Modelling of Stokes flows through a singularity method

Abstract

Steady and oscillatory viscouse flows in the presence of rigid or fluid particles are considered. The flows are represented in terms of fundamental solutions to the governing steady and non-steady Stokes equations, including Stokeslet, Stokes dipol, oscillating Stokeslet, oscillating dipole and many other multipoles.

Compendious Lorentz and Faxen's laws for solid and fluid particles are derived in terms of singularity representations. The theoretical results are applied in studies of the translational and rotational steady or oscillation motion of spherical rigid and fluid particles in a viscouse fluid. The force $\vec{F}$ of the particles executing longitudinal or transverse oscillations is computed in an extended range of frequences $\omega$.