Behavior of multiple spheres in shear and poiseuille flow fields at low Reynolds number

Abstract

The multipole truncation technique developed previously by the authors for describing the hydrodynamic interaction of three-dimensional finite clusters of spherical particles at low Reynolds number is used to obtain solutions for the motion of freely suspended particles in planar shear and/or Poiseuille flow fields. Instantaneous configurations containing up to 13 particles are studied and quasi-steady trajectories are obtained for time-varying configurations of two or three particles. Interesting applications of the theory presented in this paper include the time-dependent motion of a chain of spheres with fixed interparticle spacings in shear flow which may serve as a model to study the deformation of a polymer chain and the motion of neutrally buoyant configurations in planar Poiseuille flow to study the lateral migration of particles. The motion of a neutrally buoyant sphere in the presence of a rigidly held sphere in shear flow is also examined. This study reveals a very intriguing behavior in which the free sphere rolls along the fixed sphere but an adverse pressure gradient forces a retrograde motion of its center.