Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Abstract Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved

Kinetic models for reactive mixtures: Problems and applications

Problems related to physical consistency and practical application of kinetic BGK models for reactive mixtures are investigated. In particular, two approximation strategies are discussed, relevant to the different physical scenarios of slow and fast chemical reactions, respectively. The former is tested versus the steady shock problem in comparison to available hydrodynamic results. For the latter, allowing for an explicit proof of the H-theorem, a preliminary sample is shown of the space homogeneous calculations in progress

Qualitative analysis of kinetic-based models for tumor-immune system interaction

A mathematical model, based on a mesoscopic approach, describing the competition between tumor cells and immune system in terms of kinetic integro-differential equations is presented. Four interacting populations are considered, representing, respectively, tumors cells, cells of the host environment, cells of the immune system, and interleukins, which are capable to modify the tumor-immune system interaction and to contribute to destroy tumor cells. The internal state variable (activity) measures the capability of a cell of prevailing in a binary interaction. Under suitable assumptions, a closed set of autonomous ordinary differential equations is then derived by a moment procedure and two three-dimensional reduced systems are obtained in some partial quasi-steady state approximations. Their qualitative analysis is finally performed, with particular attention to equilibria and their stability, bifurcations, and their meaning. Results are obtained on asymptotically autonomous dynamical systems, and also on the occurrence of a particular backward bifurcation

Chemical characterization and economic evaluation of the coal fly ash pre-washing and carbonation process

In the present laboratory-scale study, the combination of washing and carbonation processes was examined to evaluate the feasibility to reduce the environmental impact of coal power plants. Three different washing solutions (tap, distilled and sea water) were used to pre-treat coal fly ash and the corresponding effect on direct gas-solid carbonation and final metal leaching was evaluated. Finally, a preliminary economic evaluation of the process was performed. In terms of captured CO2, the results have shown that significant amounts can be captured, although, as expected, the leaching of soluble salts in water such as Ca and Mg reduce the CO2 uptake. In terms of heavy metal's leaching, the application of pre-washing and carbonation treatment significantly affected the metal immobilization on the final residue. The pre-washing with sea water allowed to reach a sensible improvement since only selenium, chlorides and sulphates resulted outside the range for disposing of the carbonated residue in landfill for non-hazardous waste

Altered Mesolimbic Dopamine System in THC Dependence

To explore the functional consequences of cannabinoid withdrawal in the rat mesolimbic dopamine system, we investigated the anatomical morphology of the mesencephalic, presumed dopaminergic, neurons and their main post-synaptic target in the Nucleus Accumbens. We found that TH-positive neurons shrink and Golgi-stained medium spiny neurons loose dendritic spines in withdrawal rats after chronic cannabinoids administration. Similar results were observed after administration of the cannabinoid antagonist rimonabant to drug-naïve rats supporting a role for endocannabinoids in neurogenesis, axonal growth and synaptogenesis. This evidence supports the tenet that withdrawal from addictive compounds alters functioning of the mesolimbic system. The data add to a growing body of work which indicates a hypodopaminergic state as a distinctive feature of the “addicted brain”

Shock wave structure of multi-temperature Euler equations from kinetic theory for a binary mixture

A multi-temperature hydrodynamic limit of kinetic equations is employed for the analysis of the steady shock problem in a binary mixture. Numerical results for varying parameters indicate possible occurrence of either smooth profiles or of weak solutions with one or two discontinuities. \ua9 2014 Springer Science+Business Media Dordrecht

Electro-osmotic flows inside triangular microchannels

This work presents a numerical investigation of both pure electro-osmotic and combined electro-osmotic/pressure-driven flows inside triangular microchannels. A finite element analysis has been adopted to solve the governing equations for the electric potential and the velocity field, accounting for a finite thickness of the electric double layer. The influence of non-dimensional parameters such as the aspect ratio of the cross-section, the electrokinetic diameter and the ratio of the pressure force to the electric force on the flow behavior has been investigated. Numerical results point out that the velocity field is significantly influenced by the aspect ratio of the cross section and the electrokinetic diameter. More specifically, the aspect ratio plays an important role in determining the maximum volumetric flow rate, while the electrokinetic diameter is crucial to establishing the range of pressures that may be sustained by the electro-osmotic flow. Numerical results are also compared with two correlations available in the literature which enable to assess the volumetric flow rate and the pressure head for microchannels featuring a rectangular, a trapezoidal or an elliptical cross-section