Steady Microstructure of a Contact Line for a Liquid on a Heated Surface Overlaid With Its Pure Vapor: Parametric Study for a Classical Model

Abstract

Abstract. Based on a standard one-sided lubrication-type model, an analysis is carried out pertaining to a small vicinity of a contact line of a volatile non-polar perfectly-wetting macroscopic liquid sample surrounded with its pure vapour and attached to a smooth uniformly superheated solid surface. The behaviour 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 vapour, 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 upon 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 vapour-recoil effects are additionally incorporated and their possible importance is assessed.

Truncated versus Extended Microfilms at a Vapor−Liquid Contact Line on a Heated Substrate

“…To establish when this happens, it is just sufficient to linearize eq 31 near ξ = 1 and calculate the eigenvalues. 7 Finally, it is interesting to note that the behavior given by eq 33 is valid not only in a volatileliquid case as considered here, but also in the case of a non-volatile liquid, recovered non-singularly within eq 33 by letting E = 0 (in fact, not enough terms are written down in the series of eq 33 to appreciate the difference between E = 0 and E = 0). In this connection, as far as the nonvolatile case is concerned, let us point out that the family of solutions with truncated precursor films for a moving contact line obtained by Hervet and de Gennes 16 must satisfy eq 33 (with E = 0 and rescaled to their notations).…”

“…Up to notations and scaling factors, and excluding additional physical effects sometimes incorporated into the model, eq 17 with eq 18 is of course the same as elsewhere, 5,6,8 while for a more detailed presentation in the same terms as here see an earlier work of the present authors. 7 However, it is worthwhile emphasizing the key features of the classical model used here such as its one-sidedness (in particular, the vapor pressure inhomogeneity is considered to be negligible, 15 and so is heat conduction into the vapor) and the constancy of the wall temperature (on the scales considered here). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 l (which actually tends to be rather large in practice 7 ), one uses a steady version of eqs 17 and 18:…”

“…Some of the features of the model employed elsewhere [3][4][5][6][7][8] and here include the following.…”

“…Finally, the Marangoni and the vapor-recoil effects are neglected, which is supported by the analysis carried out elsewhere. 7 Both the microfilm regime (extended or truncated) and the spreading coefficient (for the truncated regime) in principle influence the overall behavior of the liquid film including the macroscopic scales. In the present paper, we study such an influence while focusing on a small vicinity of the contact line, possessing its own intrinsic scales (microscales).…”

Organization of microbeads in Leidenfrost drops

“…It is the opposite in the case of Q d , and therefore, the contact angle can be pulled to its maximum value. Moreover, as Q i is measured in an evaporative state, while Q d is measured in an equilibrium state, one cannot exclude either an effect of apparent contact angle increase by evaporation 28 .…”