Flow of a Colloidal Solution in an Orthogonal Rheometer

The flow of a colloidal solution between two parallel disks rotating with the same angular velocity about two non-coincident axes was studied. The problem has been approached from two perspectives, the first wherein the stress is expressed in terms of a power-law of kinematical quantities, and the second wherein we consider a non-standard model where the symmetric part of the velocity gradient is given by a power-law of the stress. For a range of power-law exponents, the class of models are non-invertible. By varying the material and geometric parameters, changes in the flow behavior at different Reynolds numbers were analyzed. We find that pronounced boundary layers develop even at low Reynolds numbers depending on the power-law exponents. The new class of stress power-law fluids and fluids that exhibit limiting stress also show the ability to develop boundary layers.