The rheology of dense suspensions lacks a universal description due to the involvement of a wide variety of parameters, ranging from the physical properties of the solid particles to the nature of the external deformation or applied stress. While the former controls microscopic interactions, spatial variations in the latter induce heterogeneity in the flow, making it difficult to find suitable constitutive laws to describe the rheology in a unified way. For homogeneous driving with a spatially uniform strain rate, the rheology of non-Brownian dense suspensions is well described by the conventional μ(J) rheology. However, this rheology fails in the inhomogeneous case due to nonlocal effects, where the flow in one region is influenced by the flow in another. In this talk, I will present a new dimensionless number, the suspension temperature Θs, which contains information on local particle velocity fluctuations. I will show how, μ(J, Θs) provides a unified description for both homogeneous and inhomogeneous flows. By employing scaling theory, we identify a set of constitutive laws for dense suspensions of frictional spherical particles and frictionless rod-shaped particles. Combining these scaling relations with the momentum balance equation for our model system, we predict the spatial variation of the relevant dimensionless numbers, the volume fraction ϕ, the viscous number J, the macroscopic friction coefficient μ and suspension temperature Θs solely from the nature of the imposed external driving. I will also show how, with the help of local inhomogeneous driving in the form of self-propelled particles, one can tune the viscosity and jamming point in dense non-Brownian suspensions.

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