Slow viscous flow of a sphere along a deformable tube

Abstract

A theoretical study of a sphere moving with a constant velocity along a deformable tube filled with a homogenous incompressible viscous fluid is presented. An axi-symmetrical shell model is used in our formulation. Approximate expressions of pressure and drag on the sphere are derived for the “hard tube” case. The bending effect cannot be neglected when the deflection of the tube wall is comparable to the film thickness. The drag on the sphere is decreased due to the deformable wall.