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

Abstract

SUMMARYThe 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.

Boundary integral study of nanoparticle flow behaviour in the proximity of a solid wall

“…By using the Hamilton-Crosser model (which has shown good behaviour for Al 2 O 3 /water nanofluids [9]), this increase in concentration roughly translates to a 0.6% higher effective thermal conductivity in the neighbourhood of the wall when compared with the values expected from the same model for a homogeneous concentration of 1.05%. One possible explanation for the increase in concentration in this case is that the shear in the fluid causes the particles to cross over each other continually, creating self-difussion patterns [26]. Given that the top particles are moving faster, the downward motion of the lower particles accumulates over the multiple passes of particles located above them, pushing them down until the electrical repulsion of the wall avoids any further downward motion, and thus accumulating at a small distance away from the wall as seen in the results.…”