TRACER-DIFFUSION IN COLLOIDAL MIXTURES - A MODE-COUPLING SCHEME WITH HYDRODYNAMIC INTERACTIONS

In this work, we develop a general theoretical scheme to study tracer- diffusion in mixtures of interacting colloidal particles where the inf luence of solvent-mediated hydrodynamic interactions is also considere d. Based;on the many-body Smoluchowski diffusion equation, we derive i n a first step an exact microscopic expression of the irreducible memo ry function (self-friction function) associated with the self-intermed iate scattering function and with the mean squared displacement of a t agged particle. By applying a mode-coupling scheme (MCS) to the irredu cible memory function, we obtain explicit expressions for the tracer-d iffusion quantities in terms of partial static structure factors and h ydrodynamic functions. The influence of hydrodynamic interactions (HI) is accounted for using a far-field expansion of the two-body hydrodyn amic diffusivity tensors. For charge-stabilized colloids, this is a go od approximation due to strong electrostatic repulsion between the par ticles. Various applications are discussed in order to illustrate the versatility of our mode-coupling scheme. (C) 1998 American Institute o f Physics.