Effects of non-uniform temperature of the ice nucleus on heterogeneous ice nucleation

Abstract

In this paper, effects of non-uniform temperature in the ice nucleus on heterogeneous ice nucleation are investigated via two approaches: changes in Gibbs free energy function and availability function. Analytical expressions for non-uniform temperature distribution inside the ice nucleus and heat transfer from the nucleus to the supercooled wall are obtained in terms of the contact angle and supercooled wall temperature based on the consideration that thermal conductivity resistance of the nucleus, interfacial resistance and thermal resistance due to curvature of ice/water interface are in series. With non-uniform temperature in the nucleus taken into consideration, it is found that the critical radius of the ice nucleation obtained based on availability analysis is slightly larger than those obtained based on Gibbs free energy analysis. Both heterogeneous critical radius and nucleation energy barrier are found to be increasing with surface contact angle. On an ice-phobic surface at small supercooling degrees, the critical radius and the nucleation energy barrier obtained with or without heat transfer taken into consideration differ greatly with the increase of the contact angle. However, at large supercooling degrees and small contact angles, differences in the critical radius and nucleation energy barrier by availability analysis are negligible with or without heat transfer effects. Thus, heterogeneous nucleation behaviors on ice-philic surfaces can be estimated based on the assumption of uniform temperature in the ice nucleus when degree of wall supercooling is large.