The sensitivity of drop motion due to the density and viscosity ratio

Abstract

The effect of the density and viscosity ratio on the motion of single drops rising in immiscible liquids is computationally investigated. The density and viscosity ratio play an important role in droplet morphology, unstable droplet behavior, and terminal droplet characteristics. The numerical method used in this investigation is a coupled level-set and volume-of-fluid method together with a sharp interface treatment for the interfacial jump conditions. The computations assume an axisymmetric geometry. Drop rise motion is highly dependent on the viscosity ratio. The results reported in this paper augment the information provided by the correlation table for bubble rise motion by Bhaga and Weber [“Bubbles in viscous liquids: Shapes, wakes and velocities,” J. Fluid Mech. 105, 61 (1981)]. A drop-system with a large viscosity ratio is susceptible to exhibiting unstable motion in the large Eötvös number regions; an unstable drop can show complicated behavior with various breakup modes that are dependent on the Morton number. With regard to the effect of the density ratio, it is observed that the difference between a bubble and a drop with “equivalent” properties is not prominent except in the low Morton number regions. The results of investigating the effect of the density and viscosity ratio on drop motion indicate that the Morton number, Eötvös numbers, and viscosity ratio are the primary governing parameters and the density ratio is a secondary governing parameter.