Chaoticity of the Wet Granular Gas

In this work we derive an analytic expression for the Kolmogorov-Sinai entropy of dilute wet granular matter, valid for any spatial dimension. The grains are modelled as hard spheres and the influence of the wetting liquid is described according to the Capillary Model, in which dissipation is due to the hysteretic cohesion force of capillary bridges. The Kolmogorov-Sinai entropy is expanded in a series with respect to density. We find a rapid increase of the leading term when liquid is added. This demonstrates the sensitivity of the granular dynamics to humidity, and shows that the liquid significantly increases the chaoticity of the granular gas.Comment: 13 pages, 10 figures, Physical Review

Translated from Pis'ma v Zhurnal Éksperimental'no oe i

In recent years, growing interest has been shown in the processes of stochastic transport because of the spatial and temporal nonlocalities inherent in this phenomenon There are many physical reasons that are responsible for the above-mentioned nonlocalities (fractional derivatives) in the transport equations (see discussion in Evidently, one should expect that evolution is continuous for any physical process satisfying the causality principle: if the solution to the equations is functionally related to the initial state by the Green's function G t , i.e., if n ( x , t ) = G t * n ( t = 0) , then transport with a fractional time derivative, including a recent excellent review [4], strictly speaking, do not possess this property. This unpleasant fact has in no way been discussed in the literature, though it is precisely the point that is expected to be helpful in the recognition of a hidden defect of the above-mentioned description, namely, of the incompleteness in the description of a particle cloud only in terms of its macroscopic concentration n ( x , t ). Interestingly, similar problems arise for strongly coupled coulombic systems in the quantum kinetic theory, where the solutions show a strong dependence on the initial correlations (1)), the defect is often "hidden under the rug." In reality, the time for approaching the microscopic evolution regime strongly depends on the initial condition and can be much longer than the microscopic time 〈τ〉 characterizing the random walk of individual particles (see below). This is especially characteristic of the subdiffusion time operators. Therefore, the memory effects considered in this work consist not in the familiar temporal nonlocality (fractional derivative) in the effective transport equation but in the fact that the form of this equation depends on the macroscopic time t (see below). When deriving the transport equations, we will use, as in Memory Effects in Stochastic Transpor