TY - JOUR

T1 - Many-particle hydrodynamic interactions in parallel-wall geometry

T2 - Cartesian-representation method

AU - Bhattacharya, S.

AU - Bławzdziewicz, J.

AU - Wajnryb, E.

PY - 2005/10/15

Y1 - 2005/10/15

N2 - This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel algorithm for accurate evaluation of the many-particle friction matrix in this system - no such algorithm has been available so far. Our approach involves expanding the fluid velocity field into spherical and Cartesian fundamental sets of Stokes flows. The interaction of the fluid with the particles is described using the spherical basis fields; the flow scattered by the walls is expressed in terms of the Cartesian fundamental solutions. At the core of our method are transformation relations between the spherical and Cartesian basis sets. These transformations allow us to describe the flow field in a system that involves both the walls and particles. We used our accurate numerical results to test the single-wall superposition approximation for the hydrodynamic friction matrix. The approximation yields fair results for quantities dominated by single particle contributions, but it fails to describe collective phenomena, such as a large transverse resistance coefficient for linear arrays of spheres.

AB - This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel algorithm for accurate evaluation of the many-particle friction matrix in this system - no such algorithm has been available so far. Our approach involves expanding the fluid velocity field into spherical and Cartesian fundamental sets of Stokes flows. The interaction of the fluid with the particles is described using the spherical basis fields; the flow scattered by the walls is expressed in terms of the Cartesian fundamental solutions. At the core of our method are transformation relations between the spherical and Cartesian basis sets. These transformations allow us to describe the flow field in a system that involves both the walls and particles. We used our accurate numerical results to test the single-wall superposition approximation for the hydrodynamic friction matrix. The approximation yields fair results for quantities dominated by single particle contributions, but it fails to describe collective phenomena, such as a large transverse resistance coefficient for linear arrays of spheres.

KW - Confinement

KW - Hydrodynamic interactions

KW - Parallel walls

KW - Stokesian dynamics

KW - Suspensions

UR - http://www.scopus.com/inward/record.url?scp=27744562336&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2005.03.031

DO - 10.1016/j.physa.2005.03.031

M3 - Article

AN - SCOPUS:27744562336

VL - 356

SP - 294

EP - 340

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 2-4

ER -