Related papers: Does the Chapman--Enskog expansion for sheared gra…
This paper deals with the convergence/divergence issue of the Chapman-Enskog series expansion of the shear and normal stresses for a granular gas of inelastic hard spheres. From the exact solution of a simple kinetic model in the uniform…
In this letter we show for the first time that the relativistic Chapman-Enskog series for a massless gas undergoing Bjorken expansion diverges. In order to fix this problem, we propose a novel type of expansion that includes…
The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This…
We study a two-dimensional fluid of hard disks undergoing chiral, energy- and momentum-conserving collisions. We show that despite the microscopic breaking of time-reversal symmetry, the H-theorem is obeyed, guaranteeing a relaxation…
The Enskog kinetic theory for moderately dense gas-solid suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the environmental fluid on solid particles is…
The shear viscosity for a moderately dense granular binary mixture of smooth hard spheres undergoing uniform shear flow is determined. The basis for the analysis is the Enskog kinetic equation, solved first analytically by the…
The analytical Chapman-Enskog formula for calculating the shear viscosity $\eta$ of a relativistic ideal gas, such as a massless quark-gluon plasma, has consistently demonstrated good agreement with the numerical results obtained using the…
We use the Chapman-Enskog method to investigate the shear viscosity of the quark-gluon plasma with a focus on its relation to parton cross sections. We use the recently obtained analytical expression for the shear viscosity $\eta$ of a…
The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done…
A quantitative comparison between the results of shear viscosities from the Chapman-Enskog and relaxation time methods is performed for selected test cases with specified elastic differential cross sections: (i) the non-relativistic,…
The interpretation of the measured elliptic and higher order collective flows in heavy-ion collisions in terms of viscous hydrodynamics depends sensitively on the ratio of shear viscosity to entropy density. Here we perform a quantitative…
The analytical expressions of the shear viscosity of both one and two particle species with Boltzmann statistics and $2 \rightarrow 2$ elastic scatterings are known from the Chapman-Enskog method and have been shown to be quite accurate.…
The determination of the shear viscosity is a central topic in various areas of modern physics. In particular, it is often necessary to evaluate the shear viscosity $\eta$ of fluids made up of more than one species, all interacting with…
We justify a Chapman-Enskog expansion for discontinuous solutions of hyperbolic conservation laws containing shock waves with small strength. Precisely, we establish pointwise uniform estimates for the difference between the traveling waves…
In contrast to normal fluids, a granular fluid under shear supports a steady state with uniform temperature and density since the collisional cooling can compensate locally for viscous heating. It is shown that the hydrodynamic description…
The flow characterized by a linear longitudinal velocity field $u_x(x,t)=a(t)x$, where $a(t)={a_0}/({1+a_0t})$, a uniform density $n(t)\propto a(t)$, and a uniform temperature $T(t)$ is analyzed for dilute granular gases by means of a…
In this paper we study the convergence of a power-law model for dilatant compressible fluids to a class of models exhibiting a maximum admissible shear rate, called thick compressible fluids. These kinds of problems were studied previously…
A kinetic model for granular mixtures is considered to study three different non-equilibrium situations. The model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle…
A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account…
In a recent Nature Materials article, Brown et al. reported a generality of shear thickening in dense suspensions and demonstrated that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased…