Numerical simulation of the deformation and breakup of a two-core compound droplet in an axisymmetric T-junction channel

Abstract

The rheological behaviors of a compound droplet in a confined geometry are of importance in many industrial and natural processes. However, a detailed numerical simulation of the finite deformation and its transition to the breakup of the multi-core compound droplet in an axisymmetric T-junction channel is still lacking. The present study is to fill this gap through the numerical simulations of a two-core compound droplet that deforms and breaks up in this channel configuration. The numerical results are obtained by the axisymmetric front-tracking method. Our new finding is that the compound droplet in the channel can experience the finite deformation or the breakup depending on the flow condition or the configuration of the channel. In the finite deformation mode (i.e. non-breakup mode), the droplet rapidly reaches the maximum deformation before approaching the perpendicular rigid wall. The most deformation occurs with the outer droplet, and the inner droplet closer to the wall is less deformed than the other inner core droplet. In the breakup mode, three breakup patterns are recognized: (i) breakup type I occurring when breaking up only the outer droplet; (ii) breakup type 2 occurring when breaking up only the inner droplets; (iii) breakup type 3 occurring when breaking up both inner and outer droplets. The transition from the non-breakup mode to the breakup mode is available when increasing the Reynolds number Re (from 0.16 to 40.0), the capillary number Ca (from 0.04 to 4.0), the size Ro of the outer droplet and the middle-to-outer fluid viscosity ratio μ21, or decreasing the size Ri of the inner droplets, the radial size C2 of the channel (normalized by the channel axial size C1) and the interfacial tension ratio of the inner to the outer droplets. The transition diagrams based on some of these parameters are also proposed to provide a more complete picture of the two-core compound droplet behaving in the axisymmetric T-junction channel..