The relation of steady evaporating drops fed by an influx and freely evaporating drops

Abstract

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning.

Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions

“…The evaporation is limited by the kinetics of the phase transition (or by the boundary layer transfer, but not by the diffusion of solvent vapour in the gas phase) in the contact line region, which is influenced by the effective molecular interactions, i.e., the saturated vapour pressure depends on the disjoining pressure and curvature in the manner employed in studies of evaporating films and drops. [74][75][76]78,79 Our evolution equation (13) reduces to the model by,Lyushnin et al 75 in the limit φ 0 → 0.…”

“…Note, that one may also obtain our evaporation model by taking the isothermal limit of the models by.Ajaev 80 , Rednikov and Colinet 81 For a further discussion see.Todorova et al 79 In the present work, we restrict our attention to line patterns deposited through evaporative dewetting, i.e., we assume a one-dimensional geometry, as sketched in Fig. 1.…”

The collective behaviour of ensembles of condensing liquid drops on heterogeneous inclined substrates

“…As in the main text, we employ a nondimensional long-wave equation to model the time evolution of the height profile h(x, y, t) that describes drops of a volatile liquid on a partially wetting, heterogeneous substrate, cf. [38,39]: The heterogeneities take the form of small circular hydrophilic regions, i.e., more wettable spots, with a small continuous transition region towards the partially wetting background substrate.…”

Precursor Films and Contact Line Microstructures

“…In the latter case, note that we will not consider the particular case K-N (kinetically-limited evaporation regime), implied, for example, by Todorova et al (2012). A parametric analysis of this problem is presented here for two important limiting cases: (i) K 5 0 (local interfacial equilibrium) and ϑ Y varied with c{1 (i.e., velocity will be considered as a perturbation); and (ii) ϑ Y 5 0 (complete wetting) and K varied, while c{1 as well.…”