Migration of a droplet in a cylindrical tube in the creeping flow regime

The migration of a neutrally buoyant droplet in a tube containing another immiscible liquid is investigated numerically in the creeping flow regime. A fully developed velocity profile is imposed at the inlet of the tube. The interface between the two immiscible fluids is captured using a coupled level-set and volume-of-fluid approach. The deformation and breakup dynamics of the droplet are investigated in terms of three dimensionless parameters, namely, the ratio between the radius of the undeformed droplet and the radius of the capillary tube, the viscosity ratio between the dispersed and the continuous phases, and the capillary number that measures the relative importance of the viscous force over the surface tension force. It has been observed that the droplet, while traversing through the tube, either approaches a steady bulletlike shape or develops a prominent reentrant cavity at its rear. Depending on the initial droplet size, there exists a critical capillary number for every flow configuration beyond which the drop fails to maintain a steady shape and breaks into fragments. The deformation and breakup phenomena depend primarily on the droplet size, the viscosity ratio, and the capillary number. Special attention has been given to the case where the drop diameter is comparable with the tube diameter. A thorough computational study has been conducted to find the critical capillary number for a range of droplets of varied sizes suspended in systems having different viscosity ratios.