Mixtures of fluids

PRESSURE SYSTEM Defined in the Pressure System Safety Regulations 2000 as a system containing one or more pressure vessels of rigid construction, any associated pipework and protective devices the pipework with its protective devices to which a transportable gas container is, or is intended to be, connected or a pipeline and its protective devices which contains or is liable to contain a relevant fluid, but does not include a transportable gas container. Here relevant fluid is steam any fluid or mixture of fluids which is at a pressure of >0.5 bar above atmospheric pressure, and which fluid or a mixture of fluids is a gas, or a liquid which would have a vapour pressure of >0.5 bar above atmospheric pressure when in equilibrium with its vapour at either tlie actual temperature of the liquid or 17.5°C or a gas dissolved under pressure in a solvent contained in a porous substance at ambient temperamre and which could be released from the solvent with the application of heat. 

As we have noted in Sec. II, one of the methods leading to the so-called singlet equations for the density profiles, originally initiated for simple fluids in Ref. 24, starts from considering a mixture of fluid particles and another species of hard spheres at density pq and diameter Dq, taking next the limit Pg - 0,Dg- oo. 

The thermodynamic properties of mixtures of fluids are usually not known. A crude estimate of a mixture s internal energy can be made by summing the internal energy of each component. 

Reffactometry is as unspecific as is absorption spectrometry, but has its merits if applied under well-characterized conditions. In 1984, Haubenreisser et al.30 reported on (a) the relation between transmission and refractive index characteristics, (b) the sensitivity, and (c) the working range of a fiber optic refractometer of mixtures of fluids. The U-shaped fiber reffactometer was shown to be useful for various physical quantities that vary with refractive index. 

The model calculated in this manner predicts that two minerals, alunite [KA13(0H)6(S04)2] and anhydrite (CaSC>4), are supersaturated in the fluid at 175 °C, although neither mineral is observed in the district. This result is not surprising, given that the fluid s salinity exceeds the correlation limit for the activity coefficient model (Chapter 8). The observed composition in this case (Table 22.1), furthermore, actually represents the average of fluids from many inclusions and hence a mixture of hydrothermal fluids present over a range of time. As noted in Chapter 6, mixtures of fluids tend to be supersaturated, even if the individual fluids are not. 

Type A Systems, All Fluid Components The state of the system is a fluid or a mixture of fluids at to- For example, the vessel may contain solvent, dissolved organics, and dissolved organometallics, ligands, inorganics (pre-dissolve if the natural state of the solute is solid). 

Filtration is the separation of undissoived particulate solids from a mixture of fluid and solid. The separation is brought about by passage of the fluid thru a pervious septum (filter medium) in or on which the solids are retained. A driving force (gravity, vacuum, pressure, or centrifugal force) produces the flow. Filter aids may be added to the fluid before filtering to counterbalance the unfavorable characteristics of badly filtering materials... 

Emulsions are mixtures of fluids that are immiscible. Usually one fluid is present as small droplets in another phase. There are emulsions of oil in water, called oil-inwater emulsions (abbreviated as O/W), but also emulsions of water in oil (W/O). The droplet phase is called the dispersed phase, the surrounding phase the continuous phase. Emulsions are important in a great diversity of products. Some examples are ... 

Mass transfer is the transport of one or more components of a mixture, of fluid or solid material, within a phase12 or over the phase boundary. Mass transport within a phase up to the phase boundary is called mass transfer. When this occurs over the phase boundary into another phase, it is then known as overall mass transfer. These terms correspond to those in heat transfer. 

Thermal diffusion is the phenomenon of subjecting a homogeneous mixture of fluids to a temperature gradient in consequence of which a partial separation of the mixture into its constituents results. 

Equations 9.3-3 to 9.3-5 resemble those obtained in Sec. 9.1 for the ideal gas mixture. There is an important difference, however. In the present case we are considering an ideal mixture of fluids that are not ideal gases, so each of the pure-component properties here will not be an ideal gas property, but rather a real fluid property that must either be measured or computed using the techniques described in Chapter 6. Thus, the molar volume Vj is not equal to RT/P, and the fugacity of each species is not equal to the pressure. 

Foams are stable mixtures of fluid and gas the fluid is the external phase, and the gas is the internal phase (Figure 1). A surfactant used to impart stability to the mixture concentrates at the gas—liquid interface to reduce the surface tension and form stable lamellae. 

For a single-component system the temperatures at which evaporation and condensation, respectively, occur (on a planar interface) are identical, that is, they correspond to the saturation temperature Fsar In a mixture of fluids, however, the temperature at which the vaporized mixture begins to condense (the so-called dew point temperature 7 dew) is different (higher) than the temperature at which the mixture in liquid form begins to evaporate (the so-called bubble point temperature Tbub)- Thus, the condensate initially formed in condensation is richer in the less volatile component, and the vapor initially formed in evaporation is richer in... 

