Determination of the quench velocity and rewetting temperature of hot surfaces. Part I: analytical solution of the micro-scale hydrodynamic model

The hydrodynamic micro-scale model, developed previously, is used to solve the non-isothermal interface equation. The complex interface equation is si mplified in a coordinate frame that moves with the three-phase contact line . This equation accounts for effects of evaporation, thermo-capillary and i ntermolecular forces. The new non-isothermal interface equation provides ge neralization of de Gennes' equation that applies to the isothermal case. Th e simplified third-order differential equation is solved numerically, and t he effect of numerical parameters and selection of boundary conditions on s olution convergence are established for a wide range of properties of solid -liquid pairs. In contrast to the smooth isothermal interfaces, non-isother mal interfaces are characterized by an undulating or wavy geometry. This be havior is a reflection of evaporation and mass transfer occurring across th e interface, and unique capillary and thermocapillary effects that arise un der non-isothermal conditions. A parametric study of the interface solution shows that increase of the capillary, C, and thermocapillary, C theta (2)( 0)/F numbers produces steeper interface profiles, whereas the factor N, eva poration coefficient S, and the Hamaker constant (A) over bar, produce the reverse effect. Larger values of N, S and (A) over bar result in higher und ulation frequencies. These effects intensify and become dominant under rewe tting conditions. The new interface equation provides an advanced tool for further studies of hydrodynamic mechanisms that govern the motion of thin l iquid films on hot solid surfaces, that involve high temperature gradients and intense evaporation. This furnishes a hydrodynamic foundation for analy sis of rewetting phenomena, and the definition of rewetting temperature and quench velocity, that are presented in a subsequent paper. (C) 2001 Elsevi er Science Ltd. All rights reserved.