Linear stability of particle-laden thin films

Abstract

Recent experiments [Zhou, Dupuy, Bertozzi, and Hosoi, Phys. Rev. Lett., 94 (2005)] of particle-laden film flow on an incline demonstrate new behavior distinct from the well-known clear fluid case, including the formation of a particle-rich ridge which can stabilize the advancing contact line with respect to “fingering" perturbations. We consider a model similar to that of Zhou et al. with the additional regularizing effect of shear-induced diffusion. A linear stability analysis demonstrates that particle settling moderately reduces the growth rate of unstable modes, while increasing the most unstable wavelength.