Fluid dynamics and jamming in a dilatant fluid

TL;DR

This paper introduces a phenomenological model for dilatant fluids that couples fluid dynamics with a state variable, revealing oscillatory instabilities and unique responses to impacts due to shear thickening and jamming.

Contribution

The study develops a novel coupled fluid dynamics and state variable model for dilatant fluids, capturing shear thickening, jamming, and dynamic instabilities.

Findings

Oscillatory instability in shear flow due to coupling.

Divergence of viscosity at jamming point.

Unique fluid response to external impacts.

Abstract

We present a phenomenological fluid dynamics model for a dilatant fluid, i.e. a severe shear thickening fluid, by introducing a state variable. The Navier-Stokes equation is coupled with the state variable field, which evolves in response to the local shear stress as the fluid is sheared. The viscosity is assumed to depend upon the state variable and to diverge at a certain value due to jamming. We demonstrate that the coupling of the fluid dynamics with the shear thickening leads to an oscillatory instability in the shear flow. The model also shows a peculiar response of the fluid to a strong external impact.