Universal Dripping and Jetting in a Transverse Shear Flow

One particularly efficient approach to making emulsions having monosized droplets is to push a fluid through an orifice into a transverse flow of a second immiscible fluid. We find that, at an intermediate particle Reynolds number, the final droplet size can be readily computed using a simple force balance. Remarkably like the well-known dripping faucet, this system displays both dripping and jetting behavior, controlled by the capillary, Weber and Ohnesorge numbers of the relevant fluids, and interesting nonlinear behavior such as period doubling near the transition between these two regimes.