Viscosity ratio effects on the coalescence of two equal-sized drops in a two-dimensional linear flow

Abstract

The effect of the dispersed to continuous-phase viscosity ratio on the flow-induced coalescence of two equal-sized drops with clean interfaces was experimentally investigated. The experimental systems consisted of polybutadiene drops suspended in polydimethylsiloxane. The bulk-phase rheological properties of the fluids are Newtonian under the very weak flow conditions of the coalescence experiment (strain rate, $G \,{<}\, 0.08\,{\rm s}^{-1})$. Both head-on and glancing collisions were studied in a purely extensional flow (flow-type parameter, $\alpha\,{=}\,1.0$) for the viscosity ratio $(\lambda)$ range from $O(0.1)$ to $O(10)$. For head-on collisions, the dimensionless drainage times increased with the capillary number (Ca) as $\textit{Ca}^{3/2}$ for all the viscosity ratios, which is consistent with theoretical predictions based on a simple film drainage model. The drainage time at a fixed Ca increased with the viscosity ratio and scaled as $\lambda^{0.82}$. In the case of glancing collisions, the critical coalescence conditions were examined by changing the initial offset, which results in different collision trajectories. In an earlier paper (Yang et al. 2001) that studied a system with a viscosity ratio of 0.096, the critical capillary number $(\textit{Ca}_{c})$ for coalescence always decreased with the increasing offset. However, the present study shows that when the viscosity ratio is greater than $O(0.1)$, the critical capillary number decreases with increasing offset only for the smallest offsets, but then increases with increasing offset until a critical offset is reached above which coalescence is not observed. This is because coalescence for the larger offsets occurs in the extensional quadrant $(\phi\,{>}\,45^\circ$) after the external flow has begun to pull the drops apart. At small offsets, drops coalesced in the compression quadrant with an orientation angle, $\phi \,{<}\,45^\circ$. At the larger offsets, drops also coalesced in the compression quadrant for small Ca, but above some critical Ca, the coalescence angle jumped abruptly (i.e. with a very small change in Ca) to coalescence in the extensional quadrant. Coalescence with $\phi\,{>}\,45^\circ$ is more prevalent for the higher viscosity ratio systems. On the other hand, the maximum offset for coalescence decreased with the viscosity ratio as expected.