Multiscale Modeling of the Three-Dimensional Meniscus Shape of a Wetting Liquid Film on Micro-/Nanostructured Surfaces

The design of structured surfaces for increasing the heat flux dissipated during boiling and evaporation processes via enhanced liquid rewetting requires prediction of the liquid meniscus shape on these surfaces. In this study, a general continuum model is developed to predict the three-dimensional meniscus shape of liquid films on micro/nanostructured surfaces based on a minimization of the system free energy that includes solid-liquid van der Waals interaction energy, surface energy, and gravitational potential. The continuum model is validated at the nanoscale against molecular dynamics simulations of water films on gold surfaces with pyramidal indentations, and against experimental measurements of water films on silicon V-groove channels at the microscale. The validated model is used to investigate the effect of film thickness and surface structure depth on the meniscus shape. The meniscus is shown to become more conformal with the surface structure as the film thickness decreases and the structure depth increases. Assuming small interface slope and small variation in film thickness, the continuum model can be linearized to obtain an explicit expression for the meniscus shape. The error of this linearized model is quantitatively assessed and shown to increase with increasing structure depth and decreasing structure pitch. The model developed can be used for accurate prediction of three-dimensional meniscus shape on structured surfaces with micro/nano-scale features, which is necessary for determining the liquid delivery rate and heat flux dissipated during thin-film evaporation. The linearized model is useful for rapid prediction of meniscus shape when the structure depth is smaller than or comparable to the liquid film thickness.