Role of contact-angle hysteresis for fluid transport in wet granular matter

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.