Contact angles for evaporating liquids predicted and compared with existing experiments

Abstract

The stationary meniscus of an evaporating, perfectly wetting system exhibits an apparent contact angle Θ which vanishes with the applied temperature difference ΔT, and is maintained for ΔT > 0 by a small-scale flow driven by evaporation. Existing theory predicts Θ and the heat flow q∗ from the contact region as the solution of a free-boundary problem. Though that theory admits the possibility that Θ and q∗ are determined at the same scale, we show that, in practice, a separation of scales gives the theory an inner and outer structure; Θ is determined within an inner region contributing a negligible fraction of the total evaporation, but q∗ is determined at larger scales by conduction across an outer liquid wedge subtending an angle Θ. The existence of a contact angle can thus be assumed for computing the heat flow; the problems for Θ and q∗ decouple. We analyse the inner problem to derive a formula for Θ as a function of ΔT and material properties; the formula agrees closely with numerical solutions of the existing theory. Though microphysics must be included in the model of the inner region to resolve a singularity in the hydrodynamic equations, Θ is insensitive to microphysical detail because the singularity is weak. Our analysis shows that Θ is determined chiefly by the capillary number Ca = μlVl/σ based on surface tension σ, liquid viscosity μl and a velocity scale Vl set by evaporation kinetics. To illustrate this result of our asymptotic analysis, we show that computed angles lie close to the curve Θ = 2.2Ca1/4; a small scatter of ±15% about that curve is the only hint that Θ depends on microphysics. To test our scaling relation, we use film profiles measured by Kim (1994) to determine experimental values of Θ and Ca; these are the first such values to be published for the evaporating meniscus. Agreement between theory and experiment is adequate; the difference is less than ±40% for 9 of 15 points, while the scatter within experimental values is ±25%.

Interfacial Fluid Mechanics

“…This local solution structure was investigated in the pioneering works of Potash and Wayner [101] and Moosman and Homsy [92]. Here, we discuss this solution using the general framework employed in later studies [4,93] and neglecting the effects of gravity. Consider a two-dimensional steady configuration sketched in Fig.…”

Precursor Films and Contact Line Microstructures

“…as found by Potash and Wayner (1972), and often supposed to extend all over the parts of the substrate not covered by macroscopic liquid portions (see, e.g., Moosman and Homsy, 1980;Stephan and Busse, 1992;Morris, 2001;Ajaev, 2005). However, it has been more recently demonstrated by Rednikov and Colinet (2011) that the absolute stability of such film is not guaranteed, because this should also depend on the short-scale tendency to wetting, characterized by the spreading parameter S Ã .…”

“…These extended microfilm solutions, which do not depend on Σ because there is obviously no dry point anywhere, have been studied since the 1970s by various authors (see, e.g., Potash and Wayner, 1972;Stephan and Busse, 1992;Morris, 2001;Ajaev, 2005). A rather extensive parametric study as a function of E and K has been published more recently by Rednikov et al (2009).…”

Inverse leidenfrost drop manipulation using menisci

“…The dynamics of droplet rebounds give nonetheless a first evaluation of the contact angle θ of liquid nitrogen, using equation 2. Interestingly, constant evaporation of liquid nitrogen (a perfectly wetting liquid) close to the wall is associated with a contact angle θ as predicted by27 , which value depends on the local heat and evaporation fluxes.…”