Testing constitutive relations by running and walking on cornstarch and water suspensions

TL;DR

This paper demonstrates that a previously proposed constitutive relation for cornstarch-water suspensions can accurately predict human walking and running behavior on the surface, extending understanding beyond traditional rheology models.

Contribution

The study applies an impact rheology-based constitutive model to predict human locomotion on cornstarch-water suspensions, showing its broader applicability beyond steady-state conditions.

Findings

Model accurately predicts foot trajectory and penetration depth.

Impact rheology model outperforms added mass explanation for certain conditions.

Constitutive relation applicable to various forcing conditions and geometries.

Abstract

The ability of a person to run on the surface of a suspension of cornstarch and water has fascinated scientists and the public alike. However, the constitutive relation obtained from traditional steady-state rheology of cornstarch and water suspensions has failed to explain this behavior. In a previous paper, we presented an averaged constitutive relation for impact rheology consisting of an effective compressive modulus of a system-spanning dynamically jammed structure (arXiv:1407:0719). Here, 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. The ability of the constitutive relation to predict the material behavior in a case with different forcing conditions and flow geometry than it was obtained from suggests that the constitutive relation could be applied more generally. We also present a detailed calculation of the added mass effect to show that while it may be able to explain some cases of people running or walking on the surface of cornstarch and water for pool depths $H >1.2$ m and foot impact velocities $V_I> 1.7$ m/s, it cannot explain observations of people walking or running on the surface of cornstarch and water for smaller $H$ or $V_I$.