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

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 $V_I$.

arXiv commentThis is a direct follow up to arXiv:1407:0719

References in corpus (10)

• Shear thickening in concentrated suspensions: phenomenology, mechanisms, and relations to jamming
• Discontinuous shear thickening without inertia in dense non-Brownian suspensions
• Generality of shear thickening in suspensions
• A dynamic jamming point for shear thickening suspensions
• High-speed ultrasound imaging in dense suspensions reveals impact-activated solidification due to dynamic shear jamming
• Quasi-2D dynamic jamming in cornstarch suspensions: visualization and force measurements
• Dramatic effect of fluid chemistry on cornstarch suspensions: linking particle interactions to macroscopic rheology
• System-spanning dynamically jammed region in response to impact of cornstarch and water suspensions
• Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions
• Giant deviation of a relaxation time from generalized Newtonian theory in Discontinuous Shear Thickening suspensions

Cited by in corpus (9)

• Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions
• Power law scaling of early-stage forces during granular impact
• Intermittent dilation and its coupling to stress in discontinuous shear thickening suspensions
• Impact-induced hardening in dense frictional suspensions
• Bouncing of a projectile impacting a dense potato-starch suspension layer
• Viscous-like forces control the impact response of shear-thickening dense suspensions
• An effective packing fraction for better resolution near the critical point of shear thickening suspensions
• Characterizing the surface texture of a dense suspension undergoing dynamic jamming
• Viscoelastic response of impact process on dense suspensions