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 C a cr 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. [ABSTRACT FROM AUTHOR]