Determination of the quench velocity and rewetting temperature of hot surfaces: Formulation of a nonisothermal...

A nonisothermal microscale model of the three-phase, solid-liquid-gas, contact zone is formulated in the context of rewetting phenomena. The model incorporates hydrodynamics, heat transfer, interfacial phenomena, and intermolecular long range forces, in a two-dimensional proximal region of the order of 1000 A in width and 100 A in thickness. The model comprises scaled mass, momentum, and energy balances, and their corresponding scaled boundary conditions. The small contact angles which are characteristic of rewetting situations facilitate the use of the lubrication approximation, and the dynamics of the liquid and gas phases is decoupled by applying the one-sided simplification. The microscale hydrodynamic model reflects the strong effect of the solid-liquid interactions on the film profile, and the attendant flow and thermal fields. Thinner films having smaller contact angles involve stronger solid-liquid attraction forces, and consequently they exhibit higher rewetting temperatures and lower evaporation and vapor recoil effects. Thermocapillary and evaporation and conduction effects are expressed by appropriate dimensionless numbers. A set of such numbers is defined in the context of the differential equations of the microscale model. This model covers the hydrodynamic aspect of rewetting phenomena, which are also controlled by thermodynamic and macroscale constraints. This calls for interfacing and appropriate combination between the microscale hydrodynamic model, thermodynamics, and other macroscale rewetting models, for the determination of rewetting temperatures and quench velocities of liquids on hot solid surfaces. This is addressed elsewhere, in subsequent papers that follow this work.