Reversal of flow of a non-Newtonian fluid in an expanding channel

The flow of an incompressible power-law fluid through convergent-divergent channels is considered where the choice of the viscosity is such that the stress tensor is not degenerate in the sense that the zero shear rate viscosity is neither zero nor infinity for any finite value of the power-law exponent in contrast to the earlier study by Mansutti and Rajagopal (1991) wherein the viscosity could be zero or infinity for certain values of the power-law exponent. We observe the appearance of boundary layers for the non-Newtonian fluid, even in the case of divergent flow. Sharp and pronounced boundary layers develop adjacent to the boundaries, even at zero Reynolds number. Furthermore, for values of the angle beyond a critical value, we detect regions of flow reversal; i.e. different flow regimes are observed wherein there is inflow and outflow. We are also able to assess the consequences of introducing a traction boundary condition at the boundaries of the channel on the behaviour of the fluid. In this case we find the possibility of asymmetric solutions. We also find a new solution in the case of the Navier-Stokes fluid, albeit numerical, by setting the power-law exponent to zero.