Hydrodynamic Interactions between Two Rigid or Fluid Particles

Abstract

In this chapter we shall consider the behaviour of two rigid or fluid particles moving through a viscous fluid under the action of external forces, typically the gravity force. When two rigid or fluid particles suspended in a viscous fluid approach one another, the motion of each one of them is influenced by the other, even in the absence of direct interparticle interactions, such as van-der-Waals and electrostatic forces. The velocity field caused by the motion of one of these particles is transmitted through the fluid medium and influences the motion and, therefore, the hydrodynamic force, torque and stresslet on the other one. This indirect particles interaction is known as a hydrodynamic interaction. The magnitude of the hydrodynamic interaction between rigid or fluid particles depends on the following variables: (a) their shapes and sizes; (b) the distance between them; (c) their orientation with respect to one another; (d) their individual orientation relative to the active external forces; (e) their velocities and spins relative to the fluid motion at infinity.