Abstract
We study non-local effects on inhomogeneous flows of soft athermal particles near the jamming transition. We employ molecular dynamics simulations to demonstrate Kolmogorov flows, where a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the rheology of soft athermal particles is strongly wave number-dependent and particle migration is not sufficient to explain the resulting stress profiles within conventional local constitutive relations. We show that stress profiles can be described by non-local constitutive relations that account for gradients to fourth order.
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