Shear-induced particle migration of semi-dilute and concentrated Brownian suspensions in both Poiseuille and circular Couette flow

Neutrally buoyant colloids with small Reynolds numbers pose interesting challenges particularly when they undergo shear thinning and Brownian diffusion. Two basic flows including Poiseuille and Couette flows accompanying shear-induced particle migration are investigated in this study using direct numerical simulations (DNSs). A scaled viscosity model of colloidal suspensions considering both the shear rate and bulk particle volume fraction is employed to describe the shear-thinning behavior of suspensions. The constitutive diffusion equation proposed by Phillips et al. [Phys. Fluids A 4, 30–40 (1992)] is used to model the dynamics of suspension flow. We vary the Péclet number Pe, from 10⁻² to 10³ for the semi-dilute and dense suspensions with the bulk particle volume fraction ϕ_b, ranging from 10% to 50%. It was found that, in the limit of vanishing inertia, the distribution of volume fraction gradually flattens by increasing Brownian force. In a Poiseuille flow, the velocity of suspensions decays as the Brownian motion becomes stronger, leading to the flow rate reduction. For a circular Couette flow, the Brownian diffusion enhances the velocity of suspensions and increases the friction coefficient at the inner cylinder wall. Our study reveals that the Brownian motion is more critical for higher volume fraction values.