Nonlinear effects in gases due to strong gradients

The behavior of a gas may be quite atypical if the velocity distribution function is significantly distorted by the presence of large gradients. Under such circumstances phenomena like shear thinning or negative effective thermal conductivity may be present. Hydrodynamic equations derived directly from Boltzmann’s equation using a moment expansion method yield predictions which are sensitive to the value of Knudsen numbers associated to the macroscopic fields themselves and provide a rational for the peculiar behavior. In the case of sheared laminar flows the law of viscous flow predicts non-Newtonian effects including shear thinning and the law of energy transport (associated to what is usually called heat flux) is more general than Fourier’s law: it is not linear and it implies a flux with a nontrivial component parallel to the isotherms. These nonlinear transport laws are well corroborated by molecular dynamic simulations based on straightforward Newtonian dynamics. More in general it is shown that the energy flux is naturally split in a component that removes heat from the system and a divergenceless component which represents a flux of energy which does not leave the system.