The Stokes resistance of an arbitrary particleIV Arbitrary fields of flow

Abstract A phenomenological scheme is formulated for calculating the quasistatic Stokes force and torque on a rigid particle of any shape immersed in a flow field which tends to an arbitrary Stokes flow at infinity. This generalizes a previous result (Part III) limited to a uniform shear flow at infinity. The phenomenological resistance coefficients are shown to be constant polyadics which are intrinsic properties of the particle, dependent only on its external shape. In particular they are independent of the density, viscosity, and state of motion of the fluid. It is demonstrated that these coefficients can be computed solely from a knowledge of the solutions of Stokes equations for translational and rotational motions of the particle, along any three non-coplanar axes, in a fluid at rest at infinity. Explicit formulae for the polyadic coefficients are given for ellipsoidal and slightly deformed spherical particles.