A general rheological framework for dense suspensions under shear and extensional flows: From frictionless to frictional

We investigate the rheology of dense suspensions under simple shear and extensional flows using lubrication dynamics-discrete element method simulations. For all deformation modes considered, the relative viscosity is described reasonably well by the Krieger–Dougherty form, suggesting that the divergence is not strongly dependent on flow type, whereas the fitted parameters, namely, the jamming point and exponent, are sensitive to the interparticle friction. To relate shear and extension within a common rate–pressure scaling, we consider a generalized viscous number and examine the effective friction coefficient across deformation modes using a flow-type-dependent normalization. Building on prior stress-decomposition approaches, we employ a minimal modification to the contact contribution by introducing an exponent which improves agreement with simulations for weakly frictional systems. As the interparticle friction increases, this exponent approaches unity, recovering the original formulation. In addition, using the modified hydrodynamic scaling in the low viscous number regime gives an improved prediction relative to the classical square-root dependence. Overall, the proposed framework provides friction-aware constitutive relations that are compatible with both shear and extensional deformations over the full ranges of interparticle friction and viscous number explored here.