Axisymmetric creeping motion of a prolate particle in a cylindrical pore

A theoretical study of the fluid flow caused by an axially symmetric prolate particle translating along its axis of revolution in a coaxial circular cylindrical pore at low Reynolds numbers is presented. A method of distribution of a set of spherical singularities along the axis of revolution within the particle is used to find the general solution of the fluid velocity field that satisfies the boundary conditions at the pore wall and at infinity. The no-slip condition on the particle surface is then satisfied by applying a boundary collocation technique to this general solution to determine the unknown constants. The drag force exerted on the particle by the ambient fluid is calculated with good convergence behavior for the cases of a prolate spheroid and a prolate Cassini oval (whose surface can be partly concave) with broad ranges of their aspect ratio (shape parameter) and distance from the pore wall. For the axially symmetric translation of a spheroid in a cylindrical pore, our drag results agree with the limited approximate solutions available in the literature. For a fixed particle-wall separation parameter, the normalized drag force increases with an increase in the axial-to-radial aspect ratio of the particle, and the boundary effect on the motion of the particle can be very significant when it gets close to the pore wall.