Three-dimensional deformation of a spherical droplet in a square duct flow at moderate reynolds numbers

Abstract

In this work, we study the dynamics of a three-dimensional neutrally buoyant droplet as it translates and deforms in a square-duct. An emphasis is placed on understanding the transient deformation history. We study the effect of the Reynolds number, capillary number, and droplet to carrier fluid viscosity ratio on deformation. In the low Reynolds number limit, we expect the droplet deformation to be independent of Reynolds number. We examine moderate Reynolds numbers in the range of 10–100 and show that inertia plays a significant role in droplet deformation both in the magnitude of steady-state as well as transient deformations. For Reynolds numbers greater than 25, we observe non-monotonic deformation histories. At higher Reynolds numbers we also observe cavity regions forming at the trailing edge of the droplets. These cavity regions appear to be unstable due to their relatively high interfacial curvature. Interfacial tension therefore plays a significant role at the trailing edge to return the cavity region to a more stable convex shape. We study droplet deformation for moderate capillary numbers in the range of 0.10–0.25 and observe a strong variation in deformation magnitude with capillary number. However, the capillary number does not appear to influence the qualitative transient deformation behavior. We also explore the effect of droplet to carrier fluid viscosity ratio on droplet deformation and observe a more complicated relationship. For small viscosity ratios, the deformation histories are non-monotonic and the steady-state deformation increases as the viscosity ratio is increased. In this regime, a cavity forms at the droplet trailing during early times. The formation of a trailing edge cavity is considerably decreased and vanishes for large droplet viscosity. For large drop viscosity, the system is considerably damped and the deformation histories are monotonic for the period of time investigated in this study.