History effects on the gas exchange between a bubble and a liquid

Diffusive processes exhibit a strong dependence on history effects. For a gas bubble at rest in a liquid, such effects arise when the concentration of dissolved gas at the bubble surface, dictated by Henry's law, depends on time. In this paper we consider several such situations. An oscillating ambient pressure field causes the occurrence of rectified diffusion of gas into or out of the bubble. Unlike previous investigators, who considered the opposite limit, we study this process for conditions when the diffusion length is larger than the bubble radius. It is found that history effects are important in determining the threshold conditions. Under a static ambient pressure, the time dependence of the gas concentration can arise due to the action of surface tension, which increases the gas pressure as the bubble dissolves or, when the bubble contains a mixture of two or more gases, due to the different rates at which they dissolve. In these latter cases history effects prove mostly negligible for bubbles larger than a few hundred nanometers.