Dynamics of spheroids in pressure driven flows of shear thinning fluids

Abstract

Particles in inertialess flows of shear thinning fluids are a model representation for several systems in biology, ecology, and micro-fluidics.In this paper, we analyze the motion of a spheroid in a pressure driven flow of a shear thinning fluid.The shear thinning rheology is characterized by the Carreau model.We use a combination of perturbative techniques and the reciprocal theorem to delineate the kinematics of prolate and oblate spheroids.There are two perturbative strategies adopted, one near the zero shear Newtonian plateau and the other near the infinite shear Newtonian plateau.In both limits, we find that a reduction in effective viscosity decreases the spheroid's rotational time period in pressure driven flows.The extent to which shear thinning alters the kinematics is a function of the particle shape.For a prolate particle, the effect of shear thinning is most prominent when the spheroid projector is aligned in the direction of the velocity gradient, while for an oblate particle the effect is most prominent when the projector is aligned along the flow direction.Lastly, we compare the tumbling behavior of spheroids in pressure driven flow to those in simple shear flow.While the time period decreases monotonically with Carreau number for pressure driven flows, the trend is non monotonic for shear flows where time period first increases at low Carreau number and then decreases at high Carreau numbers.Shear thinning does not resolve the degeneracy of Jefferey's orbits.