Real Shear Thickening Fluid (STF) Flow in Converging-Diverging Channels: Analytical and Lattice Boltzmann Study

Experimentally, a Shear Thickening Fluid (STF) combines parts-wise Newtonian, shear thinning, and shear thickening regions in the viscosity-shear rate plot. The flow characteristics of the STF fluids through the complex geometries of narrow space are essential in developing impact-resistant systems. Here, we have used the mesoscopic numerical simulation technique, the Lattice Boltzmann method (LBM), in a D2Q9 framework to study the flow characteristics of a real shear thickening fluid through converging-diverging channels. In addition, we have developed a theory based on the lubrication assumptions in the shallow cross–section of the channels. We compare the numerical results with the theoretical results for the flow of Newtonian and non-Newtonian fluids through converging-diverging conical channels followed by uniform height channels. Numerical results indicate sizable differences in the pressure distribution in the converging-diverging regions. The difference in the theoretical calculations and numerical predictions depends on the viscosity and angle of the converging and diverging sections. Further, we compare the effect of the flow of a real STF through the above channels. We find that the pressure drop is higher near the throat region than the uniform part of the channel, and consequently, shear rates are high. Due to that thickening, fluid flow happens in the throat region, which gets further displaced towards the outlet of the channel. The theory also gives approximately similar predictions as found by the LBM study.