Parametric study of the collision modes of compound droplets in simple shear flow

Abstract

Compound droplet collision has been found in various industrial and academic applications. Such colliding phenomena of two droplets in simple shear flow are numerically resolved by a front-tracking technique. Initially, each compound droplet, assumed cylindrical, contains one concentric inner droplet. They are separated at the lateral and vertical intervals denoted by Δx0 and Δy0. Because of the shear flow, the compound droplets interact with each other and exhibit three collision modes: passing-over, merging (i.e. coalescence) and reversing. These modes and their transition are affected by many parameters including the Reynolds Re and Capillary Ca numbers (based on the properties of the outer fluid), the viscosity ratios μ13 and μ23, the interfacial tension ratio σ12 of the inner to outer interfaces, the ratio of the radii of the inner to outer droplets R12 and the initial distance between them (in terms of Δx0 and Δy0). It is found that from a merging mode, decreasing Re from 2.51 to a value less than or equal to 1.0 induces a transition to a reversing mode, whereas, increasing Ca from 0.005 to a value greater than or equal to 0.04 leads to a transition to a passing-over mode. A transition from the merging to passing-over modes also appears when varying μ23 in the range of 0.1–10.0 or varying R12 in the range of 0.2–0.8. A transition from a passing-over mode to a reversing one is available when increasing Δx0 or decreasing Δy0. Three modes of collision all occur when μ13 is varied in the range of 0.1–10.0. However, the variation of σ12 does not induce any transition between different modes. Several phase diagrams in terms of Re versus Ca, or Δx0 versus Δy0 are also proposed to show the transitions between these modes.