow 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 particle-wall 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:
Pasol L.-Université Pierre et Marie Curie (FR)
Martin M.-CNRS (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Bławzdziewicz J.-Texas Tech University (US)
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
10.Adamczyk Z., Sadlej K., Wajnryb E., Nattich M., Ekiel-Jeżewska M.L., Bławzdziewicz J., Streaming potential studies of colloidal, polyelectrolyte and protein deposition, ADVANCES IN COLLOID AND INTERFACE SCIENCE, ISSN: 0001-8686, DOI: 10.1016/j.cis.2009.09.004, Vol.153, pp.1-29, 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:
Adamczyk Z.-Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences (PL)
Sadlej K.-IPPT PAN
Wajnryb E.-IPPT PAN
Nattich M.-Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences (PL)
Ekiel-Jeżewska M.L.-IPPT PAN
Bławzdziewicz J.-Texas Tech University (US)
11.Bławzdziewicz J., Ekiel-Jeżewska M.L., Wajnryb E., Motion of a spherical particle near a planar fluid-fluid interface: The effect of surface incompressibility, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.3475197, Vol.133, No.11, pp.114702-1-12, 2010
Abstract:

Hydrodynamic coupling of a spherical particle to an undeformable planar fluid-fluidinterface under creeping-flow conditions is discussed. The interface can be either surfactant-free 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 particle-interface distances, the remaining contributions are significant, but they are weakly affected by the surface incompressibility. We show that for small particle-wall 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 particle-wall 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 Cartesian-representation method.

Keywords:

Viscosity, Friction, Lubrication, Liquid liquid interfaces, Surfactants

Affiliations:
Bławzdziewicz J.-Texas Tech University (US)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
12.Bławzdziewicz J., Ekiel-Jeżewska M.L., Wajnryb E., Hydrodynamic coupling of spherical particles to a planar fluid-fluid interface: Theoretical analysis, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.3475217, Vol.133, pp.114703-1-11, 2010
Abstract:

We have developed a new technique based on our Cartesian-representation method to describe hydrodynamic interactions of a spherical particle with an undeformable planar fluid-fluid interface under creeping-flow conditions. The interface can be either surfactant-free 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, fluid-fluid interface, surfactant

Affiliations:
Bławzdziewicz J.-Texas Tech University (US)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
13.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: 0021-9606, Vol.132, pp.074704-1-12, 2010
14.Bławzdziewicz J., Goodman R.H., Khurana N., Wajnryb E., Young Y.-N., Nonlinear hydrodynamic phenomena in Stokes flow regime, PHYSICA D-NONLINEAR PHENOMENA, ISSN: 0167-2789, DOI: 10.1016/j.physd.2009.11.013, Vol.239, pp.1214-1224, 2010
15.Sadlej K., Wajnryb E., Bławzdziewicz J., Ekiel-Jeżewska M.L., Adamczyk Z., Streaming current and streaming potential for particle covered surfaces: Virial expansion and simulations, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.3103545, Vol.130, pp.144706-1-11, 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, two-body and three-body 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, particle-covered wall, Stokes equations, hydrodynamic interactions, multiple expansion, viral exapnsion

Affiliations:
Sadlej K.-IPPT PAN
Wajnryb E.-IPPT PAN
Bławzdziewicz J.-Texas Tech University (US)
Ekiel-Jeżewska M.L.-IPPT PAN
Adamczyk Z.-Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences (PL)
16.Ekiel-Jeżewska M.L., Wajnryb E., Bławzdziewicz J., Feuillebois F., Lubrication approximation for microparticles moving along parallel walls, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.3009251, Vol.129, pp.181102-1-4, 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 low-Reynolds-number 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 quasi-two-dimensional systems.

