Biomedical subjects
Publications and source records attributed to L S García-Colín.
In this work we show that moment methods devised to solve the Boltzmann kinetic equation for a simple gas exhibit some inconsistencies. This puzzle, which also appears for the Chapman-Enskog method, is solved resorting to a perturbative expansion in the Knudsen number, thus allowing for a clear way to arrive at a closure condition.
We show that while Eu's claim is true that we made a mistake regarding the asymptotic behavior of his theory is true, the correct asymptotic behavior cannot have a physical meaning. We analyze in more detail his theory for a dilute gas of rigid spheres, and show that in some cases it predicts a negative value of the xx component of the pressure tensor.
The exact expression of the one-dimensional Boltzmann multiple-scattering coefficients, for the passage of particles through a slab of a given material, is obtained in terms of the single-scattering cross section of the material, including absorption. The remarkable feature of the result is that for multiple scattering in a metal, free from absorption, one recovers the well-known Landauer result for conduction electrons. In the case of particles, such as neutrons, moving through a weak absorbing media, Landuer's formula is modified due to the absorption cross section. For photons, in a strong absorbing media, one recovers the Lambert-Beer equation. In this latter case one may therefore speak of absorption-controlled diffusive processes.
The Grad ten-moment approximation (no heat flux) is analyzed for cylindrical symmetry in a stationary situation in which the gradients of the fluxes are assumed to be small. We show that if the collision term in the transport equation, resulting from the ten-moment approximation, is linearized in the fluxes, we can obtain a viscosity (etal) that depends on the gradient of the velocity with the correct limiting behavior for small gradients. The nonlinear contribution of the fluxes to the collision term are then taken into account to derive an expression for the viscosity (eta(nl)) as a function of the gradient of the velocity. A comparison between etal and eta(nl) is performed finding that the maximum percentage deviation between them is 0.52% when the gradient of the hydrodynamic velocity is positive, but when the gradient is negative the situation changes dramatically.