Development and interactions of two inert gas bubbles during decompression

Abstract

A mathematical model has been developed to simulate the evolution of two inert gas bubbles in tissue. This is useful for understanding the dynamics of bubbles that presumably arise during decompression. It is assumed that they are spherical and that the tissue volume surrounding them is infinite. The total pressure in each bubble is determined by the barometric and metabolic gas pressures as well as the pressure due to surface tension. Bipolar coordinates are employed to determine the inert gas pressure distribution. Two coupled governing equations for bubble radii are then derived and solved numerically. The results demonstrate how bubble evolution is affected by the distance between bubbles and the initial bubble radii. The existence time and bubble surface flux of two equal-sized bubbles are calculated and compared with those of a single gas bubble model. The results indicate that when two bubbles are very close, it takes 20% more time for two bubbles to dissolve than for a single one, and the total surface flux of two bubbles is nearly 20% less than twice of a single bubble. When the center-to-center distance is 10 times of bubble radius, the effect of bubble interaction on bubble existence time and surface flux are about 6 and 9% changes, respectively. We conclude that if bubbles are not too small, the interactions among bubbles should be included in inert gas bubble models predicting bubble evolution.