Determination of the quench velocity and rewetting temperature of hot surfaces. Part II: an integrated approach of hydrodynamic–thermodynamic micro- and macro-scale models

Abstract

A new integrated approach, comprising hydrodynamic–thermodynamic micro- and macro-scale models, for analysis of rewetting systems is presented. This new approach facilitates concurrent prediction of rewetting temperature, T rew *, and quench velocity, U rew *, for a wide range of system properties. To this end, the previously developed, micro-scale hydrodynamic model is combined with a thermodynamic model and the resulting algorithm is used to derive relations between the quench velocity and rewetting temperature. This combined micro-scale thermodynamic–hydrodynamic model is then interfaced with a known macro-scale model. The former predicts a physically feasible relation between rewetting temperature and quench velocity, as dictated by the physical properties and geometry of the phases involved in the micro-scale, three-phase contact zone. This model uses iterative algorithm that seeks the conditions where the contact angle predicted by the hydrodynamic and thermodynamic models match. Results of application of the combined model to several groups of liquids, with diverse thermo-physical properties, are presented. The calculated rewetting temperature is a monotonic increasing function of the quench velocity, for all liquids investigated, and the contact angle decreases with an increase of temperature. Higher rewetting temperatures and smaller contact angles are produced by increasing the intermolecular force as expressed by the parameter ε ω / kT c. The versatility of the model and its sensitivity to small increments in the iteration procedure used in the combined model is demonstrated for the unique case of helium. The mean slope (MS) of the rewetting temperature–quench velocity curve for liquids that pertain to the same group is shown to be nearly invariable. This is a new characteristic property of rewetting systems. The macro-scale model involves operational constraints that are imposed on the system and consequently a macro-scale relation between the rewetting temperature and quench velocity is set. The intersection between the microscopic, physically feasible, and the macroscopically imposed relations of rewetting temperature and quench velocity yields ( T rew *, U rew *) that is expected to prevail, for the given conditions of the system. This intersection is required for rewetting to exist. Otherwise, no rewetting is possible, as either complete wetting or non-wetting characterizes the behavior of the system. The new integrated approach is free of the need for assumptions regarding the value of either T rew or U rew, as both are obtained as its output. This work, which completes the series on determination of quench velocity and rewetting temperature on hot surfaces, relies completely on thermo-physical properties of the solid–liquid–vapor system and its operating conditions, without the need for additional assumed inputs. In this sense, the rewetting system can be fully described, once its own micro- and macro-scale properties and constraints are known.