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.

Growing surfactant waves in thin liquid films driven by gravity

“…While a well-defined wave speed is maintained, in the frame of reference moving with that speed, the solution exhibits a self-similar growing form for t → ∞; similar behavior has been observed in other thin film problems [8,24]. We have been able to obtain expressions for the accumulation of surfactant and leading order asymptotic forms for the film and surfactant profiles subject to relatively few assumptions on the dynamics.…”

“…To depict the scaled formsh andΓ, the same profiles are plotted in the forms (18) in Figure 5 with m(t) replaced by the numerical result Γ max (t) = max x Γ(x, t). Plotted in this form, the profiles indeed appear to approach the traveling wave solution, (8) and (12), as t → ∞. This behavior can be obtained directly from (19ab) subject to the assumptions:…”

On the distinguished limits of the Navier slip model of the moving contact line problem

“…Voinov (1976), Hocking & Rivers (1982), and Lacey (1982)), and our paper seeks to highlight the idea of the non-uniformity of the perturbation methods as slip tends to zero and for different choices of time scales. This is most similar to the study of King & Bowen (2001), and Flitton & King (2004). We provide a more comprehensive listing of the vast literature on the topic of the moving contact line in §1.1.…”

Effects of annealing conditions on ferroelectric nanomesa self-assembly

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