Thin film evaporation in microchannels with slope- and curvature-dependent disjoining pressure

Physics of thin film evaporation plays a critical role in designing highly efficient micro-scale thermal management systems. In such systems, envelope of the evaporating thin film is an extended meniscus beyond the apparent contact line at a liquid/solid interface, which experiences strong intermolecular forces because of micro-scale interactions. Traditionally, such forces are represented by disjoining pressures that are postulated solely on the basis of the local film thickness, disregarding the local slope and curvature of the interfacial profile. In the present study, an improved model for evaporation in thin liquid films in microfluidic channels is developed, which explicitly takes into account the slope and curvature dependence of the disjoining pressure, under the assumption of a steady meniscus in existence with its own vapor. Such an improved formalism essentially prevents the contact line movement without slip, and allows an asymptotic merging of the evaporating interfacial profile to an infinitesimally thin non-evaporating adsorbed film. Implications of this rigorous disjoining pressure model on the thermo-physics of thin film evaporation in a kinetically controlled limit are investigated in details, and contrasting confluences as compared to the traditional descriptions of the disjoining pressure are emphatically pinpointed.