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

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 Delta x(0) and Delta y(0). 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 mu(13) and mu(23), the interfacial tension ratio sigma(12) of the inner to outer interfaces, the ratio of the radii of the inner to outer droplets R-12 and the initial distance between them (in terms of Delta x(0) and Delta y(0)). 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 mu(23) in the range of 0.1-10.0 or varying R-12 in the range of 0.2-0.8. A transition from a passing-over mode to a reversing one is available when increasing Delta(x)0 or decreasing Delta y(0). Three modes of collision all occur when mu(13) is varied in the range of 0.1-10.0. However, the variation of sigma(12) does not induce any transition between different modes. Several phase diagrams in terms of Re versus Ca, or Delta x(0) versus Delta y(0) are also proposed to show the transitions between these modes.