Accretion Dynamics on Wet Granular Materials

Wet granular aggregates are common precursors of construction materials, food, and health care products. The physical mechanisms involved in the mixing of dry grains with a wet substrate are not well understood and difficult to control. Here, we study experimentally the accretion of dry grains on a wet granular substrate by measuring the growth dynamics of the wet aggregate. We show that this aggregate is fully saturated and its cohesion is ensured by the capillary depression at the air-liquid interface. The growth dynamics is controlled by the liquid fraction at the surface of the aggregate and exhibits two regimes. In the viscous regime, the growth dynamics is limited by the capillary-driven flow of liquid through the granular packing to the surface of the aggregate. In the capture regime, the capture probability depends on the availability of the liquid at the saturated interface, which is controlled by the hydrostatic depression in the material. We propose a model that rationalizes our observations and captures both dynamics based on the evolution of the capture probability with the hydrostatic depression.

Figure 1

(a) Schematic of the experimental setup. Inset: Schematic of the meniscus for increasing $\mathrm{\Delta }h$. (b) Time evolution of the length of the aggregate for different hydrostatic depressions, expressed as a function of $\mathrm{\Delta }h$. (c) Cross section through a 3D tomogram of a wet aggregate. The liquid is colored in yellow, whereas the glass beads are red and the air is in black.

Figure 2

(a) Initial growth rate of the aggregate $v(t=0)$ as a function of the height $\mathrm{\Delta }h$. The fit gives $h^{\star }=20\mathrm{mm}$ ($X^{\star }=0.26$). Inset: Temporal evolution of the aggregate length. (b) Evolution of the liquid fraction ${\varphi }_{\mathrm{liq}}$ at the liquid-air interface in a wet granular packing as the function of the ratio $X=2d_g/R$. Data are fitted by ${\varphi }_{\mathrm{liq}}={\varphi }_{\infty }+(1-{\varphi }_{\infty })\exp (-X/{X_s}^{\star })$ with ${X_s}^{\star }=1.10$. Inset: Evolution of the dimensionless volume associated to a conical site of capture—${X_v}^{\star }=0.34$. (c) Experimental evolution of the apparent liquid surface as a function of height $\mathrm{\Delta }h$. Images are obtained by binocular microscopy with an opaque dyed liquid and zirconium beads of $500\mu \mathrm{m}$ diameter. The red line is an exponential expression with ${h_{s,\exp }}^{\star }=24\mathrm{mm}\pm 4\mathrm{mm}$ corresponding to ${X_{s,\exp }}^{\star }=1.59\pm 0.26$. Experimental parameters: $\gamma =44\mathrm{mN}/\mathrm{m}(\pm 2\mathrm{mN}/\mathrm{m})$ and $\theta =65°$ ($\pm 5°$).

Figure 3

Evolution of the rescaled growth velocity $d\zeta /d\tau$ as a function of the rescaled time $\tau$ defined in Eq. (4) for all hydrostatic depressions. Inset: Evolution of the rescaled length of aggregate $\zeta$ as the function of the rescaled time $\tau$. The dashed lines correspond to the theoretical predictions given by Eq. (8).