Equation of state of wet granular matter

Abstract

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<Tc corresponding to a first order segregation transition of clusters. For the realistic rupture length of the liquid bridge, scrit=0.07d, the critical point is located at Tc=0.274Ecb. While the critical temperature weakly depends on the rupture length, the critical density phic is shown to scale with scrit according to scrit=4d(sqrt[phiJ/phic]-1). The segregation transition is closely related to the precipitation of granular droplets reported for the free cooling of one-dimensional wet granular matter [A. Fingerle and S. Herminghaus, Phys. Rev. Lett. 97, 078001 (2006)], and extends the effect to higher dimensional systems. Since the limiting case of sticky bonds, Ecb>>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.