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Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium transition, setting in as the granular temperature falls below the bond energy. The subsequent aggregation of particles into clusters is shown to be a self-similar growth process with a cluster size distribution that obeys scaling. In the early phase of aggregation the clusters are fractals with D f = 2, for later times we observe gelation. We use simple scaling arguments to derive the temperature decay in the early and late stages of cooling and verify our results with event-driven simulations.PACS numbers: 61.43.Hv Granular systems have encountered strongly increasing interest within recent years [1, 2] as they are both close to industrial applications and relevant as model systems for collective systems far from thermal equilibrium. Most research has focused on dry granulates resulting in rich non-equilibrium phenomena [3]. The dramatic change of mechanical properties due to some wetting liquid additive is apparent, when we compare the fluid-like state of dry sand flowing through an hourglass with the shapeable plastic state of wet sand, which is suitable for molding a sandcastle. This change in bulk properties can be attributed to the differences in the underlying particle interactions [4,5]. Whereas in collisions of dry particles, a certain fraction of the initial kinetic energy is dissipated into the atomic degrees of freedom of the particles, in the wet case, the interaction is mainly due to the interfacial forces exerted by liquid capillary bridges which form between adjacent particles and dissipate energy upon rupture.More recently, the dynamics of wet granular media has been addressed in several studies [5,6,7,8,9, 10], focusing on nonequilibrium phase transitions [10], agglomeration [6,7], shear flow [8] and cooling in one dimension [9]. A particularly important aspect of free cooling in cohesive gases is the structure of the emerging clusters. It pertains to the formation of dust filaments and the microscopic mechanisms of cloud formation as well as to the size distribution and impact probability of planetesimals in accretion discs. Structure formation in wet granulates during free cooling has hardly been studied yet and is the central theme of our paper. We suggest a very simple model for the interaction of two wet grains, which only takes into account the essential features of a capillary bridge: hysteresis and dissipation with a well defined energy loss. Cooling is controlled by the proba- * Electronic address: ulrich@theorie.physik.uni-goettingen.de bility for a bridge to rupture and hence logarithmically slow in the long time limit, when a percolating structure has been formed. For smaller times the structure is characterized by coexisting fractal clusters of all sizes, whose size distribution is shown to scale.Model-Consider a gas of N hard spheres of diameter d ...

The free cooling of one-dimensional wet granular matter is presented in the framework of the minimal capillary model. We demonstrate analytically and by extensive simulations that above a critical density, the clustering of wet granular matter is not monotonic in time, but undergoes a sharp unclustering transition. This precipitation of granular droplets out of the gas takes place when the granular temperature comes close to the energy scale set by the capillary interaction.

An expression for the near-contact pair correlation function of D -dimensional weakly polydisperse hard spheres is presented, which arises from elementary free-volume arguments. Its derivative at contact agrees very well with our simulations for D=2 . For jammed states, the expression predicts that the number of exact contacts is equal to 2D, in agreement with established simulations. When the particles are wetted, they interact by the formation and rupture of liquid capillary bridges. Since formation and rupture events of capillary bonds are well separated in configuration space, the interaction is hysteretic with a characteristic energy loss Ecb. The pair correlation is strongly affected by this capillary interaction depending on the liquid-bond status of neighboring particles. A theory is derived for the nonequilibrium probability currents of the capillary interaction which determines the pair correlation function near contact. This finally yields an analytic expression for the equation of state, P=P(N/V,T), of wet granular matter for D=2, valid in the complete density range from gas to jamming. Driven wet granular matter exhibits a van der Waals-like unstable branch at granular temperatures T>T, is of relevance for aggregation in general, simulations have been performed which show very good agreement with the theoretically predicted coordination K of capillary bonds as a function of the bond length scrit. This result implies that particles that stick at the surface, scrit=0, form isostatic clusters. An extension of the theory in which the bridge coordination number K plays the role of a self-consistent mean-field is proposed.

We investigate a gas of wet granular particles covered by a thin liquid film. The dynamic evolution is governed by two-particle interactions, which are mainly due to interfacial forces in contrast to dry granular gases. When two wet grains collide, a capillary bridge is formed and stays intact up to a certain distance of withdrawal when the bridge ruptures, dissipating a fixed amount of energy. A freely cooling system is shown to undergo a nonequilibrium dynamic phase transition from a state with mainly single particles and fast cooling to a state with growing aggregates such that bridge rupture becomes a rare event and cooling is slow. In the early stage of cluster growth, aggregation is a self-similar process with a fractal dimension of the aggregates approximately equal to Df approximately 2 . At later times, a percolating cluster is observed which ultimately absorbs all the particles. The final cluster is compact on large length scales, but fractal with Df approximately 2 on small length scales.