Splitting of microbubble mediated by power-law carrier fluid inside a symmetric bifurcating channel

Abstract

We investigate the dynamics of bubble propagation in a symmetric bifurcating Y-channel by varying the power-law index (n) of the carrier fluid from 0.3 to 1.5, in the presence of gravity. To characterize the bubble evolution, the unsteady two-phase flow is solved numerically, employing a suitable phase-field model. Based on the flow rate ratio between the upper and lower branch channels and the neck-width evolution, the bubble bifurcation process is divided into three distinct stages, namely, squeezing, transition, and pinch-off. Temporal variation of neck-width demonstrates that the bubble pinch-off is somewhat delayed for shear-thickening (n > 1) fluids, while a shear-thinning carrier fluid (n < 1) triggers faster pinch-off. Our study reveals that for a large n (say, n = 1.5), viscous force strongly counters the buoyancy effect, resulting in symmetric (equal) bifurcation of the bubble. Conversely, for shear-thinning fluids, the bubble evolution is dictated primarily by the buoyancy force, leading to an asymmetric bubble breakup. We investigate the role of n on wall shear variation and determine the wall-location that is susceptible to the maximum damage. Performing simulations over wide ranges of capillary numbers (Ca) and Bond numbers (Bo), we unveil important regimes of bubble splitting phenomena, e.g., symmetric breakup, asymmetric breakup, buoyancy dominated no-breakup, and surface tension dominated no-breakup regimes. Numerically predicted regime plots, which comprehensively illustrate the roles of Ca, Bo and, n on various breakup regimes, may act as fundamental design basis of branching networks in classic applications, such as microfluidics, biofluid mechanics, and flow through porous media.