Quasi-2d Emulsion Flow Through Hopper

We study the quasi-2d hopper flow of oil-in-water emulsions as they exit an orifice. Prior work on hopper dynamics has focused on the flow rate, which is defined as the number of oil droplets exiting per unit time. This has shown a general power law dependence between flow rate, Q, the ratio of the opening width, w, to the average diameter of droplet size, d, and the fitting constant k as such: Q~(w/d-k)^α. Prior work has seen various values for the exponent α, corresponding to different experimental conditions. Recent work (cite) has suggested that the range of values for the exponent α can explained by the ratio of the viscous drag force of particles moving in their medium to the kinetic friction of two particles sliding past each other. In two dimensions, for the low kinetic friction limit, this exponent should be ½. We experimentally verify this claim by studying the flow rate of silicon oil-in-water emulsions as they pass through an orifice over a range of w/d values. We find that the flow rate collapses to the general curve with α=0.49 and k=1.47.