Irreversible thermodynamics of multicomponent fluids and its statistical mechanics basis.

The irreversible thermodynamics of a multicomponent fluid is reviewed. This includes a discussion of the role of individual component fluxes. It is argued that their differences vanish on the same time scale as that which establishes local thermodynamic equilibrium and thus do not play an independent role in fluid dynamics, but only arise in response to gradients in conserved thermodynamic variables. The contributions to the energy flux are examined and it is argued that there should be explicit contributions associated with the various component fluxes, which are not mentioned in standard kinetic theory presentations. Three different thermodynamic perspectives are discussed as to their form, with the respective equations for the entropy flux and production described and contrasted. The Onsager reciprocal relations are considered to be a consequence of the single-valuedness of the entropy production with the chemical potential gradients as the driving forces for diffusion. These are specialized to ideal gas mixtures using the component density gradients associated with Fick's laws and to using the mole fraction gradients that are standardly used in gas kinetic theory. The ideal gas Onsager relations are identical to those deduced from the Boltzmann equation. Irving and Kirkwood's statistical mechanics treatment of the evolution equations of a one-component fluid [J. Chem. Phys. 18, 817 (1950)JCPSA60021-960610.1063/1.1747782] is generalized to multicomponent fluids and agrees with the thermodynamic perspective that treats the energy transfers as reversible.

Multicomponent gas transport coefficients: alternate formulations.

The phase rule states that a fluid element is determined locally by c+1 independent intensive variables when there are c components. In solving the Boltzmann equation for gas transport coefficients, the standard procedures involve only c independent gradients of intensive variables for the local properties (exclusive of the convective motion). This paper addresses this disparity and proposes an alternative set of gradients when solving the Boltzmann equation. The consequence is added terms in the expressions for the thermal diffusion coefficients. As well, the standard expression for the binary diffusion constant is identified as being valid only at constant total density. Irreversible thermodynamics is used as a reference base for comparing the alternate formulations.

An analytical formulation of CPMAS.

An exact expression for the cross polarization between two spin-1/2 particles is derived from the quantum Liouville equation. This is given in the form of two integrodifferential equations. These can be solved exactly in the static case (no sample spinning) and a powder average easily performed numerically. With magic-angle spinning, the neglect of certain interference terms simplifies the numerical calculation. A further assumption decoupling the calculation of the sidebands gives a very simple formula that is capable of giving a qualitative interpretation of all experimental observations. Examples are given illustrating typical buildup curves and CPMAS matching profiles.