Abstract
The stability of sand castles is determined by the structure of wet
granulates. Experimental data on the size distribution of fluid pockets
are ambiguous with regard to their origin. We discovered that
contact-angle hysteresis plays a fundamental role in the equilibrium
distribution of bridge volumes, and not geometrical disorder as commonly
conjectured. This has substantial consequences on the mechanical
properties of wet granular beds, including a history-dependent rheology
and lowered strength. Our findings are obtained using a model in which
the Laplace pressures, bridge volumes, and contact angles are dynamical
variables associated with the contact points. While accounting for
contact line pinning, we track the temporal evolution of each bridge. We
observe a crossover to a power-law decay of the variance of capillary
pressures at late times and a saturation of the variance of bridge
volumes to a finite value connected to contact line pinning. Large-scale
simulations of liquid transport in the bridge network reveal that the
equilibration dynamics at early times is well described by a mean-field
model. The spread of final bridge volumes can be directly related to the
magnitude of contact-angle hysteresis.
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