Surface-tension-driven dewetting of Newtonian and power-law fluids

Abstract

The dewetting over a planar substrate of a thin layer of highly viscous fluid under the action of surface tension is considered, with a doubly-nonlinear fourth-order degenerate parabolic equation governing the flow of a power-law fluid. Asymptotic methods are applied to analyse the motion in the shear-thinning, shear-thickening and Newtonian cases, the last of these corresponding mathematically to a critical value of the relevant exponent. In particular, the role played by the local behaviour in the neighbourhood of the contact line is analysed and the dependence of the one-dimensional large-time dewetting behaviour on the fluid’s constitutive properties characterised. Stability issues are also touched upon.