Dynamics of spheroids in pressure driven flows of shear thinning fluids.

Particles in inertialess flows of shear thinning fluids are a model representation of several systems in biology, ecology, and microfluidics. In this research , we delineate the orientational kinematics of spheroids in pressure driven flows of shear thinning fluids. The shear thinning rheology is rendered by the Carreau model. We employ a combination of perturbative techniques and the reciprocal theorem to analyse the motion of both 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 of the Carreau model. In both limits, we find that a reduction in effective viscosity decreases the spheroid’s rotational time period in pressure driven flows, which is contrary to the observations reported in earlier publications for linear 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. Shear thinning does not resolve the degeneracy of Jefferey's orbits.

This work was supported by the American Chemical Society Petroleum Research Fund under grant ACS PRF 61266-DNI9.