Effect of fluid elasticity and shear-thinning viscosity on the chaotic mixi
ng between two alternately rotating cylinders has been studied. The h-p fin
ite element method is used to obtain high accurate solutions of the steady
flow. The unsteady, periodic flow is simulated using the piecewise-steady a
pproximation. Characteristics of the chaotic mixing are analyzed by examini
ng the asymptotic coverage of a passive tracer and the lineal stretching of
the fluid elements in the annulus. For the viscoelastic fluids modeled by
the upper-convected Maxwell constitutive equation (UCM), our computation pr
edicts little effect of the fluid elasticity on the mixing patterns. On the
other hand, the shear-thinning viscosity, modeled by the Carreau equation,
has a large impact on the advection of a passive tracer and the distributi
on of lineal stretching. We find that the zones of the lowest stretching ma
tch remarkably well with the regular zones in the tracer-coverage plotting.
Our study reveals the vital importance of reducing the discretization erro
rs of the velocity field in the numerical simulation of chaotic flows.