Local Meniscus Curvature During Steady-State Evaporation from Micropillar Arrays

Micropillar arrays are an ideal model system for capillary-aided thin film evaporation that can be fabricated with precise geometric control using microfabrication methods. The capillary limit leading to dryout is a critical performance metric for capillary-aided thin film evaporation and is proportional to the product of the permeability and capillary pressure. Capillary flow models for steady-state thin-film evaporation typically employ capillary pressure and permeability as separate parameters; however, it is difficult to separate the two from experimental hemiwicking characterizations or dryout observations. Furthermore, for micropillar arrays, local permeability depends on meniscus curvature varying spatially and with the evaporation rate. In this work, we use thin-film interference microscopy to profile local meniscus curvature during steady-state evaporation of water in a pure vapor environment. Local capillary pressure is calculated from curvature without requiring knowledge of contact angle or permeability. Results are compared against a Darcian semianalytical model for flow through micropillar wicks incorporating local permeability due to meniscus curvature. Although traditionally a slip boundary condition has been assumed at the liquid-vapor interface, we find much better agreement using a no-slip condition. The consequence of no-slip behavior is larger pressure gradients for a given evaporation flux and a lower dryout heat flux relative to a full slip condition. Heat transfer coefficient data are also presented and discussed in terms of curvature and sample geometry.