Planar channel flow of a discontinuous shear-thickening model fluid: Theory and simulation

In this work, an analytical solution for the pressure-driven flow of a discontinuous shear-thickening (DST) fluid in a planar channel is presented. In order to model the fluid rheology, a regularized inverse-biviscous model is adopted. This involves a region of finite thickness to model the sharp jump in viscosity, and it is consistent with momentum conservation. In the limit of vanishing thickness, the truly DST behavior is obtained. Analytical results are validated by numerical simulations under steady and start-up flow using the smoothed particle hydrodynamics method. Flow results are investigated and discussed for different values of the model parameters.