Transport Properties Diffusivity, Viscosity, Heat Conduction

Transport Properties (Diffusivity, Viscosity, Heat Conduction)... 

In addition to the equation of state, it will be necessary to describe other thermodynamic properties of the fluid. These include specific heat, enthalpy, entropy, and free energy. For ideal gases the thermodynamic properties usually depend on temperature and mixture composition, with very little pressure dependence. Most descriptions of fluid behavior also depend on transport properties, including viscosity, thermal conductivity, and diffusion coefficients. These properties generally depend on temperature, pressure, and mixture composition. 

After writing mass balances, energy balances, and equilibrium relations, we need system property data to complete the formulation of the problem Here, we divide the system property data into thermodynamic, transport, transfer, reaction properties, and economic data. Examples of thermodynamic properties are heat capacity, vapor pressure, and latent heat of vaporization. Transport properties include viscosity, thermal conductivity, and diffusivity. Corresponding to transport properties are the transfer coefficients, which are friction factor and heat and mass transfer coefficients. Chemical reaction properties are the reaction rate constant and activation energy. Finally, economic data are equipment costs, utility costs, inflation index, and other data, which were discussed in Chapter 2. 

The kinetic motion of molecules may cause them to change their spatial distribution through successive random movements. This is the process of diffusion, which is a transport property. Other transport properties include viscosity, electrical conductivity, and thermal conductivity. While diffusion is concerned with the transport of matter, these are associated with the transport of momentum, electrical charge, and heat energy, respectively. Transport is driven in each case by a gradient in the respective property. Thus, the diffusion rate of species A is given by Pick s law. 

ELDAR contains data for more than 2000 electrolytes in more than 750 different solvents with a total of 56,000 chemical systems, 15,000 hterature references, 45,730 data tables, and 595,000 data points. ELDAR contains data on physical properties such as densities, dielectric coefficients, thermal expansion, compressibihty, p-V-T data, state diagrams and critical data. The thermodynamic properties include solvation and dilution heats, phase transition values (enthalpies, entropies and Gibbs free energies), phase equilibrium data, solubilities, vapor pressures, solvation data, standard and reference values, activities and activity coefficients, excess values, osmotic coefficients, specific heats, partial molar values and apparent partial molar values. Transport properties such as electrical conductivities, transference numbers, single ion conductivities, viscosities, thermal conductivities, and diffusion coefficients are also included. 

The Helfand moment is the center of mass, energy or momentum of the moving particles, depending on whether the transport property is diffusion, heat conductivity, or viscosity. The Helfand moments associated with the different transport properties are given in Table III. Einstein formula shows that the Helfand moment undergoes a diffusive random walk, which suggests to set up a... 

The physical properties of solvents greatly influence the choice of solvent for a particular application. The solvent should be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapor pressure, temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity, also need to be considered. Electrical, optical, and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant, too. Furthermore, molecular... 

Just as diffusive momentum transfer depends on a transport property of the fluid called viscosity, diffusive heat transfer depends on a transport property called thermal conductivity. This section provides a brief discussion on the functional forms of thermal conductivity, with the intent of facilitating the understanding of the heat-transfer discussions in the subsequent sections on the conservation of energy. 

This chapter gives an overview of the fundamental physical basis for the thermodynamic (enthalpy, entropy and heat capacity) properties of chemical species. Other chapters discuss chemical kinetics and transport properties (viscosity, thermal conductivity, and diffusion coefficients) in a similar spirit. 

In the following section molecular collisions are discussed briefly in order to define the notation appearing in the exact expressions for the transport coefficients. Diffusion is treated separately from the other transport properties in Section E.2 because it has been found [7] that closer agreement with the exact theory is obtained by utilizing a different viewpoint in this case. Next, a general mean-free-path description of molecular transport is presented, which is specialized to the cases of viscosity and heat conduction in Sections E.4 and E.5. Finally, dimensionless ratios of transport coefficients, often appearing in combustion problems, are defined and discussed. The notation throughout this appendix is the same as that in Appendix D. 

Transport and interfacial properties are often neglected in favor of research and development efforts directed to phase equilibrium properties. Even less attention has been devoted to such properties for electrolytes and polymers. In industrial practice, the needs for transport and interfacial properties are numerous, i.e., detailed design of heat exchangers, and distillation column tray and packing sizing calculations. Both predictive and correlative models are needed for liquid viscosity, thermal conductivity, surface tension, diffusion coefficients, etc. 

