Thermodynamic behavior of supercritical fluid mixtures

The recent surge of interest in supercritical extraction has brought the unusual properties of supercritical mixtures into the focus of attention. We discuss some of the properties of binary mixtures in a range around the gas-liquid critical line from the point of view of supercritical solubility. The general thermodynamic relationships that govern the enhancement of supercritical solubility are readily derived by a mathematical method introduced by Ehrenfest. The enhancement is governed by a strong divergence centered at a critical end point. We give the classical and nonclassical power-law behavior of the solubility along the experimental paths of constant temperature or pressure. The factor multiplying the strong divergence contains the partial molar volume or enthalpy of the solute in the supercritical phase. These partials are quite anomalous, especially if the mole fraction of the solute is small. They diverge at the solvent's critical point. We cite experimental evidence of these divergences, especially the results of recent experiments in dilute near-critical salt solutions. The anomalies found in these salt solutions are common to all dilute near-critical mixtures with a nonvolatile second component. We show that on experimentally convenient paths the solubility in a binary liquid mixture near its consolute points is not strongly enhanced. Finally, we sketch a nonclassical model based on the decorated lattice gas that can be used to describe supercritical solubility enhancement at low solubility, with the pure solvent used as a reference.Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Thermodynamics of fluid mixtures with two-point interactions

Of the many consequences of [3] in the thermodynamics of fluid mixtures, one concerns the possibility of discussing the Woods statement [5], which tells us either that the reversible changes of entropy vanish or that there are other reversible terms contributing to the Clausius-Duhem inequality that will cancel with the previous reversible ones. We show that the Woods hypothesis [5] does not generalize to all situations of interest. In addition, we consider a relatively new expression for the generalized forces $\text{p}{}_{\mathrm{\alpha \beta }}$. in the original Drumheller-Bedford terminology [6], for the Debye plasma system and the binary mixture of hard spheres.     

On the balance equations for chemically reacting mixtures

Summary Conservation postulates for a chemically reacting mixture are introduced in which the mass, momentum and energy gained and lost by a given constituent due to chemical reaction are explicitly included. The resulting local forms of the balance equations are derived.

---

Zu den Bilanzgleichungen chemisch reagierender Mischungen

Zusammenfassung Erhaltungspostulate für chemisch reagierende Mischungen werden eingeführt, in denen die von einer gegebenen Komponente chemisch gewonnene oder verlorene Masse, Impuls und Energie explizit auftreten. Die resultierenden lokalen Bilanzgleichungen werden hergeleitet.

---

---

This research was supported in part by National Science Foundation Grant ENG 75-18404.     

Flow of two-phase mixtures in a rotary mixer

On the basis of a hydrodynamic model of a multivelocity continuum, the flow of miscible materials over the working surface of a multistage centrifugal (rotary) mixer is investigated, and the optimal dimensions of the working sections required to obtain a high-quality mixture are determined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 2, pp. 226–233, February, 1977.     

Selective particle size analysis in binary submicron particle mixtures using density dependent differential sedimentation

Particle size characterization of heterogeneous mixtures is a challenging task, as it is not feasible to assign the measured signals to the individual components. Within this framework, the study proposes a method that applies the working principle of differential centrifugal sedimentation (DCS) in order to simultaneously separate and measure the denser component within a binary material mixture of submicron particles. The method was validated using a model system consisting of polyvinyl chloride (PVC) and diamond particles in a size range of 0.5 – 1.5 µm. The results proved that by applying a proper density gradient fluid, the diamond particles can be selectively analyzed by hindering the sedimentation of the lighter PVC component. Furthermore, a very promising application could be found with respect to wet fine grinding processes in stirred media mills. In fact, the approach was utilized to individually determine the particle size distribution of the grinding media wear within an ultrafine organic product. Despite the low quantity of wear particles, it was possible to separate them from the organic product under appropriate density conditions. The size distributions of both the wear and the product particles were validated with SEM images, confirming the feasibility of the method.     

Analysis of fluid equations by group methods

Summary Using the machinery of Lie-group analysis several equations arising in fluid mechanics are studied. In particular, the Burgers' equation, the KdV equation, the Hopf equation, the two-dimensional KdV equation and the Lin-Tsien equation are analyzed. In all cases the particular group includes arbitrary functions of time which permit the transformation of time-dependent equations into the corresponding time-independent ones. Infinitely many time-dependent solutions are associated with each steady solution. Some solutions are constructed.Research supported by U.S. Army Grant DAAG-29-84-K-0083.Research supported by a NATO-CNR fellowship.     

