Stokesian Interactions Between Two Spheres Inside a Narrow Cylindrical Conduit

Creeping motion of multi-particle systems inside a cylindrical channel is an important phenomenon which affects many processes like blood-flow in bio-conduit or transportation in microfluid channels. Such systems involve both interparticle and particle-wall interactions which so far have not been fully analyzed when the size of the confining conduit is comparable to the size of the suspended bodies.

In this talk, we present our semianalytical formulation which addresses this unsolved problem. Our mathematical procedure is based on basis-function expansion of Stokesian solutions leading to an efficient simulation technique. Though the method can be used for any number of interacting particles, here we concentrate on a two-sphere system explaining dynamics of both particles under different flow-situations and geometric configurations.

First, we consider two closely situated identical spheres inside a narrow cylinder, and find their hydrodynamic frictions for motion in quiescent flow as functions of the particle-positions and cylinder-sphere size-ratios. Next, we determine the force and torque on fixed spheres in parabolic flow, as well as the motion of freely suspended system. Then, we repeat similar calculations for cylinder-bound spheres of asymmetric sizes. Finally, we analyze the flow where a large fixed sphere is blocking the conduit and a small suspended sphere is interacting with pressure-driven flow near the constriction. The last results are especially important because they can describe how suspended bodies like blood-cells behave inside a vessel partially blocked by depositions.