Viscosity-ratio-based scaling for the rise velocity of a Taylor drop in a vertical tube

Abstract

Simulations of a silicon oil Taylor drop rising in a tube filled with a glycerol-water mixture are performed to investigate the viscosity ratio effects on the rise velocity of the Taylor drop. By varying the viscosity ratio λ between the drop and the suspending liquid from O(0.1) to O(10), a simple relationship of the nondimensional terminal velocity, the Froude number (Fr), is revealed as Fr ∝ λ(-0.27). This scaling is further confirmed by recently published experimental data [Hayashi, Kurimoto, and Tomiyama, Int. J. Multiphase Flow 37, 241 (2011)]. The simulated drop shapes also compare well with the experiments. Increasing the viscosity ratio elongates the drop and tends to make the tail bulge out. The correlation applies to small Reynolds numbers and finite viscosity ratios.