Brownian motion, hydrodynamics, and the osmotic pressure

Abstract

It is shown that the osmotic pressure of a colloidal dispersion can be interpreted as the isotropic part of the macroscopic particle stress in the suspension. The particle stress is in turn expressible in terms of hydrodynamic interactions among the suspended particles. Thus, there is a completely mechanical definition of the osmotic pressure, just as there is for the pressure in a molecular fluid. For an equilibrium suspension of colloidal particles subjected to thermal Brownian forces, this mechanical definition is shown to be exactly equal to the usual ‘‘thermodynamic’’ one. The derivation given here places the equilibrium and nonequilibrium properties of macroparticle fluids on the same mechanical foundation that underlies the statistical mechanics of simple liquids. Furthermore, through this development the relationship between hydrodynamics and kinetic‐theory‐like descriptions of colloids is explained.