Instability, Dynamics, and Morphology of Thin Slipping Films
Based on the linear stability and nonlinear simulations, we show that the surface instability, dynamics, and morphology of supported thin liquid films are profoundly altered by the presence of slippage on the substrate. A general dispersion equation for flow in slipping thin films is derived and simplified to identify three different regimes of slippage (weak, moderate, and strong) and obtain the length and time scales of instability in them. For illustration, the ubiquitous van der Waals interactions have been employed. Different regimes of slip-flow can be predicted based on a nondimensional parameter, xi, which is a function of slip length, film thickness, intermolecular potential, and interfacial tension. Two distinct transitions from weak to moderate slip and from moderate to strong slip occur at xiT1 approximately 0.01 and xiT2 approximately 500, respectively. More specifically, a decrease in film thickness causes transitions from weak to moderate to strong slip regime. Even a weak slippage causes faster breakup of a thin film, whereas slippage beyond a transition value (slip length, bT1) increases the length scale of instability and reduces the number density of holes compared to the nonslipping case. Strong slippage produces holes faster, and the holes are fewer in number and have less developed rims. The exponents for the length scale (lambdam infinity h0n; h0 is film thickness) and time scale of instability (tr infinity h0m) change nonmonotonically with slippage (for nonretarded van der Waals instability, n E (1.25, 2), m E (3, 6)). Retardation in van der Waals potential increases the exponents (n E (1.5, 2.5), m E (5, 8)). The initial stage of evolution of a slipping film, simulated based on nonlinear equations, follows the length scale and time scale of instability, close to the prediction of linear analysis. It is hoped that the present analysis will help in better interpretation of thin film experiments, in estimation of slippage, and in the determination of intermolecular forces from the length and time scales of the instability.