Contact counting predicts viscosity in shear-thickening suspensions

Predicting the viscosity of shear thickening fluids remains a fundamental challenge nowadays, because, unlike Newtonian fluids, they exhibit nonlinear and sometimes discontinuous increases under shear. Traditional models of shear thickening suspensions often rely on macroscopic variables like shear rate or shear stress in combination with packing fraction, indicating a critical gap in connecting microscopic environment evolution to macroscopic flow properties. In this work, we address this gap by introducing a simple model based on the contact counting method. By a linear combination of average frictional contact number and the non-frictional one as a microscopic descriptor, we show that our model successfully collapses viscosity curves for shear thickening suspensions in both 2D and 3D over a wide range of interparticle friction coefficients, and we find intriguing connections with rigid cluster analysis, which only works in 2D so far. These results suggest that the mean-field contact statistics play a deterministic role in suspension rheology, and offer a simplified new framework for understanding and modeling the complex behavior of shear thickening fluids.