Catalytic supercritical water oxidation is an important class of solid-catalyzed reaction that utilizes advantageous solution properties of supercritical water (dielectric constant, electrolytic conductance, dissociation constant, hydrogen bonding) as well as the superior transport properties of the supercritical medium (viscosity, heat capacity, diffusion coefficient, and density). The most commonly encountered oxidation reaction carried out in supercritical water is the oxidation of alcohols, acetic acid, ammonia, benzene, benzoic acid, butanol, chlorophenol, dichlorobenzene, phenol, 2-propanol (catalyzed by metal oxide catalysts such as CuO/ZnO, Ti02, MnOz, KMn04, V2O5, and Cr203), 2,4-dichlorophenol, methyl ethyl ketone, and pyridine (catalyzed by supported noble metal catalysts such as supported platinum). ... 

In turbulent flows, the transport of momentum, heat, and/or individual species within gradients of velocity, temperature, and concentration is caused predominantly by the chaotic motion of elements of fluid (eddies). This mixing process transports properties much more effectively than the molecular processes identified with viscosity, thermal conductivity, and diffusion. A rather complete description of these processes is given in Refs. 71-73. 

Numerical solutions to simple thermal energy transport problems in the absence of radiative mechanisms require that the viscosity fi, density p, specific heat Cp, and thermal conductivity k are known. Fourier s law of heat conduction states that the thermal conductivity is constant and independent of position for simple isotropic fluids. Hence, thermal conductivity is the molecular transport property that appears in the linear law that expresses molecular transport of thermal energy in terms of temperature gradients. The thermal diffusivity a is constructed from the ratio of k and pCp. Hence, a = kjpCp characterizes diffusion of thermal energy and has units of length /time. 

All three transport properties, viscosity, diffusivity, and thermal conductivity, are important in reactor design. Viscosity is a measure of momentum transfer, diffusivity of mass transfer, and thermal conductivity of heat transfer. 

In this book, we use Truesdell s conceptually most simple idea of mixture [10-12] and we confine ourselves to a classical task important in applications we study the mixture of chemically reacting fluids (mechanically non-polar, cf. Secf.4.3 and Rem. 17 in Chap. 3), with the same temperature of all constituents and with linear transport properties (like diffusion, heat conduction, viscosity generalization on nonlinear transport, see [60, 71, 72, 104]). This model, called shortly the linear fluid mixture, contains as special cases non-reacting fluid mixtures and some further ones (see Sect. 4.8). 

This chapter addresses the three fundamental transport properties characteristic of Chemical Engineering heat transfer, momentum transfer, and mass transfer. The underlying physical properties that represent each of these phenomena are thermal conductivity, viscosity, and diffusivity and the equations describing them have a similar form. Heat flux through conduction is expressed as a temperature gradient with units of W m . Note that heat flux, mass flux, etc. are physical measures expressed with respect to a surface (m ). Momentum flux in laminar flow conditions is known as shear stress and has units of Pa (or N m ) it equals the product of viscosity and a velocity gradient. Finally, molar flux (or mass flux) equals the product of diffusivity and a concentration gradient with units of mol m s These phenomena are expressed mathematically as shown in Table 7.1. 

The aim of this chapter is to discuss the molecular transport laws of matter, of heat and of momentum, and to define the properties which characterize them diffusion coefficient, thermal conductivity and viscosity. 

We have seen that the transport processes (momentum, heat, and mass) each involve a property of the system (viscosity, thermal conductivity, diffusivity). These properties are called the transport coefficients. As system properties they are functions of temperature and pressure. 

The properties of ions in solution depend, of course, on the solvent in which they are dissolved. Many properties of ions in water are described in Chapters 2 and 4, including thermodynamic, transport, and some other properties. The thermodynamic properties are mainly for 25°C and include the standard partial molar heat capacities and entropies (Table 2.8) and standard molar volumes, electrostriction volumes, expansibilities, and compressibilities (Table 2.9), the standard molar enthalpies and Gibbs energies of formation (Table 2.8) and of hydration (Table 4.1), the standard molar entropies of hydration (Table 4.1), and the molar surface tension inaements (Table 2.11). The transport properties of aqueous ions include the limiting molar conductivities and diffusion coefficients (Table 2.10) as well as the B-coefficients obtained from viscosities and NMR data (Table 2.10). Some other properties of... 

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