Chérifa Abid

Super-diffusion in sheared suspensions

We investigate the dispersion of a layer of dye initially applied at the outer wall of a cylindrical Couette-cell into a sheared suspension of non-Brownian spherical particles. The process is directly visualized and quantified at the particle scale. A “rolling-coating” mechanism is found to convectively transport the dye at a constant rate directly from the wall towards the bulk. The fluid velocity fluctuations, u′, measured with particle image velocimetry, and the imposed shear-rate, γ, are used to define a diffusion coefficient, D∝ ⟨u′u′⟩/ γ, which is found to increase linearly with the distance from the wall. A solution of the transport equation accounting for this inhomogeneous stirring field describes quantitatively the concentration profiles measured experimentally. It exhibits a super-diffusive character, a consequence of the increase of the stirring strength with distance from the wall. Movies are available with the online version of the paper.

NATURAL CONVECTION SIMULATIONS OF BINGHAM FLUID WITHIN A SQUARE CAVITY WITH DIFFERENTIALLY HEATED VERTICAL WALLS

This study presents a numerical simulation of fluid flow and heat transfer due to natural convection within a square chamber (Square Cavity), fully filled with a yield stress fluid obeying the Bingham model of behavior. Two dimensional, steady state, laminar flow with differentially heated vertical walls (Side walls) and insulated horizontal walls (Top and Bottom) have been considered. Plasticity effects on heat mass transfer are investigated for nominal values of Rayleigh number (Ra) in the range of (10 to 10). We have fixed the Prandtl number (Pr = 10) and Bingham number (Bn = 0.5) to mimic a real incompressible plastic fluid. It is found that the average Nusselt number (Nu*) increases with the increasing of Rayleigh number for the both cases Newtonian and nonNewtonian fluids. However, for the same value of Rayleigh number, the average Nusselt number of Bingham fluid presents a diminution comparing with the Newtonian fluid, due to yield stress effects on the convective term.