A note on the flows of inhomogeneous fluids with shear-dependent viscosities

Inhomogenous fluids have not been studied with the intensity that they deserve. In fact, many studies that are supposedly concerned with the response of inhomogeneous fluids are not directed at inhomogeneous fluids, and this stems from not recognizing the fact that the properties of a fluid varying in its current configuration does not mean that the fluid is inhomogeneous. Here, we show that mild variations in the properties of the fluid which might warrant it being approximated as a homogeneous fluid with average properties could lead to significant errors in the computation of both global and local quantities, associated with the flow.