Table of contents

Microparticles in Stokes Flows – Symposium in Honor of Françcois Feuillebois' 65th Birthday was held from 21–24 August 2011 in Warsaw, Poland. There were 43 participants from Australia, Brazil, France, Germany, Ireland, Israel, Japan, the Netherlands, Poland, Russia, Tunisia, United Kingdom and the USA. They presented 5 invited lectures, 25 contributed talks and 9 posters. The abstracts can be found at microparticles2011.ippt.pan.pl. The subjects were divided into three parts and 13 sessions, listed below.

Part I. A variety of particles. Sessions: sedimentation at non-Brownian time scale, Brownian and hydrodynamic interactions of non-spherical particles, active particles, permeable particles, deformable particles and biosystems.

Part II. Particles and interfaces. Sessions: confined multiparticle systems, hydrodynamic interactions in confined systems, single particle under confinement, particle-interface interactions, slip at interfaces, slip in suspensions.

Part III. Stokes flows and beyond. Sessions: inertial effects, texture and self-assembly.

At the end of each session, presentations were followed by extensive discussions (two thirds of the presentation time). Also, two round-table general discussions took place, Methods of solving the Stokes equations - which when? and Challenges in microhydrodynamics.

This volume contains both original contributions and reviews. There were at least two referees per paper: one participating in the conference, and the other not. I would like to thank all the referees for their work, the Polish Academy of Sciences, Centre national de la recherche scientifique and the Institute of Fundamental Technological Research, Polish Academy of Sciences for supporting in part the conference, Anna Myłyk, Agnieszka Słowicka and Krzysztof Zembrzycki for the weeks spent organizing the symposium, and all the conference participants for their presentations and discussions of the highest scientific quality.

Happy Birthday, Françcois Feuillebois!

This volume of Journal of Physics: Conference Series is dedicated to our friend and colleague Françcois Feuillebois. The symposium Microparticles in Stokes Flows was organized to celebrate his 65th birthday. Françcois presented a special lecture, entitled Influence of wall slip in dilute suspensions [1], which was followed by a birthday dinner, with an after-dinner speech given by John Hinch. The symposium participants, and those who could not join the meeting, all wish Françcois all the best for his 65th birthday, and thank him for sharing with us his knowledge, and motivating us to solve interesting problems related to motion of particles in fluid flows.

An illustration of Françcois's scientific interests was shown on the conference poster.

The conference participants could participate in a contest, by submitting a written answer to the question ``What system is shown on the conference poster (equations, boundary conditions)?''. Francois was in charge of evaluating the answers to this quiz, and providing the explanation [3]. Transworld Research Network kindly provided the rewards: copies of the book co-edited by Francois [2]. The winners were Maciej Lisicki and Eric Climent. A third copy of this book was awarded to John Hinch, who (according to majority of the participants) had asked the most insightful questions during the conference.

Maria L Ekiel-Jeżewska (Editor) Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawi\'nskiego 5B, 02-106 Warsaw, Poland Email: mekiel@ippt.pan.pl

References [1] Feuillebois F, Ghalya N and Sellier A 2012 Influence of wall slip in dilute suspensions J. Phys.: Conf. Ser.392 012012 [2] Feuillebois F and Sellier A, eds., 2009 Theoretical Methods for Micro Scale Viscous Flows (Transworld Research Network, Kerala) [3] Feuillebois F 2012 The quiz J. Phys.: Conf. Ser.392 011002

The flow field represented in the following figure was shown on the cover of the Symposium book of abstracts. Its interpretation was proposed to the participants as a quiz. The answer to the quiz is given here.

The PDF contains a trascript of an interview with François Feuillebois.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Collective motion in a ferrofluid is discussed on the basis of ferrohydrodynamics. Simple examples elucidate the effect of a collection of spinning suspended particles on Stokes flow. Spin viscosity emerges as a crucial transport coefficient. In the case of a uniform rotating magnetic field applied to a ferrofluid in a cylinder or a spherical cavity the collective fluid motion is driven by the curl of the torque density, which differs from zero only in a thin boundary layer with thickness proportional to the square root of the spin viscosity.

We describe the sedimentation of a non-Brownian suspension of hard spheres by Stokesian dynamics simulations. Attention is focused on the mean settling velocity and the structure of particles distribution as the suspension attains a non-equilibrium steady sedimentation state. Many-body hydrodynamic interactions between particles are evaluated using the precise multipole method, encoded in the new FAST-HYDROMULTIPOLE program. With the complete neglect of Brownian motion, the sedimentation velocity and the particles configurational distribution in the steady state differ measurably from their equilibrium counterparts. Simulations reproduce short-range particle correlations in good agreement with the statistical description of sedimentation formulated by Cichocki and Sadlej [Europhys. Lett. 72, 936 (2005)].

