Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions

TL;DR

This paper experimentally investigates the impact response of cornstarch-water suspensions, revealing a dynamically jammed region that supports large stresses and proposing a constitutive relation to model impact rheology based on impact velocity, fluid height, and concentration.

Contribution

It introduces a new constitutive relation for impact rheology in cornstarch suspensions, linking force response to impact dynamics and the propagation of a dynamically jammed region.

Findings

Suspensions support MPa-level stresses with delay after impact

Stress correlates with the propagation of a dynamically jammed region

The constitutive model predicts impact behavior based on impact velocity and suspension properties

Abstract

We experimentally characterize the impact response of concentrated suspensions consisting of cornstarch and water. We observe that the suspensions support a large normal stress -- on the order of MPa -- with a delay after the impactor hits the suspension surface. We show that neither the delay nor the magnitude of the stress can yet be explained by either standard rheological models of shear thickening in terms of steady-state viscosities, or impact models based on added mass or other inertial effects. The stress increase occurs when a dynamically jammed region of the suspension in front of the impactor propagates to the opposite boundary of the container, which can support large stresses when it spans between solid boundaries. We present a constitutive relation for impact rheology to relate the force on the impactor to its displacement. This can be described in terms of an effective modulus, but only after the delay required for the dynamically jammed region to span between solid boundaries. Both the modulus and the delay are reported as a function of impact velocity, fluid height, and weight fraction. We report in a companion paper to this one on the structure of the dynamically jammed region when it spans between the impactor and the opposite boundary (arXiv:1709.01133). In a direct follow-up, we show that this constitutive model can be used to quantitatively predict, for example, the trajectory and penetration depth of the foot of a person walking or running on cornstarch and water.