Simple Model for Wet Granular Materials with Liquid Clusters

We propose a simple phenomenological model for wet granular media to take into account many particle interaction through liquid in the funicular state as well as two-body cohesive force by a liquid bridge in the pendular state. In the wet granular media with small liquid content, liquid forms a bridge at each contact point, which induces two-body cohesive force due to the surface tension. As the liquid content increases, some liquid bridges merge, and more than two grains interact through a single liquid cluster. In our model, the cohesive force acts between the grains connected by a liquid-gas interface. As the liquid content increases, the number of grains that interact through the liquid increases, but the liquid-gas interface may decrease when liquid clusters are formed. Due to this competition, our model shows that the shear stress has a maximum as a function of the liquid-content. Introduction. – It is well known that just adding small amount of liquid to dry granular materials changes their behaviors drastically [1–3]. Liquid forms bridges between grains, and the bridge induces cohesion between grains due to the surface tension. When the amount of liquid is small, liquid bridges are formed between two grains at contact points; such a state is called the pendular state (Fig. 1(a)). As the amount of liquid is increased, several liquid bridges are connected to form a liquid cluster that includes more than two grains as in Fig. 1(b), which is called the funicular state. As we add the liquid further, all the pores will be filled with the liquid. It is called the capillary state if the liquid pressure is still lower than the air pressure, and finally the system becomes the slurry state if the amount of liquid is enough to make the liquid pressure as high as the air pressure. The liquid content dependence of the mechanical properties of wet granular materials has not been well understood yet. The most studied case is the pendular state, both experimentally and numerically [1–7]. There, the situation is rather simple because the grain-grain interactions, including the cohesion due to liquid bridges, are mainly two-body interactions. However, as the liquid content is increased, liquid clusters become non-negligible, which induce many-body interaction via the liquid. Methods and/or models to deal with such a situation have not been established yet and still under active research (a) (b) Fig. 1: Schematic description of the distribution of liquids in the wet granular materials. (a) The pendular state, where liquid bridges are formed at contact points. (b) The funicular state, where some liquid clusters that connect more than two grains are formed.