Numerical study of a compound droplet moving toward a rigid wall in an axisymmetric channel

Abstract

Dynamical behaviors of compound droplets including those interacting with rigid walls in an axisymmetric channel appear in various industrial and natural processes. However, so far, no detailed investigation has been carried out for such interactions of compound droplets. Motivating from this missing gap, we here numerically study the finite deformation and breakup of an initially concentric compound droplet when it moves toward a rigid wall at the bottom of an axisymmetric vertical channel. The method used is a finite difference-based front-tracking method. The numerical results reveal that when the compound droplet is delivered toward the wall, it is deformed and can break up into smaller droplets. For the cases of finite deformation (i.e. non-breakup), while the outer droplet is radially stretched, the inner droplet first moves downward in the direction of the outer flow but then gets back. Thereby, a thin film is created between the outer and inner interfaces at the droplet top and thus prevents the outer droplet further deforming and breaking up. In contrast, if breakup happens, the outer droplet is further stretched, and most of the middle fluid moves outward toward the outer droplet edge to form a blob. Breakup can be available in one of three patterns: off-axis breakup, on-axis breakup, and inner breakup. The off-axis breakup mode only happens with the outer droplet while the inner breakup mode is only for the inner droplet. Various parameters are investigated to show the transition between a non-breakup mode to a mode of breakup. Such parameters contributing the transition include the Capillary number Ca (varied in the range of 0.01–2.5), the channel aspect ratio (varied in the range of 0.4–2.0), the ratio of the inner to outer droplet radii (varied in the range of 0.3–0.8), the droplet size relative to the channel size (varied in the range of 0.2–0.9), the interfacial tension ratio of the inner to outer interfaces (varied in the range of 0.1–4.0), and the viscosity ratio of the middle to outer fluids (varied in the range of 0.16–6.3). In contrast, some others, e.g. the Reynolds number, the viscosity ratio of the inner to the outer, do not induce any transition. From the numerical results, regime diagrams of breakup and non-breakup based on these parameters are proposed.