The dramatic viscosity increase observed in dense suspensions under shear poses a major challenge in our understanding of how microscopic contact mechanics translate into macroscopic flow resistance. Here, we introduce a constraint-counting model that incorporates friction and dimensionality naturally without additional assumptions and allows for collapsing of rheological data onto a universal master curve. In this model, we borrow ideas from dry granular jamming physics and classify contacts as either locked or non-locked to define a single state variable, the constraint ratio, which measures the average strength of mechanical constraint per particle. By identifying the constraint ratio as the key control parameter, our framework provides a unifying route toward predictive modeling and rational design of shear-thickening materials.
@article{arxiv.2603.13611,
title = {Constraint ratio controls viscosity in shear thickening suspensions},
author = {Qinghao Mao and Michael van der Naald and Abhinendra Singh and Heinrich M. Jaeger},
journal= {arXiv preprint arXiv:2603.13611},
year = {2026}
}