We have performed calculations, verified by experiment, to explain why the sensitivity of biological EPR can be dramatically increased by dividing the aqueous sample into separate compartments. In biological EPR, the major factor affecting sensitivity is the number of spins in the sample. For an aqueous sample at ambient temperature, this is limited by the requirement for a small volume, due to strong non-resonant absorption of microwaves by water. However, recent empirical studies have shown that this volume limitation can be greatly relieved by dividing the aqueous sample into separate volumes, which allows much more aqueous sample to be loaded into a resonant cavity without significant degradation of the cavity quality factor. Calculations, based on the Bruggeman mixing rule, show quantitatively that the composite aqueous sample has a permittivity much less than that of bulk water, depending on the aqueous volume fraction f. Analysis for X-band EPR spectroscopy shows that the optimal volume fraction of an aqueous composite sample, producing maximum sensitivity, is f = 0.15, increasing the sensitivity by a factor of 8.7, compared with an aqueous sample in a single tube.