We review results of the non-equilibrium properties of semidilute polymer solutions under shear flow. A hybrid simulation approach is adopted, combing molecular dynamics simulations and the multiparticle collision dynamics method, which has been shown to fully capture hydrodynamic interactions. The polymers exhibit a shear rate dependent deformation and alignment. In addition, shear thinning is observed, which is related to the finite polymer extensibility. It is characterized by the shear-rate dependent viscosity and the first normal-stress coefficient. The conformational and rheological properties are universal functions of a concentration dependent Weissenberg number. The cyclic dynamics of an individual polymer is described in terms of a shear-rate dependent tumbling time. The tumbling time is tightly linked to the polymer end-to-end vector relaxation time and depends on concentration, which is attributed to screening of hydrodynamic interactions in semidilute solutions.

General expressions for the frequency-dependent Brownian contribution to the intrinsic viscosity of arbitrary-shaped particles have been derived from the Smoluchowski equation.

Blood flow is dictated by the dynamics of red blood cells (RBCs), which constitute by far the major component. RBCs are made of a a two dimensional fluid bilayer of phospholipids, having underneath a network of proteins conferring to them shear elasticity, and they possess many membrane and transmembrane proteins (like ion channels). Simplified systems, like vesicles (made of a pure bilayer of phospholipid) and capsules (made of an extensible polymer shell) are used as models for RBCs. Both systems reproduce several features known for RBCs under flow. Their interest lies, besides some simplicity, in the fact that they can be fabricated in the laboratory, and their properties (size, stiffness, internal content....) can be varied in a wide range allowing thus to explore a quite significant parameter space that is essential to test predictions and discriminate between different models. We shall review the main recent achievement in this field, both for a single entity, collective effects and the impact on rheology.

The dynamics of droplets and elastic capsules in a low Reynolds number flow is investigated by Front-Tracking method. The motions of droplets under gravity field, shear flow and Poiseuille flow are shown as examples. The capsules are migrated to the center line of the Poiseuille flow due to the lateral migration. The hydrodynamic conductance of the Poiseuille flow is reduced as the capsule goes to the center of the channel. The small capsules move to the boundary wall of the Poiseuille flow in the mixture of large and small capsules.

We study the hydrodynamic interactions between colloids suspended in a compressible fluid inside a rigid channel. Using lattice–Boltzmann simulations and a simplified hydrodynamic theory, we find that the diffusive dynamics of density perturbations (sound) in the confined fluid give rise to particle correlations of exceptionally long spatial range and algebraic temporal decay. We examine the effect of these sound-mediated correlations on two-particle dynamics and on the collective dynamics of a quasi-one-dimensional suspension.

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.

Flow and drainage of very thin liquid films play an important role in mineral recovery, drop coalescence and emulsion stability, as well as lubrication of micromechanical devices. Studies of liquid flow under strong confinement (i.e., film thickness below a few hundred of nanometers and down to a few nanometers) can reveal the limits of applicability of a classical hydrodynamics description, but are very challenging. The Surface Force Apparatus (SFA) technique has enabled studies of drainage at nanoscale separation between atomically smooth mica sheets. The development of the colloid probe Atomic Force Microscope (AFM) as an alternative technique has allowed a significantly wider variety of confining solid surfaces to be studied. Both the SFA and the colloid probe AFM have been adapted to permit the surfaces confining the film to be soft, e.g., the surface of a drop or bubble, and therefore deformable. We present a succinct review of the experimental and theoretical modeling challenges for such studies and critically discuss the outcomes of recent experiments.

Hydrodynamic interactions between particles and walls are relevant for the open problem of specifying boundary conditions for suspension flows. The Reynolds number around a small particle close to a wall is usually low and creeping flow equations apply. From the solution of these equations, the drag coefficient on a sphere becomes infinite when the gap between the sphere and a smooth wall vanishes, so that contact may not occur. Physically, the drag is finite because of various reasons, one of them being the particle and wall roughness. Then, for vanishing gap, even though some layers of fluid molecules may be left between the particle and wall roughness peaks, it may conventionally be said that contact occurs. In this paper, we are considering the example of a smooth sphere moving towards a rough wall. The roughness considered here consist of random rough planes or parallel periodic wedges, the characteristic length of which is small compared with the sphere radius. This problem is considered both experimentally and theoretically. The motion of a millimetre size bead settling towards a corrugated horizontal wall in a viscous oil is measured with laser interferometry giving an accuracy on the displacement of 0.2μm. Several random rough planes and wedge shaped walls were used, with various wavelengths and wedge angles. From the results, it is observed that the velocity of the sphere is, except for small gaps, similar to that towards a smooth plane that is shifted down from the top of corrugations.

