Stability of gravity-driven particle-laden flows - roles of shear-induced migration and normal stresses

In this paper, we study the role of shear-induced migration and particle-induced normal stresses in the formation and stability of a particle-laden, gravity-driven shallow flow. We first examine the modification of the base-state Nusselt flow due to the underlying microstructure, how shear-induced migration leads to viscosity stratification. We inspect the development of the base state via the boundary layer formation in the 'shallow' limit and find a reduction in entrance length with increasing bulk particle concentration and an increase in entrance length with increasing Peclet number (Pe(p) = (gamma) over dota(2) /D-0, where (gamma) over dot is the average shear rate, a is the particle size and D-0 is the single particle diffusivity). A linear stability analysis is then performed on the fully developed state to identify two modes of instability typically found in gravity-driven falling films - the long-wave surface and the short-wave shear modes. We find that when the associated Peclet number is Pe(p) << 1, increasing bulk particle volume fraction delays the onset of instability for both the surface mode and shear mode. However, with Pe(p) = O(1), we find an enhancement in both modes of instability. We also find that, beyond a critical Peclet number, for a fixed particle volume fraction, the surface mode is unstable even in the absence of fluid inertia. The enhanced destabilisation is attributed to the combined effects of base-state viscosity stratification and momentum forcing via particle concentration perturbations. We also show that the physics behind the enhancement of instability is independent of the choice of the constitutive model used to describe the dynamics of the particle phase, provided the chosen model has elements of shear-induced migration.

Automated summary

In this paper, the role of shear-induced migration and particle-induced normal stresses in the formation and stability of a particle-laden, gravity-driven shallow flow is studied. Through experiments and analysis, it is found that shear-induced migration leads to viscosity stratification and affects the development of the boundary layer formation in different conditions. It is also observed that increasing bulk particle concentration delays the onset of instability when the associated Peclet number is small, but enhances both modes of instability when the Peclet number is large. Additionally, it is shown that beyond a critical Peclet number, the surface mode becomes unstable even in the absence of fluid inertia.