One-phase fluid system

We concentrate here on the stability of our model of regular linear fluid (giving the classical Gibbs stability) modelling one-phase fluid. We try to And such properties of constitutive equations which permit to realize equilibrium states in our model at some p, T (and also motivate some of the regularity conditions above). If such stability properties are not fulfilled then, typically, our (one-phase) fluid system disintegrates into more phases, cf. Rem. 45. 

In an equilibrium one-phase fluid system of one substance, three macroscopic variables such as temperature, volume, and amount of substance can be independent variables and can be used to specify the macroscopic equilibrium state of the system. At least one of the variables used to specify the state of the system must be proportional to the size of the system (be extensive). Other macroscopic variables are mathematical functions of the independent variables. 

The intensive state, which includes only intensive variables (variables that are independent of the size of the system), is specified by only two variables in the case of an equiUbrium one-phase fluid system of one substance. 

Many of the thermodynamic equations that we have presented are valid only in the case that surface contributions to the energy can be neglected. For example, we assumed that the thermodynamic energy of a one-component one-phase fluid system depended on T, V, and n, but not on the surface area. Although this is ordinarily an excellent approximation, there is a significant surface contribution to the energy of a liquid in the case of a small droplet or a liquid in a small capillary tube. 

When a pure liquid is placed in an evacuated bulb, molecules will leave the liquid phase and enter the gas phase until the pressure of the vapor in the bulb reaches a definite value, which is determined by the nature of the liquid and its temperature. This pressure is called the vapor pressure of the liquid at a given temperature. The equilibrium vapor pressure is independent of the quantity of liquid and vapor present, as long as both phases exist in equilibrium with each other at the specified temperature. As the temperature is increased, the vapor pressure also increases up to the critical point, at which the two-phase system becomes a homogeneous, one-phase fluid. 

Equation (11.2) is the fundamental property relation for single-phase fluid systems of constant or variable mass and constant or variable composition, and is tlie foundation equation upon which the structure of solution thermodynamics is built. For the special case of one mole of solution, n = 1 and n, = xf. 

Alder and Wainwright [5,6] published the first paper of a molecular dynamics simulation of a condensed phase fluid system and this paper began a trend that did have a strong impact on statistical mechanics. These authors tackled one of the open questions of the day, whether a solid-fluid phase transition existed in a system of hard spheres. This problem could not be solved by existing analytical methods and Alder and Wainwright s simulation demonstrated that such analytically intractable problems could be studied and solved by direct MD simulation of the equations of motion of a many-body system. Of course, the simulation was modest by today s standards and was carried out on systems containing 32 and 108 hard spheres. This research set the stage for the development of MD as a basic tool in statistical mechanics. 

Another model for which (2.1), (2.2) may be applied is the two-phase fluid system without memory which models two-phase equilibria in pure fluid. It has one constituent in two phases which are uniform bodies where the masses and volumes of which are denoted by m and respectively. For the whole volume... 

These conditions identify both vapor-liquid and liquid-liquid critical points. For vapor-liquid equilibria, they are satisfied when the spinodal coincides with the vapor-liquid saturation curve. However, that point need not occur either at the maximum in the saturation envelope or at the maximum in the spinodal see Figure 8.12. Along a spinodal the one-phase metastable system is balanced on the brink of an instability at a critical point that balance coincides with a two-phase situation and the resulting fluctuations cause critical opalescence, just as they do at pure-fluid critical points. 

Fieid—Fiow Fractionation. Field-flow fractionation (FFF) employs a one-phase chromatographic system (251,252). Commercial instrumentation is available from Postnova Analytics and Tecan. Separation occurs in a thin channel containing a single moving fluid. The field applied across the channel may be selected on the basis of the solute. Possible fields include sedimentation, cross-flow, concentration, dielectric, thermal, and magnetic. A book (253) and a review (254) of this technique and its comparison with GPC for the characterization of polymer molecular weights have been published. 

Figure 6. Tentative boundary surface for one-phase fluid conditions at 1000 bar for the ternary system HiO-CO -NaCl...

A system is defined as the material object that one is studying at a specific time. The state of a system is the circumstance in which it is found, expressed by numerical values of a sufficient set of variables. A macroscopic system has two important kinds of states the macroscopic state, which concerns only variables pertaining to the system as a whole, and the microscopic state, which pertains to the mechanical variables of individual molecules. The equilibrium macroscopic state of a one-phase fluid (liquid or gas) system of one component is specified by the values of three independent state variables. All other macroscopic state variables are dependent variables, with values given by mathematical functions of the independent variables. 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

Thermoplastic elastomers are often multiphase compositions in which the phases are intimately dispersed. In many cases, the phases are chemically bonded by block or graft copolymerization. In others, a fine dispersion is apparentiy sufficient. In these multiphase systems, at least one phase consists of a material that is hard at room temperature but becomes fluid upon heating. Another phase consists of a softer material that is mbberlike at RT. A simple stmcture is an A—B—A block copolymer, where A is a hard phase and B an elastomer, eg, poly(styrene- -elastomer- -styrene). 

Many times solids are present in one or more phases of a solid-hquid system. They add a certain level of complexity in the process, especially if they tend to be a part of both phases, as they normally will do. Approximate methods need to be worked out to estimate the density of the emulsion and determine the overall velocity of the flow pattern so that proper evaluation of the suspension requirements can be made. In general, the solids will behave as though they were a fluid of a particular average density and viscosity and won t care much that there is a two-phase dispersion going on in the system. However, if solids are being dissolved or precipitated by participating in one phase and not the other, then they will be affected by which phase is dispersed or continuous, and the process will behave somewhat differently than if the solids migrate independently between the two phases within the process. 

Chapter 11 treats reactors where mass and component balances are needed for at least two phases and where there is interphase mass transfer. Most examples have two fluid phases, typically gas-liquid. Reaction is usually confined to one phase, although the general formulation allows reaction in any phase. A third phase, when present, is usually solid and usually catalytic. The solid phase may be either mobile or stationary. Some example systems are shown in Table 11.1. 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

If simple sample pretreatment procedures are insufficient to simplify the complex matrix often observed in process mixtures, multidimensional chromatography may be required. Manual fraction collection from one separation mode and re-injection into a second mode are impractical, so automatic collection and reinjection techniques are preferred. For example, a programmed temperature vaporizer has been used to transfer fractions of sterols such as cholesterol and stigmasterol from a reversed phase HPLC system to a gas chromatographic system.11 Interfacing gel permeation HPLC and supercritical fluid chromatography is useful for nonvolatile or thermally unstable analytes and was demonstrated to be extremely useful for separation of compounds such as pentaerythritol tetrastearate and a C36 hydrocarbon standard.12... 

This regime is characterized by the presence of one continuous fluid phase and one discrete fluid phase in tubular systems. The existence of the discrete phase generates a large interfacial area per unit tube volume for all flow configurations included in this regime. For that reason, Regime IV is of pragmatic interest when interphase heat and mass transfer are of key importance. 

The ancient categories of water, earth, and air persist in classifying the phases that make up geochemical systems. For purposes of constructing a geochemical model, we assume that our system will always contain a fluid phase composed of water and its dissolved constituents, and that it may include the phases of one or more minerals and be in contact with a gas phase. If the fluid phase occurs alone, the system is homogeneous the system when composed of more than one phase is heterogeneous. 

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