Geometry-dependent constitutive law for granular slow frictional drag

TL;DR

This study experimentally investigates how the geometry, especially the ratio of rod to grain diameters, influences the granular frictional law during very slow withdrawal, challenging the notion of a universal law based solely on the inertial number.

Contribution

It reveals that system geometry, particularly the rod-to-grain diameter ratio, is crucial for describing granular friction in slow regimes, contrary to previous assumptions of universality.

Findings

Granular friction depends on system geometry in slow withdrawal.

The ratio of rod to grain diameter is an essential parameter.

The physical basis involves grains-contact-number dependence.

Abstract

Frictional constitutive law for very slow vertical withdrawing of a thin rod from a granular bed is experimentally studied. Using a very precise creep meter, geometry-dependent granular frictional constitutive law is particularly examined. In some previous works, a dimensionless number $I=\dot{\gamma}D_g/\sqrt{p/\rho_g}$ has been used to characterize granular frictional constitutive laws, where $\dot{\gamma}$, $D_g$, $p$, and $\rho_g$ are the shear strain rate, grain diameter, confining pressure, and bulk density of granular bed, respectively. It has been considered that granular frictional constitutive law expressed by $I$ is universal (almost geometry-independent) in dense flow regime. In this study, however, we find that the geometry of the system is much more crucial to characterize granular friction in a very slow withdrawing regime. Specifically, the ratio between rod and grain diameters must be an essential parameter to describe the granular frictional constitutive law. Physical meaning of the geometry-dependent constitutive law is discussed on the basis of grains-contact-number dependence of granular behavior.