Homogeneous fluid system

Equations 54 and 58 through 60 are equivalent forms of the fundamental property relation apphcable to changes between equihbtium states in any homogeneous fluid system, either open or closed. Equation 58 shows that ff is a function of 5" and P. Similarly, Pi is a function of T and C, and G is a function of T and P The choice of which equation to use in a particular apphcation is dictated by convenience. Elowever, the Gibbs energy, G, is of particular importance because of its unique functional relation to T, P, and the the variables of primary interest in chemical technology. Thus, by equation 60,... 

The definitions of enthalpy, H, Helmholtz free energy. A, and Gibbs free energy, G, also give equivalent forms of the fundamental relation (3) which apply to changes between equiUbrium states in any homogeneous fluid system ... 

To complete the thermodynamic description of a homogeneous fluid system, we need to specify an equation of state relating three thermodynamic properties. We shall not generally be concerned with gases, but we note that away from the critical point for moderate and low densities the perfect or ideal... 

Figure 2 Illustrations for homogeneous fluid system (left) and inhomogeneous fluid system (right). The spheres in different color denote different components.

In this section we discuss the frequency spectrum of excitations on a liquid surface. Wliile we used linearized equations of hydrodynamics in tire last section to obtain the density fluctuation spectrum in the bulk of a homogeneous fluid, here we use linear fluctuating hydrodynamics to derive an equation of motion for the instantaneous position of the interface. We tlien use this equation to analyse the fluctuations in such an inliomogeneous system, around equilibrium and around a NESS characterized by a small temperature gradient. More details can be found in [9, 10]. 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

Fluid mixing is a unit operation carried out to homogenize fluids in terms of concentration of components, physical properties, and temperature, and create dispersions of mutually insoluble phases. It is frequently encountered in the process industry using various physical operations and mass-transfer/reaction systems (Table 1). These industries include petroleum (qv), chemical, food, pharmaceutical, paper (qv), and mining. The fundamental mechanism of this most common industrial operation involves physical movement of material between various parts of the whole mass (see Supplement). This is achieved by transmitting mechanical energy to force the fluid motion. 

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

Consider a closed, nonreacting PTT system containing n moles of a homogeneous fluid mixture. The mole numbers of the individual chemical species sum to... 

Partial Molar Properties Consider a homogeneous fluid solution comprised of any number of chemical species. For such a PVT system let the symbol M represent the molar (or unit-mass) value of any extensive thermodynamic property of the solution, where M may stand in turn for U, H, S, and so on. A total-system property is then nM, where n = Xi/i, and i is the index identifying chemical species. One might expect the solution propei fy M to be related solely to the properties M, of the pure chemical species which comprise the solution. However, no such generally vahd relation is known, and the connection must be establi ed experimentally for eveiy specific system. 

For some fluid systems, the motionless mixer may not practically achieve total homogeneity. In some situations of widely diverse fluid densities, the centrifugal motion created may throw some of the fluid to the outside of the flow path when it emerges from the unit. These are concepts to examine with the manufacturer, as only the manufacturer s data can properly predict performance, and the design engineer should not attempt to actually physically design a unit. 

The flow problems considered in previous chapters are concerned with homogeneous fluids, either single phases or suspensions of fine particles whose settling velocities are sufficiently low for the solids to be completely suspended in the fluid. Consideration is now given to the far more complex problem of the flow of multiphase systems in which the composition of the mixture may vary over the cross-section of the pipe or channel furthermore, the components may be moving at different velocities to give rise to the phenomenon of slip between the phases. 

As pointed out in the previous chapter, the separation of a homogeneous fluid mixture requires the creation of another phase or the addition of a mass separation agent. Consider a homogeneous liquid mixture. If this liquid mixture is partially vaporized, then another phase is created, and the vapor becomes richer in the more volatile components (i.e. those with the lower boiling points) than the liquid phase. The liquid becomes richer in the less-volatile components (i.e. those with the higher boiling points). If the system is allowed to come to equilibrium conditions, then the distribution of the components between the vapor and liquid phases is dictated by vapor-liquid equilibrium considerations (see Chapter 4). All components can appear in both phases. 

Both homogeneous and heterogeneous reaction systems are frequently encountered in commercial practice. The term homogeneous reaction system is restricted in this text to fluid systems in... 

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. 

Initial Times Immediately after the introduction of a reagent into a CSTR-recycle system, and for the first ca. 100 s, the compositions of the fluid elements throughout the liquid phase homogeneous catalytic system are measurably different. 

Longer Reaction Times For homogeneous catalytic systems without reactants in a second phase (P or Pl), the fluid elements in the CSTR, recycle loop, and cells are quite similar at times greater than ca. 100 s. Furthermore, for homogeneous catalytic systems with reactants in a second phase (Pq or Pj ), the fluid elements in the CSTR, recycle loop, and cells are quite similar at times greater than ca. 100 s if transport is fast compared to reaction i. e. Hatta regimes F-H. 

The third reason for using fluid-fluid systems is to obtain a vastly improved product distribution for homogeneous multiple reactions than is possible by using the single phase alone. Let us turn to the first two reasons, both of which concern the reaction of materials originally present in different phases. 

A multicomponent solid material has many more degrees of freedom in arrangement than an isotropic and homogeneous fluid. The thermal conductivity of a composite material, formed by the lamination of sheets of two components with different thermal conductivities, is a well-analyzed system. When heat is flowing parallel to the sheet surfaces, the composite thermal conductivity is given by linear additivity of conductivities... 

In this section, we consider a solute or vapor diffusing through fluid-filled pores of a porous medium (note that both liquids and gases are called fluids). There are several reasons why in this case the flux per unit bulk area (that is, per total area occupied by the medium) is different from the flux in a homogeneous fluid or gas system. 

Two reasons are responsible, for the greater complexity of chemical reactions 1) atomic particles change their chemical identity during reaction and 2) rate laws are nonlinear in most cases. Can the kinetic concepts of fluids be used for the kinetics of chemical processes in solids Instead of dealing with the kinetic gas theory, we have to deal with point, defect thermodynamics and point defect motion. Transport theory has to be introduced in an analogous way as in fluid systems, but adapted to the restrictions of the crystalline state. The same is true for (homogeneous) chemical reactions in the solid state. Processes across interfaces are of great... 

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