Mathematical modeling for colloidal dispersion undergoing Brownian motion

An averaged motion approach for modeling Brownian dynamics for suspension systems of electrically charged particles in liquid is developed. The continuum model for the motion of particles consists of a system of integral equations coupled with a degenerate parabolic equation. Existence and uniqueness of global solution for the coupled system are established, and numerical results for the non-Newtonian viscosity of the mixture in terms of shear rate or Pechlet number are obtained. The model reveals some non-Newtonian properties such as the well-known shear thinning phenomenon for the viscosity of colloidal dispersions.