ABSTRACT

The evaporation of a liquid into the atmosphere of its pure vapor on a uniformly heated solid substrate is investigated. Five physical phenomena are considered and modeled in the framework of lubrication theory: (i) hydrodynamics, (ii) heat conduction, (iii) phase change, (iv) kinetics of evaporation, and (v) slip length. The model is in fact an inner problem − contact line (CL) vicinity, microregion − of the model investigated by Anderson and Davis [D.M. Anderson and S.H. Davis, "The spreading of volatile liquid droplets on heated surfaces," Phys. Fluids, vol. 7, pp. 248−265 (1995)] and extends the inner and intermediate solution of Hocking [L.M. Hocking, "On contact angles in evaporating liquids," Phys. Fluids, vol. 7, pp. 2950–2955 (1995)] to more general considerations of the slip length. Decoupling from the outer problem − the macroscopic part of a liquid object − allows us to quantify the impact of evaporation in the CL vicinity on the apparent contact angle and microregion heat transfer. The linearized problem with respect to the substrate overheating is solved analytically. The analytical solutions are compared with full numerical solutions and to predictions of Hocking. We also define and determine the thermal regularization length associated with the present problem.