Chapter 4 - Colloidal hydrodynamics and transport

Abstract

This chapter deals with the types of forces, which act on or between colloidal particles and are responsible for bringing the particles together, and hence, the result in collisions. These are Brownian motion of colloidal particles arising from the erratic bombardment of molecules of the surrounding fluid, frictional drag force exerted on colloidal particles by the surrounding fluid, hydrodynamic interactions mediated by the surrounding fluid and modifying the frictional drags on individual colloidal particles, and, if present, external forces such as gravity. The interplay among all these different types of forces determines the properties or behavior of colloidal dispersions, including their tendency to aggregate or become deposited onto a surface (or “collector”). The chaotic, or Brownian, motion of colloidal particles is a direct result of collisions between the colloids and the fluid molecules surrounding them. The trajectory of a colloidal particle undergoing Brownian motion, obtained by tracking its movements at the usual experimental timescale intervals (e.g. seconds), is of the self-similar nature. That is, if any portion of a given Brownian trajectory is magnified (that is, the sampling time interval is decreased), the magnified trajectory will look qualitatively similar to the original one. Thus, a Brownian trajectory is not a mathematically smooth curve, and the apparent velocity of a Brownian particle derived from it does not represent the true, physically well-defined, velocity of the particle. For this reason, the mean-square displacement is generally used to describe the motion of Brownian particles.