Numerical study of rheological behaviors of a compound droplet in a conical nozzle

The dynamics of compound droplets is more and more attractive because of their applications in a wide range of industrial and natural processes. This study aims to improve the understanding of dynamical rheological behaviors of a compound droplet moving in a nozzle with a conical shape in the downstream region via front tracking-based simulations. The numerical results show that the compound droplet experiences three stages of deformation: the entrance stage (in front of the conical region), the transit stage (within the conical region), and the exit stage (in the exit of the nozzle). The droplet receives the maximum deformation in the axial direction during the transit stage, and the radially maximum deformation occurs during the exit stage. Because of the acceleration induced by the conical region, the inner droplet of the compound droplet can break up into smaller droplets during the exit stage. To reveal the transition between the finite deformation and the breakup, many parameters including the Capillary number Ca (varied in the range of 0.0125-1.6), the droplet size relative to the nozzle size R-1/R-0 (varied in the range of 0.2-0.9), the droplet radius ratio R-21 (varied in the range of 0.3-0.8), the viscosity ratios mu(21) and mu(31) (varied in the range of 0.05-3.2), the interfacial tension ratio sigma(21) (varied in the range of 0.125-8.0), the conical angle alpha (varied in the range of 4 degrees-34 degrees) and the initial location of the inner droplet (i.e. the droplet eccentricity) are considered. From the finite deformation mode, the transition to the breakup mode of the inner droplet occurs when increasing any of Ca, R-1/R-0, R-21 and alpha, or decreasing any of mu(21) and sigma(21). The breakup mode is also enhanced when the inner droplet is initially located closer to the leading side of the outer droplet. However, varying mu(31) induces no transition between these modes. The regime diagrams of these modes, based on these parameters, are also proposed.