The correspondence between equations of thermodiffusion and theory of mixtures

Summary The balance equations of mass, momentum, energy and entropy have been studied in the paper. A comparison has been made between these equations and equations describing conjugate thermodiffusion flows in solids.With 2 FiguresThis paper has been written during my Humboldt fellowship at Ruhr-University in Bochum.     

Transport properties of fluid mixtures in the critical region

Transport properties of fluid mixtures exhibit anomalous behavior near the vapor-liquid critical line. These anomalies are a result of long-range fluctuations in the system in the vicinity of a critical point. We use mode-coupling theory to describe the critical enhancements of the thermal conductivity, the viscosity, the mutual diffusivity, and the thermal-diffusion coefficients of binary mixtures. The resulting expressions not only are valid in the asymptotic critical region but also describe the crossover to regular behavior far away from a critical point. The crossover functions depend on the thermodynamic properties of the mixtures, background values of all transport coefficients, and two concentration-dependent cutoff wave numbers. We compare the proposed crossover model with experimental thermal-conductivity data for mixtures of carbon dioxide and ethane in the critical region and find good agreement between theory and experiment.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Toward a theory of fluid mixtures with two-point interactions

We describe a fluid mixture in those situations where the microscopic particles can be considered to interact according to the laws of classical mechanics. It motivates our strong feeling that some essential changes in the form of macroscopic equations governing the behavior of a mixture of fluids are necessary (for the better understanding of the fundamental processes in the system). We provide a clue in the determination of the limits of validity of the Drumheler-Bedford approach [5] to the mixture theory and strongly generalize their main results.     

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 L²- 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.     

Reproducing polynomial particle methods for boundary integral equations

Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen the effectiveness of meshless methods, Oh et al. developed meshfree reproducing polynomial particle (RPP) shape functions, patchwise RPP and reproducing singularity particle (RSP) shape functions with use of flat-top partition of unity. All of these approximation functions satisfy the Kronecker delta property. In this paper, we report that meshfree RPP shape functions, patchwise RPP shape functions, and patchwise RSP shape functions effectively handle boundary integral equations with (or without) domain singularities.     

Wavelet transforms of some equations of fluid mechanics

Summary This paper explores the application of wavelet transforms to equations rather than to data sets. An entire class of wavelets, obtained from recursive shifts and changes in scale of Gaussian filters, transforms Laplacians into first order derivatives in the scale factor. As a result, parabolic and elliptic equations are transformed into first-order wave equations or into ordinary differential equations. Examples are given for the diffusion, Burgers, Poisson and Navier-Stokes equations, which are formally integrated by the method of characteristics. It is also shown that the even-indexed Gaussian wavelets decompose a function into the local spectral contributions to its amplitude as well as to its variance. This gives a simpler inversion formula and a new form of the convolution of wavelet transforms.     

Flow of a thermomicropolar fluid with stretch

The linear theory of micropolar fluids with stretch including the heat conduction and heat dissipation effects and restrictions imposed by the second law of thermodynamics are stated. The final equations of motion are discretized and solved for the case of a flow between two parallel and heated horizontal plates, stationary with respect to the flow. The effect of microstructure on heat transfer and fluid flow is studied thoroughly, including the contribution of terms involving inertial spin.

The microrotation boundary conditions are discussed along with their influence on the velocity, gyration, and microstretch fields as well as on heat transfer. An interesting and experimentally observed phenomenon involving the appearance of two maximums in the velocity profile is noted.     

Flow of non-newtonian fluid through porous media

This article shows the solutions of the nonlinear equations describing the transient flow of power law fluids through a porous medium. These are obtained by means of a generalized Boltzmann transformation approach for several cases of practical interest in interpretation of well-flow tests of short duration, used currently in oil reservoir engineering for obtaining the reservoir properties. A formulation of a moving boundary problem for a short time, appearing during the production of fluids by elastic decompression, is used in deriving the exact solutions in closed form for certain cases. The presence of a decompression front is physically demonstrated and its location in the reservoir at a given time is determined. The limitations associated with the generalized Boltzmann transformation approach in solving the nonlinear equations of power law fluid flow in oil reservoirs are shown and discussed with regard to the interpretation of the well-flow test analysis.