Hydrodynamic interactions: a manybody problem in the theory of suspensions
Abstract
The problem of multiple spheres suspended in a viscous fluid is solved using a method of induced forces. The scheme developed describes the static mobility tensors for an arbitrary number of spheres in an unbounded liquid as a power series of their reciprocal distances. The scheme is extended with respect to finite frequencies and inclusion of the influence of a plane wall in the static case; it can also be applied without major modifications to the motion through a viscous fluid in the Oseen regime of a single sphere or an infinite circular cylinder with its axis perpendicular to the direction of its motion. Finally, the definition of the tensors is used to examine the shorttime selfdiffusion coefficient, as well as the hydrodynamic interaction in a concentrated suspension.
 Publication:

Canadian Journal of Physics
 Pub Date:
 January 1985
 DOI:
 10.1139/p85003
 Bibcode:
 1985CaJPh..63...24M
 Keywords:

 Hydrodynamic Equations;
 Spheres;
 Suspending (Mixing);
 Tensor Analysis;
 Two Phase Flow;
 Viscous Fluids;
 Incompressible Flow;
 Many Body Problem;
 NavierStokes Equation;
 Power Series;
 Steady Flow;
 Wall Flow;
 Fluid Mechanics and Heat Transfer