Theoretical study of the creeping motion of axially and fore-and-aft symmetric slip particles in an arbitrary direction

Abstract

The problem of the translation of a rigid particle of revolution with fore-and-aft symmetry perpendicular to its axis of revolution in a viscous fluid, which may slip at the particle surface, is studied theoretically in the steady limit of low Reynolds number. A method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solution of the fluid velocity field that satisfies the boundary condition at infinity. The slip condition on the particle surface is then satisfied by applying a boundary collocation technique to this general solution to determine its unknown coefficients. The drag force acting on the particle by the fluid is calculated, with good convergence behavior for various cases. The agreement between our results and the available analytical solutions is excellent. It is found that the normalized drag force exerted on the translating spheroid with a specified slip parameter based on its equatorial radius increases monotonically with an increase in the axial-to-radial aspect ratio of the spheroid. For a spheroid with a given aspect ratio, its drag force is a monotonically decreasing function of the slip parameter of the particle. For the general problem of a slip particle of revolution with fore-and-aft symmetry translating in an arbitrary direction with respect to the axis of revolution, the hydrodynamic drag solution can be obtained as a superposition of the solution obtained previously for the axisymmetric motion of the particle and the current result.