Does Gravity Cause Load-Bearing Bridges in Colloidal and Granular Systems?

We study structures which can bear loads, “bridges”, in particulate packings. To investigate the relationship between bridges and gravity, we experimentally determine bridge statistics in colloidal packings. We vary the effective magnitude and direction of gravity, volume fraction, and interactions, and find that the bridge size distributions depend only on the mean number of neighbors. We identify a universal distribution, in agreement with simulation results for granulars, suggesting that applied loads merely exploit preexisting bridges, which are inherent in dense packings.

Figure 1

Bridge size distribution $P(m)$ for $0.39<\varphi <0.60$ for the density-matched slightly soft spheres (a) and the non-density-matched hard-spheres (b). (Only selected data sets labeled for clarity.) The lines represent $P(m)=\alpha e^{-\alpha m}$ for $\alpha =\{0.2,0.3,0.4,0.5,0.7,0.9\}$ in (a) and $\alpha =\{0.2,0.3\}$ in (b). Inset to (b): $P(m)$ for the density-matched (△) and the non-density-matched (◊) samples, as well as a simulated granular material (+). All of these samples had $\varphi \approx 0.57$. The dashed line represents $P(m)=1.8m^{-2}$.

Figure 2

Mean bridge size $⟨m⟩$ as a function of mean coordination number $⟨z⟩$ and of volume fraction $\varphi$ (inset) for the density-matched soft spheres (▵) and non-density-matched hard spheres (◊).

Figure 3

Exponent $\alpha$ in the fit $P(m)=\alpha e^{-\alpha m}$ as a function of $⟨z⟩$ (and, in the inset, of $\varphi$) for the non-density-matched hard- (◊) and density-matched slightly soft spheres (▵). The right-hand axis shows the corresponding probability $p=e^{-\alpha }$.

Figure 4

Mean coordination number $⟨z⟩$ as a function of volume fraction $\varphi$ for the density-matched soft (▵) and non-density-matched hard spheres (◊).

Figure 5

Bridge size distribution $P(m)$ for density-matched amorphous ($Q_6/Q_6^{\mathrm{FCC}}<0.05$, ◊) and (partially) crystalline ($Q_6/Q_6^{\mathrm{FCC}}>0.70$, *) samples with similar $⟨z⟩$ ($2.877\pm 0.054$ and $2.873\pm 0.032$ respectively), and for a non-density-matched sample, $\varphi \approx 0.647$, obtained in its natural orientation (•), electronically rotated by 90° (■), and upside down, i.e., $z$ coordinates artificially inverted (◆).