An analytical model of the growth of invisible bubbles on solid surfaces in a supersaturated solution

Abstract

Heterogeneous nucleation of gas bubbles is central to many engineering fields, from boiling and heat transfer to cavitation and particle separation. In this paper, models accounting for the origin and growth of gas bubbles on solid surfaces in a supersaturated solution are proposed by applying the diffusion theory and the molecular-kinetic model. Both are validated by the available experimental results during the specific period. The theory provides an explanation for the bubbles’ growth from the pre-existing invisible nanobubbles on the submerged surface. The non-linear evolution of the bubble is attributed to the progression from the pinning stage to the floating stage, transition stage and expansion stage. In the pinning stage, when the base radius of the optically invisible surface bubbles is smaller than the critical value, they are speculated to be stable with the constant base radius because of the equilibrium between the driving force of diffusion and the Laplace pressure. Otherwise, the contact line of the surface bubble will start to move, is no longer pinned, and continues to grow with a constant bubble radius, which is called the floating stage. This is followed by the transition stage in which both the bubble radius and contact angle change with time. The final expansion stage is characterised by the bubble growth with the constant contact angle. Unlike the classical Epstein-Plesset model for bubble growth in the bulk, the diffusion theory can satisfactorily predict the growth of surface bubbles while the molecular-kinetic model can only fit the floating and expansion stages.