Dynamics of a compound droplet in shear flow

The deformation dynamics of a compound liquid droplet in shear flow is numerically investigated in two- and three-dimensional space. The computational model is based on the immersed boundary method. This accurately and efficiently tracks the interfaces of immiscible multi-phase fluids. We extend a recently developed volume-conserving immersed boundary method for two-phase fluid flow to ternary compound droplet flows. For long time simulations, we also apply a surface remeshing algorithm. Chorin's projection method is employed, and the resulting system of discrete equations is solved by a multigrid technique. We study the effects of radius, interfacial tension ratios, and inner droplet location on the deformation of a compound droplet, and compute the inclination angles of inner and outer droplets. Simulation results indicate that the angle of the inner droplet is always greater than or equal to that of the outer one. The effect of wall confinement on compound droplet deformation is compared with that of a simple droplet. The result shows that the more confined the wall is, the more different the compound and simple droplets' behavior.