"Drag law for an intruder in granular sediments" by Andreea Panaitescu, Xavier Clotet et al.
 

Physics

Drag law for an intruder in granular sediments

Document Type

Article

Abstract

We investigate the drag experienced by a spherical intruder moving through a medium consisting of granular hydrogels immersed in water as a function of its depth, size, and speed. The medium is observed to display a yield stress with a finite force required to move the intruder in the quasistatic regime at low speeds before rapidly increasing at high speeds. In order to understand the relevant time scales that determine drag, we estimate the inertial number I given by the ratio of the time scales required to rearrange grains due to the overburden pressure and imposed shear and the viscous number J given by the ratio of the time scales required to sediment grains in the interstitial fluid and imposed shear. We find that the effective friction μe encountered by the intruder can be parametrized by I=ρg/Ppvi, where ρg is the density of the granular hydrogels, vi is the intruder speed, and Pp is the overburden pressure due to the weight of the medium, over a wide range of I where the Stokes number St=I2/J1. We then show that μe can be described by the function μe(I)=μ0+αIβ, where μ0, α, and β are constants that depend on the medium. This formula can be used to predict the drag experienced by an intruder of a different size at a different depth in the same medium as a function of its speed.

This paper was published online on 2 March 2017 with typographical errors on page 5 of the PDF version. On page 5, the text in the third line above Eq. (3) should read as " j=n s γ/P where n s is the viscosity of the liquid. As in the⋯" Equation (4) should read as (Formula Presented). The paper has been corrected as of 6 March 2019. The text and equation are incorrect in the printed version of the journal.

Publication Title

Physical Review E

Publication Date

3-2-2017

Volume

95

Issue

3

ISSN

2470-0045

DOI

10.1103/PhysRevE.95.032901

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