Particle migration of colloidal and Brownian suspensions in both Poiseuille and circular Couette flow

The flow of neutrally buoyant and hard-sphere colloidal particles concentrated in a Newtonian viscous fluid is examined by direct numerical simulations (DNS) at various bulk particle volume fraction (0.1$\le \phi _{b}\le $0.5) and Peclet number (10$^{\mathrm{-2}}\le $\textit{Pe}$\le $10$^{\mathrm{3}})$. We use the diffusive flux model (DFM) to describe the behavior of suspensions and employ the viscosity introduced by de Kruif et al. [J. Chem. Phys. 1985] which is given as a function of shear rate and volume fraction. First, we consider pressure-driven flow of colloidal particles in a channel. For low \textit{Pe} number the concentration profile flattens, as \textit{Pe} grows the influence of Brownian motion diminishes and the distribution of concentration reaches the profile of non-colloidal suspensions flow. Also, as Brownian motion becomes dominant, the volume flow rate decreases steadily. We then study a circular Couette flow of colloidal suspensions where the inner cylinder rotates with a constant angular velocity and the outer one is fixed. The concentration profile flattens out and the local shear rate decays with the reduction of \textit{Pe} number. The torque acting on the inner cylinder builds up due to colloidal suspensions.