Equation of State of Wet Granular Matter

TL;DR

This paper develops a theoretical model for the equation of state of wet granular matter in two dimensions, revealing phase transitions, critical points, and agreement with simulations, advancing understanding of granular clustering and segregation.

Contribution

The paper introduces an analytic expression for the equation of state of wet granular matter, incorporating nonequilibrium currents and capillary interactions, extending previous models to higher densities and phase transitions.

Findings

Identifies a van-der-Waals-like unstable branch at T<T_c.

Locates the critical point at T_c=0.274 E_cb for s_crit=0.07 d.

Shows good agreement between theory and simulations for bond coordination.

Abstract

A theory is derived for the nonequilibrium probability currents of the capillary interaction which determines the pair correlation function near contact. This yields an analytic expression for the equation of state, P = P(N/V,T), of wet granular matter for D=2 dimensions, 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_c corresponding to a first order segregation transition of clusters. For the realistic rupture length of the liquid bridge, s_crit=0.07 d, the critical point is located at T_c = 0.274 E_cb. While the critical temperature weakly depends on the rupture length, the critical density phi_c is shown to scale with s_crit according to s_crit = 4d (sqrt(phi_J / phi_c) -1). The segregation transition is closely related to the precipitation of granular droplets reported for the free cooling of one-dimensional wet granular matter [Phys. Rev. Lett. 97, 078001 (2006)], and extends the effect to higher dimensional systems. Since the limiting case of sticky bonds, E_cb >> 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 s_crit. This result implies that particles that stick at the surface, s_crit=0, form isostatic clusters.