Interaction and Wall Corrections for the Slow Motion of Two Fluid or Solid Particles Parallel to the Axis of a Circular Cylinder through a Viscous Fluid

Abstract

Numerical values are provided which enable the drag force on the reference spherical fluid or solid particle, and the torque on the reference spherical solid particle, to be computed for the particular case when two spherical particles move in a direction parallel to their line of centres parallel to the axis of a circular cylinder. Results for this motion are also expressed in terms of the ratio of drag forces experienced by (1) the particle of arbitrary shape in a bounded, two particle system, and the particle in an unbounded, two particle system, and (2) the particle in a bounded, two particle system, and the particle moving alone with the same speed and orientation in the same, but unbounded, fluid. The computation furnishes the interaction and wall corrections correctly to the first-order in the ratios of characteristic particle dimension to characteristic distance of the particle from both another particle and from the cylinder wall.

The axisymmetric problem was extended to the more general case where the two particles may be placed eccentrically within the cylinder and the torque was also computed. Furthermore, the two particles may be fluid droplets as well as solid particles.