Mathematikgebäude, Seminarraum M614/616 (6. Etage)

Recently the Rheology of dense suspensions of non-colloidal spheres in yield-stress fluids has been studied (Dagois-Bohy et al. 2015). The results show that in the Stokesian regime of viscometric flows, the particle pressure and shear stress have forms similar to that of Newtonian suspensions. However, the apparent viscosity of the suspending fluid is the viscosity seen by the particles, which depends on the local shear rate. Here, we study channel flows of dense suspensions of non-colloidal particles in yield-stress fluids. These flows are challenging in that the combination of non-Newtonian rheology and particle migration results in sharp variations in shear rate and effective viscosity. Therefore, the suspensions vary from Stokesian behavior to inertial behavior across the width of the channel. In this work the Suspension Balance Model of Nott and Brady 1994 is extended to include non-Newtonian and inertial effects. This results in a set of scaled equations of motion for the mixture of non-colloidal particles suspended in a yield stress fluid plus a transport equation for the solid volume fraction. Asymptotic approach is used to derive the leading order governing equations in the limit of long and thin channel. It is shown that a 1D nonlinear advection equation governs the streamwise dispersion of solid volume fraction to the leading order. The flow profiles and solid dispersion are computed for a range of dimensionless flow parameters. The results show that the solid dispersion strongly depends on inertial and non-Newtonian effects.

Reference:
Dagois-Bohy, S., Hormozi, S., Guazzelli, E. & Pouliquen, O. Rheology of dense suspensions of non-colloidal spheres in yield-stress fluids. J. Fluid Mech. 776, R2 1–11 (2015).
Nott, P.R & Brady, J.F., Pressure-driven flow of suspensions: simulation and theory. J Fluid Mech 275 (1994) 157-199

Prof. Sarah Hormozi

Ohio University