1,879 research outputs found
Relaxation time for the temperature in a dilute binary mixture from classical kinetic theory
The system of our interest is a dilute binary mixture, in which we consider
that the species have different temperatures as an initial condition. To study
their time evolution, we use the full version of the Boltzmann equation, under
the hypothesis of partial local equilibrium for both species. Neither a
diffusion force nor mass diffusion appears in the system. We also estimate the
time in which the temperatures of the components reach the full local
equilibrium. In solving the Boltzmann equation, we imposed no assumptions on
the collision term. We work out its solution by using the well known
Chapman-Enskog method to first order in the gradients. The time in which the
temperatures relax is obtained following Landau's original idea. The result is
that the relaxation time for the temperatures is much smaller than the
characteristic hydrodynamical times but greater than a collisional time. The
main conclusion is that there is no need to study binary mixtures with
different temperatures when hydrodynamical properties are sought
Entropy Production in Relativistic Binary Mixtures
In this paper we calculate the entropy production of a relativistic binary
mixture of inert dilute gases using kinetic theory. For this purpose we use the
covariant form of Boltzmann's equation which, when suitably transformed, yields
a formal expression for such quantity. Its physical meaning is extracted when
the distribution function is expanded in the gradients using the well-known
Chapman-Enskog method. Retaining the terms to first order, consistently with
Linear Irreversible Thermodynamics we show that indeed, the entropy production
can be expressed as a bilinear form of products between the fluxes and their
corresponding forces. The implications of this result are thoroughly discussed
Hydrodynamic time correlation functions in the presence of a gravitational field
This paper shows that the ordinary Brillouin spectrum peaks associated to
scattered radiation off acoustic modes in a fluid suffer a shift in their
values due to gravitational effects. The approach is based in the ordinary
linearized Navier-Stokes equations for a fluid coupled to a Newtonian
gravitational potential. The formalism leads to a dispersion relation that
contains both gravitational and dissipative effects. It is also shown that the
Brillouin peaks tend to condense into a single peak when the fluid modes
approach the critical Jeans wave number.Comment: 6 pages, no figures. To appear in Physica
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