Many-body hydrodynamic effects in suspensions

Colloidal dispersions exhibit complex behavior concerning their stability and rheological properties. This complex behavior is due to the various forces acting between the particles and determining their spatial distribution and their dynamical responses. Well characterized concentrated dispersions, new experimental methods and theoretical understanding have made possible the exploration of properties of concentrated suspensions in a fundamental manner. The objective of the experimental and theoretical work in this field has been to correlate the structural and dynamical features of concentrated dispersions with the nature of the interactions among particles. Current theories focus on the understanding of colloid dynamics based upon the behavior of isolated particles or particles interacting in a pair-wise fashion. In this thesis, we integrate these phenomena into a broad many-body hydrodynamic theory of colloidal dispersions. The theory is based upon a multiple scattering formalism to solve the equation of motion of the effective fluid, i.e., the suspension. Angular momentum algebraic techniques are used to manipulate the final formulas into graphical expressions that are readily evaluated. The method is valid to any order in concentration and can handle any general interparticle interaction. We have successfully applied the theory to determine the one-, two- and three-body coefficients in virial type expansions for the viscosity, friction coefficients and diffusion coefficients. Two different types of interaction between particles have been considered: suspensions of hard-spheres and suspensions of particles surrounded by electrical double-layers. In the first case, we have obtained the numerical values of the first three many-body coefficients for a monodisperse suspension. In the second case, we have shown that these coefficients are very sensitive to small changes in the parameters that characterize the interparticle forces between charged particles