Analysis of levitation of saturated liquid droplets on permeable surfaces

Abstract

Steady-state evaporation of a saturated liquid droplet and its levitation over a solid surface due to momentum-induced pressure in the vapor film is studied by solving the axisymmetric governing equation numerically. A previous one-dimensional analysis shows that the distance (or gap) between the solid surface and the droplet decreases when the vapor can penetrate the solid. For porous layers, this onedimensional analysis which is based on Brinkman's extension to Darcy's law predicts momentum boundary layer thicknesses of the order of the square root of the permeability. In typical porous solids, this thickness is smaller than the pore or particle size. In the present study the Beavers-Joseph semi-empirical boundary condition at the interface of the plain (i.e. vapor underneath the droplet) and permeable layers is used instead of this one-dimensional model. The reduction in the gap size with respect to variations in permeability and thickness of the porous layer is determined for the ranges where this boundary condition is valid. The effect of vapor escape through the bottom surface of the porous layer is also studied. This axisymmetric model predicts an asymptotic value for the slip velocity and the gap size as the permeability increases beyond a certain value. This failure of the model to predict the collapse of the droplet is due to the breakdown of the Beavers-Joseph interfacial condition for high permeabilities. However, for practical applications the surface roughness is expected to dominate when the gap size approaches zero. The onedimensional model, i.e. the Brinkman extension, on the other hand, predicts an unrealistic rapid drop of the gap size when the permeability is increased beyond a certain value, because of the assumption of equal pressure gradients in the porous and plain layers.