Theoretical Modeling of Levitated Clusters of Water Droplets Stabilized by Infrared Irradiation

Abstract

This paper reports modeling of heat and mass transfer of clusters of radiation-stabilized water droplets levitated above a water surface using Spalding's self-similarity theory with Stefan flow. The model describes equilibrium droplet states, including stability conditions, as well as non-equilibrium (quasi-steady) transient evolution. Equilibrium states are shown to exist when Stefan-flow supersaturation, which has a quadratic-like variation with height above the water surface, and radiation-stabilized equilibrium supersaturation, which is nearly constant with height, are equal. This work shows how modeling results that were obtained by empirical curve-fitting and numerical computation and reported with the experiments could have been readily calculated with simple, analytically obtained algebraic equations already in the literature. The algebraic expression for equilibrium supersaturation as a function of droplet radius, absorbed radiant flux, and thermophysical properties that was found analytically and published previously predicts an empirical/numerical correlation reported for the same. A previously published algebraic solution for droplet condensative growth or evaporative shrinkage under the influence of absorbed radiation is shown to predict the same results as were computed numerically. The basis of these simple analytical results is the quasi-steady droplet energy condition, which is applicable and useful in analyzing and modeling these phenomena, along with continuum (Fick's law) diffusion mass-transfer theory. Knudsen-layer modeling appears not to be necessary.