Influence of the size dependence of surface tension on the dynamics of a bubble in a liquid

The Gibbs dividing surface method is used to derive the differential equation defining the dependence of the surface tension of a bubble in a nonpolar single-component liquid on its radius. Exact and asymptotic solutions of this equation have been obtained. It follows from the calculations that the bubble surface tension increases with decreasing radius. The Rayleigh-Plesset equation describing the bubble collapse dynamics is solved numerically by taking into account the size dependence of surface tension. The size dependence of surface tension is shown to affect significantly the final bubble collapse stage and, on the whole, accelerates this process.