Study of a thin film of colloidal suspension flowing over a vertical cylinder

Stability of a liquid film containing colloidal particles flowing along the exterior of a vertical cylinder due to gravity is studied. The effect of colloidal concentration on diffusion coefficients, bulk viscosity, and surface tension is considered. The Marangoni stress at the interface stabilizes the curvature-driven instability at moderate Marangoni numbers, but introduces another unstable mode driven by surfactant at larger values. The pattern for the curvature mode indicates in-phase waves for film thickness and surface concentration, while a phase-lag is observed between the two waves for the surfactant mode.