The Enskog theory for dense multicomponent fluid mixtures is developed. Two versions are considered—the standard theory and the revised theory. Explicit expressions for all the transport coefficients (shear and bulk viscosity, thermal conductivity, mutual and thermal diffusion coefficients) in terms of the sizes, masses, and concentrations of the constituents of the mixture are given in the third Enskog approximation. Applications will be discussed in subsequent papers.

Using the revised Enskog theory we derive equations for the thermal diffusion ratios k_Ti and thermal diffusion factors α_ij of multicomponent hard‐sphere mixtures for systems in mechanical equilibrium. The first ten Enskog approximations to the thermal diffusion factor α_ij[N] (N=1,2,...,10) are evaluated numerically for a variety of system parameter choices appropriate to binary and ternary mixtures. We find that the first Enskog approximation does not vanish; the sequence of Enskog approximations converges most rapidly when the mass of the spheres are nearly equal. The seventh Enskog approximation was estimated to lie within about 1% of the exact value for all choices of system parameters. A comprehensive numerical study of the properties of the thermal diffusion factor for binary mixtures is given, including special mixtures such as the dusty gas, the Lorentz, quasi‐Lorentz and Rayleigh gases, and isotopic mixtures. Particular emphasis is placed on showing how the properties of α₁₂ change as the density is increased. The most striking difference between the low‐density (Boltzmann) and high‐density values for α₁₂ is that the region of the mass ratio—diameter ratio plane for which α₁₂ is either strictly positive or negative, as a function of composition, is much smaller at high densities. Also, at higher densities α₁₂ is not a monotonic function of the mole fraction. For ternary mixtures in which two of the components are isotopes we show how the properties of the third component affect the separation of the two isotopes.

An equation of state for a fluid of hard disks is proposed: Z=[1−2η+(2η₀−1)(η/η₀)²]⁻¹. The exact fit of the second virial coefficient and the existence of a single pole singularity at the close‐packing fraction η₀ are the only requirements imposed on its construction. A comparison of the prediction of virial coefficients and of the values of the compressibility factor Z with those stemming out of other known equations of state is made. The overall performance of this very simple equation of state is quite satisfactory.

In order to gain insight into the effects of elasticity on the dynamics of fluids in porous media, we have analyzed the flow of a Maxwell fluid in a tube. The entire problem is transformed to the frequency domain through a time Fourier transform and this allows for the derivation of a dynamic generalization of Darcy’s law. Analytical results are provided showing a dramatic enhancement at certain frequencies. We present a parametric analysis of the dissipative and elastic behavior of the system, and we obtain an analytic expression for the maximum value of the permeability and the frequency at which this maximum occurs in terms of the physical properties of the fluid and the radius of the tube. With these results, we show that the human pulse occurs at a frequency that produces a permeability in the neighborhood of the maximum permeability.