2 - Hydrodynamics

Summary

Introduction

Because colloidal particles generally reside in a viscous fluid, the behavior of a dispersion is strongly influenced by hydrodynamic forces generated by the relative particle–fluid motion. Although many hydrodynamic effects can be deduced from the behavior of an isolated particle, the disturbance it causes decays so slowly with distance that interparticle effects are seldom negligible. Consequently, hydrodynamic forces transmitted from one particle to another through a viscous fluid must be understood. Interactions, as well as the behavior of isolated particles, are discussed here. The presentation is not meant to be a scaled-down text on hydrodynamics, but is intended to provide tools to deal with phenomena encountered in colloidal systems.

The next section presents the basic differential equations governing the behavior of an incompressible Newtonian fluid and an analysis of the relative importance of viscous and inertial effects. The analysis of two simple flows illustrates some basic principles about the kinematics of fluid motion. Then we turn our attention to flows for which inertial effects are negligible, Stokes flows. Special emphasis is given to singular solutions resulting from forces applied at points in the fluid. Subsequent sections deal with isolated spheres and two interacting spheres, first in a quiescent fluid and then in fluid undergoing laminar shear flow.