The collapsing bubble in a liquid by molecular dynamics simulations

Abstract

Molecular dynamics simulations have been made of a collapsing bubble or cavity in a simple liquid. Simulations of a Lennard-Jones liquid reveal that the collapsing process takes place in a series of stages. First, the ‘hottest’ molecules from the high kinetic energy tail in the Maxwell—Boltzmann distribution diffuse into the empty cavity. This is followed by a gradual filling in of the cavity until the density in the centre is a little lower than that of the bulk liquid. The system eventually reaches a final new equilibrium liquid state through a subsequent slower equilibration phase. The bubble fills in an oscillatory manner, by partly filling in, and then partially emptying, and so on, with ever decreasing amplitude towards the final uniform liquid state. These density oscillations are more obvious in systems with a larger bubble. Similar oscillations are observed in the kinetic energy of the molecules at selected radii from the centre of the initial bubble. The maximum temperature occurs typically at the end of the initial fillingin stage during which the density of the core undergoes a vapour-to-liquid phase transition, the released latent heat probably contributing to the temperatures achieved in this region. The average maximum temperature found in the smallest system examined is about nine times the critical temperature, which is about 6000 K for water, thus suggesting a simple mechanism for producing molecules with the sorts of kinetic energies and lifetimes required for sonoluminescence.