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

Abstract

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 [Formula: see text], mobility parameter [Formula: see text], and solvent viscosity ratio [Formula: see text] on steady-state droplet deformation. We find for [Formula: see text] that as [Formula: see text] increases, the steady-state droplet deformation decreases until eventually approaching the one in the pure Newtonian case with the viscosity ratio of [Formula: see text], which is attributed to the strong shear-thinning effect at high [Formula: see text]. While for lower [Formula: see text], the droplet deformation exhibits a complex nonmonotonic variation with [Formula: see text]. Under constant [Formula: see text], the droplet deformation decreases monotonically with [Formula: see text] but increases with [Formula: see text]. Force analysis shows that [Formula: see text] modifies the droplet deformation by altering the normal viscous and elastic stresses at both poles and equators of the droplet, while [Formula: see text] mainly alters the normal stresses at the poles. Finally, we explore the roles of [Formula: see text] and [Formula: see text] on the critical capillary number [Formula: see text] of the droplet breakup. By establishing both [Formula: see text] and [Formula: see text] phase diagrams, we find that the critical capillary number increases with [Formula: see text] or [Formula: see text] except that a plateau critical capillary number is observed in [Formula: see text] phase diagram.