Friction of a slider on a granular layer: Nonmonotonic thickness dependence and effect of boundary conditions

We investigate the effective friction encountered by a mass sliding on a granular layer as a function of bed thickness and boundary roughness conditions. The observed friction has minima for a small number of layers before it increases and saturates to a value that depends on the roughness of the sliding surface. We use an index-matched interstitial liquid to probe the internal motion of the grains with fluorescence imaging in a regime where the liquid has no significant effect on the measured friction. The shear profiles obtained as a function of depth show a decrease in slip near the sliding surface as the layer thickness is increased. We propose that the friction depends on the degree of grain confinement relative to the sliding surfaces.

Figure 1

(Color online) (a) Schematic of experimental apparatus. (b) Three kinds of boundary surface conditions: (I) rough on rough, (II) rough on smooth, and (III) smooth on rough. Rough surfaces are fabricated by gluing a layer of glass beads to the surfaces. (c) Two-point cross-correlation function $g\left(r\right)$ as a function of distance of separation $r$ of two beads on the surface. Peaks at multiples of bead diameters are observed indicating the absence of hexagonal packing.

Figure 2

(a) Effective coefficient of sliding friction $\left({\mu }_{\mathrm{eff}}\right)$ as a function of granular layer of thickness $h$ normalized by grain diameter $d$. All surfaces are rough. (b) ${\mu }_{\mathrm{eff}}$ for the case of the dry system and three boundary conditions shown in Fig. 1b. The measured fluctuations in friction are also shown $(v_p=0.3d∕\mathrm{s})$.

Figure 3

Images of vertical slice of the granular bed away from the side boundaries for different layer thicknesses with rough-on-smooth boundary conditions. $h∕d$=(a) 1, (b) 2, (c) 4, and (d) 7.

Figure 4

Normalized density of the grains as a function of depth for the rough-on-rough (first column) and the rough-on-smooth (second column) boundary conditions and slider velocities $v_p=0.3d∕\mathrm{s}$ (solid lines) and $v_p=1.3d∕\mathrm{s}$ (dashed lines).

Figure 5

Normalized mean velocity of the grains as a function of depth for different boundary conditions and slider velocities. (a)–(d) $h∕d=1$, 2, 4, and 7, respectively, and $v_p=0.3d∕s$. (e) $h∕d=10$, $v_p=0.3d∕s$ (엯), $v_p=1.3d∕s$ (▵). Rough-on-rough case (open symbols) and rough-on-smooth case (filled symbols). Inset: Corresponding plot in log-linear scale. The thick solid line represents the fit (see text).

Figure 6

Vertical component of the trajectory of a particle for different layer thicknesses and $v_p=0.3d∕s$. $h∕d$=(a) 1, (b) 2, (c) 4, and (d) 7. Rough-on-rough boundary conditions are used. (e) Average gap between sliding surface and top layer. The data is averaged over all boundary conditions and slider speeds.