EFFECT OF DENSITY RATIO ON THE HYDRODYNAMIC INTERACTION BETWEEN TWO DROPS IN SIMPLE SHEAR FLOW

Abstract- The effect of density ratio on the hydrodynamic interaction between two drops in simple shear flow at finite Reynolds numbers is studied considering the gravity influence. In this study the full Navier-Stokes equations are solved by a finite difference/front tracking method. The interaction of two drops contains approach, collision, and separation. For a range of density ratios, the interaction between deformable drops increases the cross-flow separation of their centres. The distance between the drop centres along the velocity gradient direction increases irreversibly after collision and reaches a new steady-state value after separation. The interaction between drops is affected by the density ratio. As the density ratio increases, the final equilibrium position of drops moves to the higher velocity region and the drop deformation increases. Drop deformation prevents drop coalescence at finite Reynolds numbers; the reduced collision cross-section of the drops allows them to glide past each other. The drops accelerate while sliding over each other. As the density ratio decreases, drops rotate more slowly, and the point at which the drops separate is delayed. To simulate the flow of a concentrated suspension successfully, the calculation procedure must be able to describe the interaction of two closely interacting drops. Hydrodynamic interaction between a pair of drops may result in coalescence, breakup or gliding past each other. Magna and Stone [5] reported the time-dependent interactions between two buoyancy-driven deformable drops in a low Reynolds number flow. They introduced three modes for film drainage between the drops: rapid drainage, uniform drainage and dimple formation. As the separation distance between the two drops decreases, the mode of film drainage may change from rapid drainage to uniform drainage and eventually a dimple may form. Zhou and Pozrikidis [6] studied the flow of periodic suspension of two-dimensional viscous drops in a channel bounded by two parallel plane walls. They found that there exists a critical Capillary number below which the suspensions exhibit stable periodic motion, and above which the drops elongate and tend to coalesce, altering the topology of the initial configuration. They studied the effects of Capillary number, viscosity ratio, volume fraction, lattice geometry, and instantaneous drop shape, on the effective stress tensor of the suspension. Li, Zhou and Pozrikidis [7] studied the motion of two-dim