Cooling and Aggregation in Wet Granulates

Abstract

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 ...

Droplet and cluster formation in freely falling granular streams

“…The dynamics in this regime consist of an intricate interplay between the effects of the velocity profile at the aperture, the stretching and diluting of the stream via gravity, and low energy collisions which permit initially separated grains to become permanently connected. The capture process can start once the stream has fallen and cooled to a low enough level such that the cohesive energy F coh l c exceeds the pre-collisional kinetic energy [5,6]. This does not continue indefinitely, however, because the stretching due to gravity drives the collision frequency toward zero.…”

“…In modeling granular flows these interactions are typically taken as purely repulsive. However, there are important circumstances, from agglomeration in fluidized particle beds to dust accretion in proto-planetary discs, where attractions can compete with the particle weight or with forces produced by particle collisions and then lead to the formation of stable granular clusters [4][5][6][7]. In dry, nominally free-flowing granular material the attractions are small and short-ranged, and are usually associated with van der Waals forces or capillary bridges due to a few layers of adsorbed molecules [7,8].…”

“…Under dynamic conditions, energy is also dissipated due to the inelastic nature of collisions, including rolling and sliding friction during non-central impacts [5,[11][12][13][14]. Simulations have started to address the competition between inelasticity and cohesion during collisions in freely cooling granular systems, but so far have focused on the limit of a dilute granular 'gas' [6,13,15]. Little is known about the complex dynamics that lead to clustering in the dense limit, where many weakly cohesive particles collide and interact in rapid succession.…”

Probing Colloidal Gels at Multiple Length Scales: The Role of Hydrodynamics

“…Gels can be soft or biological materials such as proteins [5,6], clays [7], foods [8], hydrogels [9], and tissues [10,11]. However, a more diverse range of systems including granular matter [12], phase-demixing oxides [13], and metallic glassformers [14] also exhibit gelation. The mechanical properties of gels are influenced by their structure both locally [15][16][17][18] and at a global level through percolation of particles [19] and clusters [20], network topology [21], and confinement [22].…”

Micro–macro transition and simplified contact models for wet granular materials

“…However, wet granular materials are ubiquitous in geology and many real-world applications, where interstitial liquid is present between the grains. Simplified models for capillary clusters [2,3] and wet granular gases [4] were introduced before. The rheology of flow for dense suspension of non-Brownian particles have been studied in Refs.…”