Droplet deformation and breakup in shear-thinning viscoelastic fluid under simple shear flow

A three-dimensional lattice Boltzmann method, which couples the color-gradient model for two-phase fluid dynamics with a lattice diffusion-advection scheme for the elastic stress tensor, is developed to study the deformation and breakup of a Newtonian droplet in the Giesekus fluid matrix under simple shear flow. This method is first validated by the simulation of the single-phase Giesekus fluid in a steady shear flow and the droplet deformation in two different viscoelastic fluid systems. It is then used to investigate the effect of Deborah number De, mobility parameter α, and solvent viscosity ratio β on steady-state droplet deformation. We find for 0.025<α<0.5 that as De increases, the steady-state droplet deformation decreases until eventually approaching the one in the pure Newtonian case with the viscosity ratio of 1/β, which is attributed to the strong shear-thinning effect at high De. While for lower α, the droplet deformation exhibits a complex nonmonotonic variation with De. Under constant De, the droplet deformation decreases monotonically with α but increases with β. Force analysis shows that De modifies the droplet deformation by altering the normal viscous and elastic stresses at both poles and equators of the droplet, while α mainly alters the normal stresses at the poles. Finally, we explore the roles of De and α on the critical capillary number Cacr of the droplet breakup. By establishing both Ca–De and Ca–α phase diagrams, we find that the critical capillary number increases with De or α except that a plateau critical capillary number is observed in Ca–De phase diagram.