Viscous resistance in drop coalescence

Abstract

Hydrodynamics of drop coalescence has been studied theoretically and numerically by solving the Navier Stokes equation considering a single fluid after the minimum bridge formation. Many experiments have been performed to document bridge growth over time with the use of high speed videography and electrical methods. However, internal fluid motion during coalescence has not been extensively studied, in part due to the spherical shape of the drops. This work observed overall fluid motion (except at the site of early coalescence) using particle image velocimetry for two-dimensional (sandwiched drop) coalescence. Fluid motion inside the bulk drops is inertial, and governing fluid flow in the bridge region is one dimensional. At the merging interface, incoming liquids join and coflow in the perpendicular direction. These observations were extended to a three-dimensional counterpart, and a scaling law was developed that was validated through experimentation. While flow in the bulk drops is inertial, the dominant resistance comes through a viscous effect in the merging interface region and at the lesser extent in the bridge region. Early dynamics of drop coalescence is dominated by the Ohnesorge number (Oh), and later dynamics are dependent on how drops are bounded.