Dense suspensions under inhomogeneous flow

Predicting the rheology of dense suspensions under 

inhomogeneous

flow is crucial in many industrial and geophysical applications,

yet the conventional `$mu(J)$' framework is limited to homogeneous conditions

in which the shear rate and solids fraction are spatially invariant.

To address this shortcoming,

we use particle-based simulations of frictionless dense suspensions to derive new constitutive laws that unify the rheological response under both homogeneous and inhomogeneous conditions.

By defining a new dimensionless number associated with particle velocity fluctuations

and combining it with the viscous number, the macroscopic friction and the solids fraction,

we obtain scaling relations that collapse data from homogeneous and inhomogeneous simulations.

The relations allow prediction of the steady state velocity, stress and volume fraction fields using only knowledge of the applied driving force.