Comparison of Boundary Conditions at Liquid-Vapor Interface for Modeling Droplet Film Boiling

The present study theoretically investigates the film boiling characteristics of a Leidenfrost droplet deposited on a solid substrate. The model consists of mathematical formulae describing the droplet surface curvature, vapor layer dynamics and evaporation rate from the whole droplet surface. Different boundary conditions are applied at the liquid-vapor interface, i.e., the no-slip, no-shear, and Marangoni shear conditions. Their effect on the droplet film boiling characteristics, including the droplet morphological parameters, vapor layer thickness, and droplet evaporation rate, are compared and discussed. The calculated results show that the vapor layer thickness decreases but the droplet evaporation rate increases in the sequence of no-slip, no-shear, and Marangoni shear conditions. Overall, the type of boundary condition does not affect the bulk droplet morphology because all the predicted values of droplet radius in the neck region and droplet height agree well with experimental data. However, the no-slip condition shows the highest accuracy in predicting the vapor layer thickness and droplet evaporation rate, followed by the no-shear and Marangoni shear conditions. Both the minimum vapor layer thickness under a Leidenfrost droplet and the droplet evaporation rate increase with the droplet radius and substrate temperature, the latter of which exhibits a more significant influence for larger droplets.