Heterogeneous bubble nucleation and conditions for growth in a liquid–gas system of constant mass and volume

Abstract

The conditions are considered under which heterogeneous bubble nucleation takes place in a conical pit in the boundary of a constant size volume containing a liquid–gas solution, and the size to which the nucleate bubble grows is predicted. Four possible equilibrium states are found for the nucleate bubble: two unstable, one metastable, and one stable. The unstable state corresponding to the smallest equilibrium size is the one that acts as the threshold size that must be exceeded in the nucleation event. The metastable and second unstable state are encountered as the nucleate bubble emerges from the conical pit and the stable state corresponds to the largest equilibrium size. It arises from the bubble being in a finite volume with fixed mass. The pressure produced in the volume by the growth of the bubble depends on the final state it attains (i.e., either the metastable or stable state). The theoretical expressions obtained from the analysis are applied to predict the conditions under which bubble nucleation and growth take place within a type of bone cell, and the results are used to explain certain types of damage to the bone of animals undergoing decompression from high pressures that have been previously reported in the literature. The expressions are also applied to predict the superheat necessary to produce bubble emergence from a conical pit and are shown to be in agreement with results previously reported.