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

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.

v3: added more stress data. We removed reflected light intensity tracking data which was irreproducible, and retract our claim of a 2nd front. v4: Visualization data was moved to a separate paper(arXiv:1709.01133). v5: some content was moved to a separate arxiv submission: "Testing constitutive relations by running and walking on cornstarch and water suspensions"

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Cited by in corpus (14)

• A general constitutive model for dense, fine particle suspensions validated in many geometries
• 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
• Stress controlled rheology of dense suspensions using transient flows
• Testing constitutive relations by running and walking on cornstarch and water suspensions
• Simulation of dense non-Brownian suspensions with the lattice Boltzmann method: Shear jammed and fragile states
• Intermittent dilation and its coupling to stress in discontinuous shear thickening suspensions
• Lasting effects of discontinuous shear thickening in cornstarch suspensions upon flow cessation
• 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
• Unsteady flow, clusters and bands in a model shear-thickening fluid
• Early-stage impact dynamics in dense suspensions of millimeter-sized particles
• Viscoelastic response of impact process on dense suspensions