Mobility of shear thinning viscous drops in a shear Newtonian carrying flow using DR-BEM

The study of drop behaviour has attracted great interest in the last years due to its importance in different industrial and biological systems. Most available works focus on Newtonian drops, excluding some very important applications such as polymer mixing. Simulations of non-Newtonian drops have had only limited study, mostly in time-dependent rheologies or simple flow cases. This work presents a boundary-only formulation based on the dual reciprocity method to model the motion and deformation of non-Newtonian shear thinning drops due to a shear Newtonian unbounded carrying flow. Pair-wise interactions at low Reynolds number between two viscous shear thinning non-Newtonian drops are numerically simulated in order to obtain mobility magnitudes under linear shear flow of different strengths. Separation of the drops in the direction perpendicular to the imposed flow field at high capillary number (small surface tension) and low viscosity ratio was favoured by shear thinning, increasing in magnitude as the capillary number increases and the viscous ratio decreases. Higher values of this separation occur at higher values of the viscosity ratio when compared with the case of Newtonian drops. In order to obtain a good physical description of the non-Newtonian drop behaviour, while maintaining good computational performance, the non-Newtonian viscosity is made to obey the truncated power law model.