Fingering instability of a suspension film spreading on a spinning disk

Abstract

The spreading of a thin film of suspension on a spinning disk and the accompanying contact line instability is studied through flow visualization experiments. The critical radius for the onset of instability shows an increase with increase in the particle fraction ($ϕ_{p}$) before decreasing slightly at the highest value of $ϕ_{p}$ studied, while the instability wavelength ($λ$) exhibits a non-monotonic dependence. The value of $λ$ is close to that for a partially wetting liquid at lower $ϕ_{p}$, it decreases with increasing $ϕ_{p}$ to a minimum before increasing again at largest $ϕ_{p}$. The non-monotonic trends observed for $λ$ are discussed in light of the linear stability analysis of thin film equations derived for suspensions by Cook {\it et al.} [Linear stability of particle-laden thin films, Eur. Phys. J.: Spec. Top. {\bf 166}, 77 (2009)] and Balmforth {\it et al.} [Surface tension driven fingering of a viscoplastic film, J. Non Newtonian Fluid Mech. {\bf 142}, 143 (2007)].