Bubble Formation in a Finite Cone: More Pieces to the Puzzle

We investigate the stability of bubble formation, starting with a convex or a concave meniscus, from a liquid solution (of water and a dissolved gas) inside a finite cone at constant temperature and constant liquid pressure (above the saturation pressure of the pure solvent). It is assumed that the dissolved gas (nitrogen) forms a dilute solution at equilibrium, which can be described by Henry's law. The number and nature of equilibrium states are determined with Gibbsian composite-system thermodynamics, both from the intersection of the equilibrium Kelvin radius with the geometry radius and from the extrema in the plot of free energy of the system versus size of the new phase. Bubble stability is studied along the whole growth path, as the bubble grows inside, gets pinned, and grows further outside the finite cone. The changes in the concentration of the liquid bulk phase and the vapor phase during the growth of the bubble are carefully incorporated in the equations. The effects of various parameters, including cone apex angle, cone half mouth radius, contact angle, total number of moles, and initial degree of saturation, on the stability of the bubble are also investigated. Stability of bubble formation from a liquid solution inside a confined geometry such as a finite cone is of interest in areas such as restoring underwater superhydrophobicity and adhesion of particles to the roughness of synthetic biomaterials.