Influence of the viscosity ratio on drop dynamics and breakup for a drop rising in an immiscible low-viscosity liquid

Abstract

AbstractIn a low Morton number ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M$) regime, the stability of a single drop rising in an immiscible viscous liquid is experimentally and computationally examined for varying viscosity ratio $\eta $ (the viscosity of the drop divided by that of the suspending fluid) and varying Eötvös number ($\mathit{Eo}$). Three-dimensional computations, rather than three-dimensional axisymmetric computations, are necessary since non-axisymmetric unstable drop behaviour is studied. The computations are performed using the sharp-interface coupled level-set and volume-of-fluid (CLSVOF) method in order to capture the deforming drop boundary. In the lower $\eta $ regimes, $\eta = 0.02 $ or 0.1, and when $\mathit{Eo}$ exceeds a critical threshold, it is observed that a rising drop exhibits nonlinear lateral/tilting motion. In the higher $\eta $ regimes, $\eta = 0.1$, 1.94, 10 or 100, and when $\mathit{Eo}$ exceeds another critical threshold, it is found that a rising drop becomes unstable and breaks up into multiple drops. The type of breakup, either ‘dumbbell’, ‘intermediate’ or ‘toroidal’, depends intimately on $\eta $ and $\mathit{Eo}$.