Role of shear induced migration on the development and stability of a particle-laden falling film

We study the role of shear induced migration and particle induced normal stresses on the boundary layer formation and stability of a particle-laden, gravity-driven shallow flow. Looking at the boundary layer formation at the 'shallow' limit, we find that increasing bulk particle volume fractions lead to a reduction in the entrance length. In the absence of particles, gravity-driven shallow flows are known to exhibit a long-wavelength instability, as first identified by Yih (1963), and a short wave instability, as identified by Kelley (1989). We perform a linear stability analysis and find that the shear-induced migration of particles leads to an enhancement of both modes of instability. We also find that this prediction of an enhanced instability is independent of the choice constitutive model used to describe the particle phase as long as the chosen model has elements of shear induced migration.