Retarded hydrodynamic interaction between two spheres immersed in a viscous incompressible fluid
Abstract
Retarded or frequencydependent hydrodynamic interactions are relevant for velocity relaxation of colloidal particles immersed in a fluid, sufficiently close that their flow patterns interfere. The interactions are also important for periodic motions, such as occur in swimming. Analytic expressions are derived for the set of scalar mobility functions of a pair of spheres. Mutual hydrodynamic interactions are evaluated in onepropagator approximation, characterized by a single Green function acting between the two spheres. Selfmobility functions are evaluated in a twopropagator approximation, characterized by a single reflection between the two spheres. The approximations should yield accurate results for intermediate and long distances between the spheres. Both translations and rotations are considered. For motions perpendicular to the line of centers, there is a translationrotation coupling. Extensive use is made of Faxén theorems, which yield the hydrodynamic force and torque acting on a sphere in an incident oscillating flow. The derived results are important for the study of velocity relaxation of two interacting spheres immersed in a fluid and for the study of swimming of assemblies of spheres.
 Publication:

Physics of Fluids
 Pub Date:
 May 2019
 DOI:
 10.1063/1.5099179
 arXiv:
 arXiv:1904.03849
 Bibcode:
 2019PhFl...31e3604F
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 31 pages, 0 figures