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

In a low Morton number ( $ #1{} #1{ {#1}} ≤ = ≤ = ≥ = ≥ = {Pr} {Fr} {Re}M$ ) regime, the stability of a single drop rising in an immiscible viscous liquid is experimentally and computationally examined for varying viscosity ratio $η $ (the viscosity of the drop divided by that of the suspending fluid) and varying Eötvös number ( $Eo$ ). 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 η regimes, η = 0.02 or 0.1, and when Eo exceeds a critical threshold, it is observed that a rising drop exhibits nonlinear lateral/tilting motion. In the higher η regimes, η = 0.1 , 1.94, 10 or 100, and when 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 η and Eo .