Rheology of a Dilute Emulsion of Low-Viscosity Drops at High Shear Rates

A theoretical analysis is presented for the rheology of a dilute emulsion of low-viscosity drops or bubbles in shear flow at high shear rates. In the high-shear-rate limit, the predicted relative shear viscosity of the emulsion is 1 - 2c, where c is the volume fraction of drops. A first normal stress difference proportional to the square-root of the drop viscosity ratio is also predicted; in a suspension of bubbles, the first normal stress decreases with the 3/4 power of the capillary number. Confining boundaries reduce the normal stress but do not strongly influence the shear viscosity.