Granular clogging across gravities: a unified scaling

Abstract

Lacking a universal law for granular flows across gravitational environments, fundamental processes such as hopper discharge remain vulnerable to failure in low gravity environments. A central challenge is clogging, the spontaneous arrest of flow through a constriction; yet previous studies report contradictory results on its dependence on gravitational acceleration. We identify the granular Bond number as the missing control parameter, defined as the ratio of intrinsic cohesive interactions among particles to gravity. Based on an in-bulk measurement of this quantity, we propose to rescale Earth-measured data for predicting granular behavior in low gravity. We present experiments of granular flow through an orifice under true reduced gravity (Moon and Mars), using an active drop tower, and extraterrestrial soil simulants as model cohesive materials. Our experiments reveal substantially increases in clogging probability, contrary to previously predicted, which depends on the properties of the material itself. When rescaled by the Bond number, seemingly conflicting results can be explained and collapse into a unified state diagram, predicting clogging across materials and gravitational accelerations. This establishes a general framework for cohesion--gravity competition. Future space missions to the Moon, Mars, and asteroids will rely on such predictions of granular behavior in low gravity.

Figures (12)

• Figure 1: Experimental setup. A quasi-2D hourglass, placed in a vacuum chamber, is installed in the capsule of the active drop tower gtb (, Bremen, Germany). A camera records the hourglass discharge through the chamber window; a typical image recorded is shown in the center panel, featuring regolith simulant JSC-1A and an orifice diameter $D=$ 10. The quasi-2D hourglass is equipped with two hopper angles, $\alpha=$ 60° (upper chamber here) and $\alpha=$ 120° (lower chamber).
• Figure 2: Characterization of granular materials versus gravity (Earth, Mars, Moon) by the granular Bond number. The values for $\mathcal{B}$ are based on Eq. \ref{['eq:BondNbr']}, using the $g_\text{L, M}$ recorded during experiments; details on $\Upsigma_\text{t}$ are given in the Methods section; error bars indicate the variability in $\Upsigma_\text{t}$. The dashed line at $\mathcal{B}=1$ represents the theoretical limit at which material start to behave as cohesive. In the inset, $\mathcal{B}$ is plotted versus the median diameter ($d_{50}$) for the granular materials tested; the theoretical estimates (lines) are fits for $\mathcal{B}\propto 1/d^3$.
• Figure 3: Last instant of hopper flow experiment for different lunar regolith simulants, under Earth and Moon gravitational accelerations. Pictures are taken after 2.3 in Earth gravity (A, B, C) and after 2.3, at the end of the lunar gravity phase (D, E, F), for the material indicated below each picture. Note that in D, the basalt is still flowing at the end of the lunar gravity period. The hopper geometry is the same in all frames: orifice width of 10, hopper angle $\alpha=60°$.
• Figure 4: Hopper clogging probability, $\bf P_c$: free flowing ($P_c = 0$); clogged in at least one repetition ($0<P_c<1$); or clogged at each repetition ($P_c = 1$). Clogging statistics for all three materials studied (regolith simulants LHS-2E, JSC-1A and basalt beads), for varying orifice sizes $D\in[1,2,4,6,8,10,15,20]$ mm, at funnel angles 60° (left) and 120° (right), and for Earth (E), Mars (M) and Moon (L) effective gravitational acceleration. Cells left white are untested; cells with lighter hue are untested but extrapolated from neighboring cases.
• Figure 5: Cumulative clogging probability as a function of orifice-to-particle size ratio. The clogging probabilities are plotted for results in Earth and Moon effective gravitational acceleration, for regolith simulants (A,B) LHS-2E and (C,D) JSC-1A, and hopper angles of (A,C) 60° and (B,D) 120°. Note the change in $x$-axis scale between (B) and (C). Black arrows represent the shift in clogging probability solely due to a change in effective $g$. The corresponding fit parameters and materials' particle size distributions are provided in the Methods section (Tab. \ref{['tab:fitparamcloggingproba']}). Shaded areas indicate tolerance bands, which accept relative average deviations of $2/3$ per data point; details in the Methods section.