Pseudoplasticity and Dilatancy in Shallow Channel Flows

Abstract A novel formulation is presented applicable to flows of inelastic, shear-thinning and shear-thickening, fluids between parallel plates. The solution is documented by comprehensive contour maps allowing flow descriptions to be reconstructed for the Ostwald-deWaele and the Cross-/Carreau fluid model fluids within an exhaustive range of rheological and flow parameters, 0 < n ≤ 2 and 0 ≤ q ≤ 2. The description of pseudoplastic behavior is extended to values approaching zero, numerical stability permitting (0.01 ≤ n < 1). The paper highlights the dilatant behavior, 1 ≤ n ≤ 2, reported previously to arise in certain heterogeneous systems, and shown to affect significantly other types of non-Newtonian flows. It is suggested that in thermally and compositionally developing flows, typical of reactive processing, where dilatancy may arise, the present formulation can facilitate solutions to the coupled rheological and heat/mass transfer problems encountered. The newly generated data on dilatant liquids suggest a dramatic increase in energy dissipation with the increasing degree of dilatancy.