Usually, the gas supply system is simply a laboratory-sized cylinder. However, for applications where pure SF CO2 is inadequate, mixtures of fluids may be used. Mixtures of fluids may be made in two different ways (i) premixed fluids may be directly supplied in one unique cylinder or (ii) both fluids are supplied in separate cylinders and mixed before the pump, where the mixture is pressurized to the desired value. 

The purpose of this chapter is to test the combining rules that result from three approximations for random mixtures of fluids. The square-well (SW) approximation yields very good results for systems of small molecules. The complexity of the problem for large molecules, aggravated by the dependence of u(r) on the reduced density of the system, is outlined. 

For a mixture of fluids with equal viscosity, the stress tensor may be expressed as ... 

The transfer of heat in a fluid may be brought about by conduction, convection, diffusion, and radiation. In this section we shall consider the transfer of heat in fluids by conduction alone. The transfer of heat by convection does not give rise to any new transport property. It is discussed in Section 3.2 in connection with the equations of change and, in particular, in connection with the energy transport in a system resulting from work and heat added to the fluid system. Heat transfer can also take place because of the interdiffusion of various species. As with convection this phenomenon does not introduce any new transport property. It is present only in mixtures of fluids and is therefore properly discussed in connection with mass diffusion in multicomponent mixtures. The transport of heat by radiation may be ascribed to a photon gas, and a close analogy exists between such radiative transfer processes and molecular transport of heat, particularly in optically dense media. However, our primary concern is with liquid flows, so we do not consider radiative transfer because of its limited role in such systems. 

For the cases where a major portion of the heat is to be removed by latent or sensible heat transfer to a fluid inside the container, a different method of design is employed. All the power is transferred to the fluid but the y power transfer depends on the y absorption properties of the combined mixture of fluid and heat-generating substances within the vessel. Self-absorption calculations, using Fig. 10-6, are required. The design method is best illustrated by the solution of a typical problem. 

The physical analogy to the averaging problem occurs when a sample consists of a mixture of fluids, as can occur when a well draws water from two or more producing intervals. In this case, the mixture may be supersaturated even when the individual fluids are not. 

Adkins, J.E. Non-Unear diffusion, I diffusion and flow of mixtures of fluids. PhU. Trans. Roy. Soc. Lond. A255,607-633 (1963)... 

Muller, I. A thermodynamic theory of mixtures of fluids. Arch. Ration. Mech. Anal. 28, 1-39... 

Muller, I. Thermodynamics of Fluids and Mixtures of Fluids. Gesamthochschule Paderbom, Paderbom (1976)... 

Muller, I. Rational thermodynamics of mixtures of fluids. In GrioU, G. (ed.) Thermodynamics and Constitutive Equations. Lecture Notes in Physics, vol. 228. Springer, Berlin (1985)... 

Chemically Reacting Mixture of Fluids with Linear Transport Properties... 

In this book, we confine ourselves only to the special case of fluids mixture (4.128) which is linear in vector and tensor variables.We denote it as the chemically reacting mixture of fluids with linear transport properties or simply the linear fluid mixture [56, 57, 64, 65]. Then (see Appendix A.2) the scalar, vector and tensor isotropic functions (4.129) linear in vectors and tensors (symmetrical or skew-symmetrical) have the forms ... 

We now deduce basic thermodynamic properties of the mixture of fluids with linear transport properties discussed in Sect. 4.5. Among others, we show that Gibbs equations and (equilibrium) thermodynamic relationships in such mixtures are valid also in any non-equilibrium process including chemical reactions (i.e. local equilibrium is proved in this model) [56, 59, 64, 65, 79, 138]. 

Therefore, the classical relations of thermochemistry were obtained. Especially, the Gibbs equations (4.201)-(4.206) are valid in arbitrary process in this chemically reacting mixture of fluids with linear transport properties, i.e. the principle of local equilibrium is valid in this mixture. But we show in the following relations that this accord with classical thermochemistry (e.g. [138]) is not quite identical indeed, if we differentiate (4.211) and use (4.22), (4.23) we obtain... 

At the end, we summarize the results of the model of a reacting mixture of fluids with linear transport properties from Sects. 4.5 and 4.6 (properties such as kinematics, stoichiometry and balances of mass, momentum and their moment, energy and entropy inequality are as in Sects. 4.2, 4.3 and 4.4). Constitutive equations, their properties and final form of entropy production are given in the end of Sect. 4.5 (from Eq. (4.156)), further thermodynamic quantities and properties are given at the... 

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