A theoretical analysis of the generation of electrical streaming currents and electrical power by two-phase flow in a rectangular capillary is presented. The injection of a second, non-conducting fluid phase tends to increase the internal electrical resistance of the electrical generator, thereby increasing the power output. If the viscosity of the injected fluid is large, the resulting high shear rate in the low-viscosity fluid at the wall generates a large streaming current and the power generated is further enhanced. However, if the injected fluid viscosity is low, the wall shear rate in the more viscous suspending fluid is reduced, as are streaming currents. Power generation would be small but for capillary effects at the ends of the bubbles that increase the pressure drop along the capillary above that expected for annular flow.