The present invention provides devices and methods for achieving mixing and gas exchange in chambers having a small volume. According to the invention a chamber includes one or more walls that are made of a gas-permeable material and that include multiple portions that are selectively deflectable into the interior of the chamber. The deflectable portions are in communication with a hollow cavity or space that can be pressurized. Pressurization results in deflection of the deflectable portion into the chamber. Pressurization is achieved using a gas or fluid that contains a gas of interest such as oxygen. The portions are deflected in a sequence that results in peristaltic action that mixes and oxygenates the contents of the chamber. In a preferred embodiment of the invention the hollow cavities are an assembly of tubes that deflect into a plurality of chambers. A particular use for the invention is as a culture vessel for cells such as bacteria.