Fluid Mixtures In Porous Media Research Articles

Existence Analysis of a Single-Phase Flow Mixture with van der Waals Pressure

The transport of single-phase fluid mixtures in porous media is described by cross-diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy's law, and the van der Waals equation of state for mixtures. The model consists of parabolic equations with cross diffusion with a hypocoercive diffusion operator. The global-in-time existence of weak solutions in a bounded domain with equilibrium boundary conditions is proved, extending the boundedness-by-entropy method. Based on the free energy inequality, the large-time convergence of the solution to the constant equilibrium mass density is shown. For the two-species model and specific diffusion matrices, an integral inequality is proved, which reveals a minimum principle for the mass fractions. Without mass diffusion, the two-dimensional pressure is shown to converge exponentially fast to a constant. Numerical examples in one space dimension illustrate this convergence.

Double-Diffusive Instability of Couple-Stress Binary Rivlin-Ericksen Visco-Elastic Fluid Mixture in Porous Medium

The paper critically examines, within the framework of linear stability analysis, the double diffusive instability of couple-stress binary Rivlin-Ericksen visco-elastic fluid mixture in porous medium. In the present paper, by a number of theorems providing conditions for stability or instability, bounds on the growth rate of unstable modes and the characterization of modes providing a clear cut effects of viscosity and medium permeability.

Influence of chemical reaction, Soret and Dufour effects on heat and mass transfer of a binary fluid mixture in porous medium over a rotating disk

Soret and Dufour effects on heat and mass transfer in steady flow over a rotating disk in porous medium are investigated. A set of coupled ordinary differential equations are obtained from the governing nonlinear partial differential equations which are then solved numerically by using MATLAB's built in solver bvp4c. The effects of material parameters like the porosity parameter, chemical reaction parameter, Dufour number, Soret number, Schmidt number and Prandtl number on temperature and concentration distributions are discussed through graphs. It is concluded that the porosity of the medium and the chemical reaction parameter play crucial role on the heat and mass transfer.

Long-time behaviour of multi-component fluid mixtures in porous media

The long-time behaviour of a triply convective–diffusive fluid mixture saturating a porous horizontal layer in the Darcy–Oberbeck–Boussinesq scheme, is investigated. It is shown that the L 2- solutions are bounded, uniquely determined (by the initial and boundary data) and asymptotically converging toward an absorbing set of the phase-space. The stability analysis of the conduction solution is performed. The linear stability is reduced to the stability of ternary systems of O.D.Es and hence to algebraic inequalities. The existence of an instability area between stability areas of the thermal Rayleigh number (“ instability island”), is found analytically when the layer is heated and “salted” (at least by one “salt”) from below. The validity of the “linearization principle” and the global nonlinear asymptotic stability of the conduction solution when all three effects are either destabilizing or stabilizing, are obtained via a symmetrization.

Roll convection of binary fluid mixtures in porous media

We investigate theoretically the nonlinear state of ideal straight rolls in the Rayleigh–Bénard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck–Boussinesq approximation, binary mixtures with positive separation ratio are studied and compared with one-component fluids. Our results for the structural properties of roll convection resemble qualitatively the situation in the Rayleigh–Bénard system without porous medium except for the fact that the streamlines of binary mixtures are deformed in the so-called Soret regime. The deformation of the streamlines is explained by means of the Darcy equation which is used to describe the transport of momentum. In addition to the properties of the rolls, their stability against arbitrary infinitesimal perturbations is investigated. We compute stability balloons for the pure fluid case as well as for a wide parameter range of Lewis numbers and separation ratios that are typical for binary gas and fluid mixtures. The stability regions of rolls are found to be restricted by a crossroll, a zigzag and a new type of oscillatory instability mechanism, which can be related to the crossroll mechanism.

Diffusivity of simple fluid mixtures in porous media: molecular dynamics simulations and correlation models

Equilibrium molecular dynamics simulations have been used to calculate the diffusivity of simple fluid mixtures in macrovolume systems and in porous media at different temperatures, densities, and pore widths. Based on the Chapman–Enskog theory and the Heyes relationships, two correlation models, which can describe the diffusivity of simple fluid mixtures in porous media as a function of the reduced temperature, density, and pore width, are proposed. The validity of the models is evaluated by comparing the calculated diffusivity data with those from the simulation data.

The diffusion–spin relaxation time distribution function as an experimental probe to characterize fluid mixtures in porous media

The distribution function between diffusion and spin relaxation time is shown to be a powerful tool to characterize fluid mixtures in porous media. We discuss the nuclear magnetic resonance measurements using diffusion-editing sequences that were developed to measure this quantity. A recently developed two-dimensional inversion routine is used to extract the distribution function from the data. We show both theoretically and experimentally that the technique is suitable for ex situ applications in the presence of grossly inhomogeneous fields. We apply this technique to characterize sedimentary rocks saturated with oil–water mixtures. From the measured diffusion–relaxation time distribution function it is possible to quantify the oil and water saturation, to get a direct indication of the wettability of the porous media, to characterize the bulk properties of the oil and estimate the oil viscosity, and to get information about the geometrical arrangement of the fluid phases in the pore space. We have also identified effects due to susceptibility induced gradients in a sandstone and effects of strongly restricted diffusion in a limestone.

Critical dynamics of random-field Ising systems with conserved order parameter.

Motivated by recent experiments on critical binary fluid mixtures in porous media, the dynamics of random-field Ising systems with conserved order parameter are considered. In the one-phase regime a new dynamic crossover length ${l}_{x}$ is found: for q\ensuremath{\ll}${q}_{x}$=2\ensuremath{\pi}/${l}_{x}$ the temporal decay of S(q,t) is well approximated by a single exponential whose decay rate is determined by diffusive dynamics, while for q\ensuremath{\gtrsim}${q}_{x}$ the temporal decay has a strongly nonexponential component, reflecting the activated dynamics of this system. As the ordering transition is approached, this dynamic length ${l}_{x}$ diverges as ${l}_{x}$\ensuremath{\sim}exp(c${\ensuremath{\xi}}^{\ensuremath{\psi}}$), where \ensuremath{\xi} is the static correlation length, and the activation free-energy barriers are of order cT${\ensuremath{\xi}}^{\ensuremath{\psi}}$ (T being the temperature and c a nonuniversal constant).