For the periodic wedges, the creeping flow is calculated as a series in the slope of the roughness grooves. The convergence of the series for the shift distance in term of the slope is accelerated by use of Euler transformation and of the existence of a limit for large slope. The cases of a flow along and across the grooves are considered separately. The shift is larger in the former case. Slightly flattened tops of the wedges used in experiments are also considered in the calculations. The effective theoretical shift for a sphere approaching a wall is obtained from Lorentz reciprocal theorem with an expansion for small roughness compared with the gap between the sphere and the wall. The effective shift is found to be the average of the shifts for shear flows in the two perpendicular directions. A good agreement is found between theory and experiment.

The theoretical description of the flow close to the random rough wall represents a difficult, nearly insurmountable problem except in lattice Boltzmann simulations. Statistical analysis is presented in this paper to deduce the effective shift for sand-blasted rough surfaces. To overcome the difficulties of modelling, a regular perturbation expansion is developed, and from Lorentz reciprocal theorem, the first order correction to the drag force due to random roughness is evaluated.

The near-wall dynamics of a sphere is experimentally resolved at microscale using a specially designed interferometry-related device. The millimeter size sphere, settling in a viscous oil towards a horizontal wall, is used as a reflector. The accuracy on the sphere displacement is smaller than 0.2 μm. Since its first implementation, this technique has been used to investigate various issues related to near-wall hydrodynamics. This presentation focuses on two recent developments of this device. In the first case of a sphere entering the near-wall region with a Reynolds number of order unity, it is shown how the dynamics of the sphere is modified by small inertia effects. In the second case, if a textured wall with microscopic periodic grooves is used, the velocity of the sphere increases, as compared to the velocity near a "smooth" wall. This velocity enhancement is measured accurately and correlated to the texture geometry. The results are useful for specifying effective boundary conditions at microscale, with possible applications in the field of microfluidics.

Navier's (1823) slip condition, where the tangential velocity is proportional to the shear stress, may apply at micro-scales for a viscous liquid on walls with modified surfaces, e.g. hydrophobic ones in water. Experiments by Lumma et al (2003) show the difficulties involved in measuring such a slip.

At small scales, particle-wall hydrodynamic interactions are important. They are modeled here for a dilute suspension of spherical solid particles near a slip wall. Consider a translating and rotating sphere (on which the no-slip condition applies) in an ambient parabolic flow. Analytical solutions of Stokes equations for the various elementary flow fields were obtained (Feuillebois et al 2009, 2011) as series in bispherical coordinates. The coefficients in the series are solutions of an infinite linear system, which is solved by an extension of Thomas' algorithm, allowing to calculate a large number of terms. Accurate results are available for the force, torque and stresslet on a sphere, velocity of a freely moving sphere and diffusion tensor.

The Aris-Taylor dispersion of Brownian particles in a shear flow near a slip wall gives a large bias in the measurement of slip (Vinogradova et al, 2009). It is calculated here from the advection-diffusion equation, using the expressions for the particle velocity and diffusion tensor near a slip wall.

This work is concerned with the rigid-body migration of a solid and arbitrary-shaped particle immersed in a Newtonian liquid in vicinity of a plane, motionless and impermeable wall where a Navier slip condition [1] holds. The net hydrodynamic force and torque exerted on the moving particle are obtained by appealing to a new boundary elements approach which makes use of a specific Green tensor recently determined elsewhere [2]. The advocated technique results in the treatment of a Fredholm boundary-integral equation of the first kind on the particle surface and, by contrast to earlier works in this field, makes it possible to cope with non-spherical particles. The proposed numerical implementation is benchmarked against results obtained for a sphere by using the bipolar coordinates. Preliminary new results for the friction coefficients of an non-spheroidal ellipsoid are also reported and compared with those for a volume-equivalent sphere. The variations of the friction coefficients with the slip length are analogous for both particles.

In this preliminary work we introduce a new method for verification of the no-slip boundary condition on the liquid-solid interface, by analyzing variations in Brownian motion coefficients of colloidal nanoparticles as a function of distance from the wall. The experimental investigations are performed in a small channel using an epi-fluorescent microscope. For precise measurements close to the wall an evanescent wave illumination is used. The experimental data obtained for 300nm particles gave us evidence of relatively large (0.3μm) slip length. The experiments are supplemented by two-dimensional Molecular Dynamics simulations.