Keywords:

Lubrication, Friction, Poiseuille flow, Particle velocity, Fluid equations

Affiliations:
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Bławzdziewicz J.-Texas Tech University (US)
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
17.Bławzdziewicz J., Wajnryb E., Equilibrium and nonequilibrium thermodynamics of particle-stabilized thin liquid films, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.3009558, Vol.129, pp.194509-1-14, 2008
18.Barón M.D., Bławzdziewicz J., Wajnryb E., Hydrodynamic crystals: collective dynamics of regular arrays of spherical particles in a parallel-wall channel, PHYSICAL REVIEW LETTERS, ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.100.174502, Vol.100, pp.174502-1-4, 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 Stokesian-dynamics algorithm relies on simplifications associated with the Hele-Shaw asymptotic far-field form of the flow scattered by the particles. The simulations reveal propagation of particle-displacement waves, deformation, and rearrangements of a particle lattice, propagation of dislocation defects in ordered arrays, and long-lasting coexistence of ordered and disordered regions.

Affiliations:
Barón M.D.-Princeton University (US)
Bławzdziewicz J.-Texas Tech University (US)
Wajnryb E.-IPPT PAN
19.Bławzdziewicz J., Wajnryb E., An analysis of the far-field response to external forcing of a suspension in the Stokes flow in a parallel-wall channel, PHYSICS OF FLUIDS, ISSN: 1070-6631, DOI: 10.1063/1.2976306, Vol.20, pp.93303-1-20, 2008
20.Zurita-Gotor M., Bławzdziewicz J., Wajnryb E., Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, Vol.592, pp.447-469, 2007
21.Zurita-Gotor M., Bławzdziewicz J., Wajnryb E., Motion of a rod-like particle between parallel walls with application to suspension rheology, JOURNAL OF RHEOLOGY, ISSN: 0148-6055, DOI: 10.1122/1.2399084, Vol.51, pp.71-97, 2007
22.Bhattacharya S., Bławzdziewicz J., Wajnryb E., Far-field approximation for hydrodynamic interactions in parallel-wall geometry, JOURNAL OF COMPUTATIONAL PHYSICS, ISSN: 0021-9991, DOI: 10.1016/j.jcp.2005.07.015, Vol.212, pp.718-738, 2006
23.Bhattacharya S., Bławzdziewicz J., Wajnryb E., Hydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls, PHYSICS OF FLUIDS, ISSN: 1070-6631, DOI: 10.1063/1.2195992, Vol.18, pp.53301-0, 2006
24.Bławzdziewicz J., Wajnryb E., Phase equilibria in stratified thin liquid films stabilized by colloidal particles, EUROPHYSICS LETTERS, ISSN: 0295-5075, DOI: 10.1209/epl/i2004-10534-5, Vol.71, No.2, pp.269-275, 2005
25.Bhattacharya S., Bławzdziewicz J., Wajnryb E., Hydrodynamic interactions of spherical particles in suspension confined between two planar walls, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/S002211200500593, Vol.541, pp.263-292, 2005
26.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: 1070-6631, DOI: 10.1063/1.1852315, Vol.17, No.3, pp.033602-1-9, 2005
27.Bhattacharya S., Bławzdziewicz J., Wajnryb E., Many-particle hydrodynamic interactions in parallel-wall geometry: Cartesian-representation method, PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, ISSN: 0378-4371, DOI: 10.1016/j.physa.2005.03.031, Vol.356, pp.294-340, 2005
28.Tokarzewski S., Bławzdziewicz J., Andrianov I., Two-point Pade Approximants for Stieltjes Series, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.30, pp.1-17, 1993

Conference papers
1.Bławzdziewicz J., Wajnryb E., The swapping-trajectory effect: lattice evolution and buckling transition in wall-bounded hydrodynamic crystals, Symposium on Microparticles in Stokes Flows in Honor of Francois Feuillebois 65th Birthday, 2011-08-21/08-24, Warszawa (PL), DOI: 10.1088/1742-6596/392/1/012008, Vol.392, pp.012008-1-11, 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 swapping-trajectory 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 swapping-trajectory interactions at all stages of the evolution.

Affiliations:
Bławzdziewicz J.-Texas Tech University (US)
Wajnryb E.-IPPT PAN