Steady microstructure of a contact line for a liquid on a heated surface overlaid with its pure vapor: parametric study for a classical model

摘要

On the basis of a standard one-sided lubrication-type model, an analysis is carried out pertaining to a small vicinity of a contact line of a volatile nonpolar perfectly wetting macroscopic liquid sample surrounded with its pure vapor and attached to a smooth uniformly superheated solid surface. The behavior of the liquid film is governed by the effects of evaporation, capillarity, and the disjoining pressure. The kinetic resistance to evaporation, as well as the dependence of the local saturation temperature on the local liquid pressure are accounted for. Within the localized approach pursued, a steady configuration of the film on a flat substrate is studied such that at one end (say, to the left) it asymptotically attains an adsorbed microfilm in equilibrium with the vapor, while to the right it gets on to a constant slope (contact angle of the "microstructure"). For moving contact lines in the situations like drop spreading or bubble growth in the boiling process, this microstructure is relevant in the quasi-steady sense, provided that the displacement velocity is not too large. The paper focuses on a numerically based parametric study expressing the contact angle and evaporation flux characteristics as functions of the system parameters. Asymptotic expansions at both ends of the film are elaborated in some detail and relied on in the numerics. Asymptotic results from the literature involving certain limiting cases of the system parameters are critically examined. At last, the Marangoni and the vapor-recoil effects are additionally incorporated and their possible importance is assessed.