Single-component fluid

Single-component fluid. For a single component, y 22 y222  

---

For a single component fluid, such as methane, a Mollier diagram, such as Figure 4-7, can be used to calculate temperature drop directly. 

In the case of a single-component fluid, both equations (14) and (16) reduce to the relations obtained by Wertheim [52], by Lovett et al. [53], and by Sullivan and Stell [54]. 

Equations 12.62 and 12.63 are for boiling single component fluids for mixtures the coefficient will generally be lower than that predicted by these equations. The equations can be used for close boiling range mixtures, say less than 5°C and for wider boiling ranges with a suitable factor of safety (see Section 12.11.6). 

Efforts have been made to develop EOS for detonation products based on direct Monte Carlo simulations instead of on analytical approaches.35-37 This approach is promising given recent increases in computational capabilities. One of the greatest advantages of direct simulation is the ability to go beyond van der Waals 1-fluid theory, which approximately maps the equation of state of a mixture onto that of a single component fluid.38... 

Of course, if considering a single-component fluid or a fluid in which the differences between fluid components is negligible, then the average velocity is simplified to... 

In later chapters we discuss the evaluation of transport properties for multicomponent mixtures of gases. At this point, however, the intent is to provide only a brief introduction on viscosity, since it is the principal fluid property that appears in the Navier-Stokes equations. The discussion here is limited to single-component fluids. 

Introducing specific length and velocity scales provides a more intuitive approach to nondi-mensionalization. In this section the thermal-energy equation is also included in the analysis. Assuming constant transport properties and a single-component fluid, a subset of the governing equations is derived from Section 6.2 as... 

Let us consider the simplest case of a homogeneous, single-component fluid of fixed mass, with two degrees of freedom. We seek to evaluate a general partial derivative V of the form... 

The single-component fluid is far from its thermodynamic critical point (T, < 0.9Tct or PI < 0.5Pcr). Note the or if the relieving temperature, for example, is equal to the critical temperature but the relieving pressure is below 50% of the critical pressure, then the condition is verified. 

The single-component fluid is far from its thermodynamic critical point (Tj < 0.9TcrorP1 < 0.5PCT). 

For any single component fluid at constant temperature and composition,... 

II. NONPRIMITIVE MODEL OF AN INHOMOGENEOUS SINGLE COMPONENT FLUID... 

The actual consequence of H2O undersaturation in the context discussed here is that mixed fluid phases, i.e., solutions, will shift phase equilibria in P-T-X space, whereas the presence or absence of a single component fluid (e.g., a purely aqueous fluid) determines whether or not a reaction takes place, without changing the reaction s position in P-T space. 

The governing equations determining the evolution of single-component fluid flow are ... 

Strictly speaking, for a multicomponenet fluid, this should be the mass average velocity v as defined in Note 2. However, in this section we restrict our discussion to a single-component fluid for which the volume average velocity u and the mass average velocity v are equal. 

Vapor-Liquid Equilibrium in a Single-Component Fluid.351... 

To illustrate the use of this equilibrium criterion, consider the very simple, initially nonuniform system shown in Fig. 7.1-1. There a single-phase, single-component fluid in an adiabatic, constant-volume container has been divided into two subsystems by an imaginary-boundary. Each of these subsystems is assumed to contain the same chemical species of uniform thermodynamic properties. However, these subsystems are open to the flow of heat and mass across the imaginary internal boundary, and their temperature and-pressure need not be the same. For the composite system consisting of the two subsystems, the total mass (though, in fact, we will use number of moles), internal energy, volume, and entropy, all of which are extensive variables, are the sums of these respective quantities for the two subsystems, that is. 

A further possibility would be to use the VDW procedure but replace Equation 39 with some better hard-sphere isotherm such as Equation 15. Results of this procedure which are labelled VDW-1 (to indicate that a single-component fluid is used to obtain an expression for A0 and P0) are given in Table VI. The results are somewhat worse than the VDW results. 

Equations 71 and 72 or 73 and 74 can be used with any equation of state and not just with the VDW or LHW equations. The physical content of these equations is that, within the VDW-1 approximation, the equation of state of the mixture is (apart from the entropy of mixing terms) identical to that of a single-component fluid specified by the parameters given by Equations 71 and 72 or 73 and 74. 

The momentum equation, as represented by the Navier-Stokes equation, is not restricted to a single-component fluid but is valid for a multicomponent solution or mixture so long as the external body force is such that each species is acted upon by the same external force (per unit mass), as in the case with gravity. In the following section we consider external forces associated with an applied external field, which differ for different species. The reason for there being no distinction between the various contributions to the stress tensor associated with diffusive transport is that the phenomenological relation for the stress is unaltered by the presence of concentration gradients. This is seen from the fact that the stress tensor must be related to the spatial variations in fluid... 

We restrict ourselves here for simplicity to a single-component fluid with 0(1 2) that is orientation independent for all r. We expect the Fourier transform c k) of c(l 2) [Eq. (60)] to have the form, as ->0,... 

The most difficult task is to identify the physical quantities that comprise , s. Several researchers [1-6] have considered 17 itself as non-equilibrium entropy and in the case of a single component fluid, the physical fluxes of heal and dissipalive momenlum are laken as j s. In ihis coniexi, Eq. (1) explicilly reads as. 

---