Advanced dynamic-equilibrium model for a nanobubble and a micropancake on a hydrophobic or hydrophilic surface

The dynamic-equilibrium model for stabilization of a nanobubble on a hydrophobic surface by Brenner and Lohse [M. P. Brenner and D. Lohse, Phys. Rev. Lett. 101, 214505 (2008)] has been modified taking into account the van der Waals attractive force between gas molecules inside a nanobubble and solid surface. The present model is also applicable to a nanobubble on a hydrophilic surface. According to the model, the pressure inside a nanobubble is not spatially uniform and is relatively higher near the solid surface. As a result, there is gas outflux near a hydrophilic surface, while near a hydrophobic surface there is gas influx which has been already suggested. In the present model, the radius of curvature for a nanobubble depends on the distance from the solid surface because the pressure depends on it. The shape of the micropancake, which is a nearly-two-dimensional bubble, is reproduced by the present model due to the strong dependence of the radius of curvature on the distance from the solid surface. The effect of temperature on the stability of a nanobubble or micropancake is also discussed.