Abstract: A high capacity primary (single-use; non-rechargeable) battery pack for high current portable appliances such as cellular phones employs electrochemical cells that use ambient oxygen for one of the electrodes. The pack makes possible a simple low cost design by providing for oxygen supply in a completely passive yet compact configuration. Cells may be arranged inside a housing in a tightly packed arrangement by providing internal spaces that are sized to permit diffusion and, if possible, bulk air flow. The highest volumetric energy density is achievable by permitting bulk flow of air into the housing. It has been found that in practical use, in applications such as cellular telephones, that bulk air flow can play a significant role in gas exchange required for operation. A number of design criteria are developed for providing for a mix of molecular diffusion and bulk flow in the design of battery packs according to the invention.