Numerical investigation of an evaporating meniscus in a heated capillary slot

Abstract

This paper numerically studies heat transfer and fluid flow from an evaporating meniscus of a wetting fluid within a heated capillary. A simplified steady state mathematical model is developed for predicting the wicking height of the meniscus and the evaporation mass flow rate which includes: (1) one-dimensional flow and energy equations for the liquid and vapor regions, (2) one-dimensional model for the evaporating meniscus region, and (3) two-dimensional energy equation for the capillary wall. Three parameters, namely, apparent contact angle, cumulative heat transfer, and evaporating meniscus height characterize the evaporating meniscus region. In this paper, the apparent contact angle in the evaporating meniscus is uniquely deduced from the meniscus curvature at the centre of the capillary using the thickness profile obtained from standard extended meniscus theory (which includes the evaporating thin film and bulk meniscus regions). Correlations are obtained for the cumulative heat transfer, apparent contact angle and evaporating meniscus height as a function of the difference between the wall and saturation temperatures from the evaporating thin film theory for the meniscus region, which is called as micromodel. The macroscopic model accounts for wall heat conduction and heat transfer with fluid flow in the liquid and vapor regions. The micromodel deals with heat transfer and fluid flow in the evaporating meniscus region. In this paper, a novel scheme to link the “macroscopic” momentum and energy equations in the capillary slot and the evaporating meniscus through the correlations developed above is proposed. Using this numerical model, the wicking height and the evaporation mass flow rate are estimated and the results are compared with previously conducted experiments. The trends in the numerical results of the mathematical model correlate reasonably well with the experimental data.