Focused Force Transmission through an Aqueous Suspension of Granules

Bin Liu, Michael Shelley, and Jun Zhang

Phys. Rev. Lett. 105, 188301 – Published 25 October 2010

Abstract

We investigate force transmission through a layer of shear-thickening fluid, here a concentrated aqueous cornstarch suspension. When a solid body is pushed through this complex fluid and approaches its containing wall, a hardened volume of the suspension is observed that adds to the leading side of the body. This volume leads to an imprint on the wall which is made of molding clay. By studying the geometry of the hardened volume, inferred by the imprint shapes, we find that its geometry is determined by the size and speed of the body. By characterizing the response of the clay to deformation we show that the force transmitted through the suspension to the wall is localized. We also study other aspects of this dynamical hardening of the suspension, such as the effect of the substrate and body shape, and its relaxation as the imposed straining is stopped.

Received 6 September 2009

DOI:https://doi.org/10.1103/PhysRevLett.105.188301

Authors & Affiliations

Bin Liu¹, Michael Shelley¹, and Jun Zhang^1,2,*

¹Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA
²Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA

^*jun@cims.nyu.edu

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Vol. 105, Iss. 18 — 29 October 2010

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Images

Figure 1
A sphere, moving through a cornstarch suspension, creates a focused depression on flat molding clay. (a) The depression created by a sphere of radius $R = 12.7 mm$ driven downward by a linear motor. The sphere stops just short of the clay surface. (b) The depression profile is digitized and shown as its elevation $z$ against radius $r$ . (c) Depression profiles created at different speeds $V$ suggest hemispherical shapes. The slower the speed, the smaller and sharper the depression. The dashed line shows the corresponding profile of the sphere that caused all depressions.Reuse & Permissions
Figure 2
The depressions in the clay resulting from a sphere ( $R = 12.7 mm$ ) moving at various speeds $V$ and stopping at heights $H$ . (a) The dependence of depression depth $h$ on $H$ . (b) The dependence of the normalized depression curvature $κ R$ as a function of $H$ .Reuse & Permissions
Figure 3
The dimensionless curvature $κ R$ (a) and the dimensionless depth $h / R$ (b) of the depression, which describe the shape of the hardened volume, plotted as a function of the characteristic strain rate $\dot{γ} = V / R$ . The insets show two groups of depression profiles, rescaled by the radius of sphere $R$ , at two strain rates $\dot{γ} = V / R = 0.5$ and $3.1 s^{- 1}$ , respectively. These profiles (five solid curves in each group) collapse for fixed $\dot{γ}$ . For comparison, the rescaled sphere with radius 1 is also shown.Reuse & Permissions
Figure 4
(a) Calibrating the clay as force recorder. In the absence of an intervening suspension, the clay exerts a speed-dependent resistive force upon a hemispherical intruder that scales with near linearity on the deformation area. The slope gives the deformation stress $S (V)$ plotted in (a) as a function of speed $V$ . (b) For a sphere moving with speed $V$ through the cornstarch suspension, the transmitted force $F_{T} = S (V) A$ , where $A$ is the resulting depression area, plotted against the resistive force $F_{R}$ .Reuse & Permissions
Figure 5
Recovery of a depression on an elastic PDMS substrate. (a) The height of the PDMS surface (open circles) evolves after the sphere stops at $t = 0$ at the original height of the surface. The dashed line shows the trajectory of the sphere. Panels (b)–(e) show side views of the PDMS surface after the sphere stops moving. The position of the sphere is superimposed as the dashed curves. A depression made in clay, under the same conditions, is shown on the left side of (b), and has a profile similar to the PDMS depression.Reuse & Permissions
Figure 6
A circular cylinder of diameter 12.7 mm approaches and stops near the surface of a clay substrate. The curves show the profiles of the resulting depressions left in the clay.Reuse & Permissions

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