Modeling the effect of shape deformation induced by gravity on the evaporation of pendant and sessile drops

Abstract

Pendant and sessile drops form a spherical cap only in the absence of gravity. The effect of gravity on drop shape is often neglected on the basis of the assumption that the drop size is smaller than the capillary length [Lc=(σ/gρ)1/2], although the deformation may not be fully negligible even in those cases. This paper focuses on evaluation of the effect that deformation due to gravity has on the evaporation characteristics of pendant and sessile drops. The drop shape is described by the Bashforth–Adams equation, a non-linear second order ordinary differential equation, which is solved numerically using a Runge–Kutta method with variable time steps. Under quasi-steady approximation, the species and energy conservation equations in the gas phase have analytical solutions, even for temperature-dependent gas thermophysical properties, once the solution of a basic Laplace problem is known. The Laplace equation is solved in axial symmetric geometry by using COMSOL Multiphysics®, for a wide range of drop sizes and contact angles, yielding vapor distribution, vapor fluxes, and evaporation rates. Comparison with the results from drops of same size in microgravity (i.e., having a spherical cap shape) shows that the effect is also perceptible for drops with a size smaller than the capillary length and that it can become quite important for those with larger sizes. Complementary results are found for sessile and pendant drops with respect to wall wettability, suggesting that the phenomenon can be analyzed using a unitary approach.