Theory of nonlinear transport in Burnett order

Abstract

Constitutive equations for a fluid are worked out to the order corresponding to the Burnett approximation of kinetic theory, using the method of time-dependent correlation functions. These equations describe effects such as normal stresses which are characteristic of non-Newtonian fluids. Coefficients of the various terms are identified as integrals of correlation functions; those associated with linear second-order terms involve space and time moments of the same two-point correlation functions which occur in the first-order theory, while the coefficients of nonlinear terms depend in addition on three-point correlation functions.

Fluctuation-induced pressures in fluids in thermal nonequilibrium steady states

“…Divergent Burnett and higher-order transport coefficients are not new and, in general, as the number of gradients increases, the strength of the divergence does as well [19,36,37,[56][57][58][59]. Hence, one would expect that Eq.…”

Physical origin of nonequilibrium fluctuation-induced forces in fluids

“…Here κ NL is a kinetic coefficient commonly referred to as a nonlinear Burnett coefficient [33,34]. As has been discussed elsewhere [35][36][37][38], it is well known that κ NL diverges linearly in the large system size, L, due to longtime-tails effects.…”

Damping and dispersion of oscillating modes of a multicomponent ionic mixture in a magnetic field

“…Burnett terms have been discussed previously in the context of systems of neutral particles [8][9][10][11][12]. For such systems the Burnett terms generally lead to small effects in the dynamical behaviour, so that they can usually be neglected.…”

“…As we will show, so-called Burnett terms will be needed to obtain a consistent picture. For systems of neutral particles these Burnett terms [8][9][10][11][12], which describe non-local effects in transport phenomena, are of rather limited importance. They play a role only when one is interested in contributions to mode frequencies that are of higher than second order in the wave number.…”