Instability and dynamics of thin slipping films

Abstract

The linear stability analysis of the full Navier-Stokes equations shows that the surface instability and dynamics of thin liquid films are profoundly altered by the presence of slippage on the substrate. For example, the exponents for the length scale (λ_m ∞ hⁿ₀; h₀ is film thickness) and time scale of instability (t_r ∞ h^m₀) change nonmonotonically with slippage [for van der Waals force induced instability, nε (1.25,2), mε (3,6)]. Slippage always encourages faster rupture and can greatly reduce the number density of holes for moderate to strong slip. Thus, any interpretation of thin film experiments, including determination of intermolecular forces from the length and time scales, needs to account for the possibility of slippage.