Transport properties Viscosity, Diffusion

For dilute, teal gases, where ternary and higher collisions can be neglected, the angle of deflection can be employed to evaluate a number of physical properties. Of course appropriate distributions of the values of g and b must be introduced. The resulting expressions for the virial coefficients and the transport properties (viscosity, diffusion and thermal conductivity) are quite complicated. The interested reader is referred to advanced books on this subject... 

Collision Cross-Section The model of gaseous molecules as hard, non-interacting spheres of diameter o can satisfactorily account for various gaseous properties such as the transport properties (viscosity, diffusion and thermal conductivity), the mean free path and the number of collisions the molecules undergo. It can be easily visualised that when two molecules collide, the effective area of the target is no1. The quantity no1 is called the collision cross-section of the molecule because it is the cross-sectional area of an imaginary sphere surrounding the molecule into which the centre of another molecule cannot penetrate. 

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. 

The important aspect for present purposes concerns the critical point, a combination of temperature and pressure above which there is no distinction between gas and liquid (P = 1 so F = 2) and thus no phenomena like evaporation and condensation. A compound in this condition is said to be a supercritical fluid (SCF) and possesses physical properties intermediate between those of a gas and a liquid (Table 4.2). A SCF retains solvent power properties approximately the same as those of the corresponding liquid, but simultaneously has the transport properties (viscosity, diffusivity) of the gaseous form. This combination makes an SCF ideal for extracting compounds that are soluble in the fluid in its liquid form, from pores and othCT occlusion sites within a solid matrix that are relatively inaccessible to the liquid. 

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... 

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. 

Interest in the use of SC solvents as a reaction media is founded upon recent advances in our understanding of their unique thermo-physical and chemical properties. Worthy of special note are those thermophysical properties (6) which can be manipulated as parameters to selectively direct the progress of desirable chemical reactions. These properties include the solvent s dielectric constant (7), ion product (8,9), electrolyte solvent power (10,11), transport properties"[viscosity (12), diffusion coefficients (13) and ion mobilities (14)], hydrogen bonding characteristics (15), and solute-solvent "enhancement factors" (6). All these properties are strongly influenced by the solvent s density P in the supercritical state. 

In addition to its unique solubility characteristics, a supercritical fluid possesses certain other physicochemical properties that add to its attractiveness. For example, even though it possesses a liquid-like density over much of the range of industrial interest, it exhibits gas-like transport properties of diffusivity and viscosity (Schneider, 1978). Additionally, the very low surface tension of supercritical fluids allows facile penetration into microporous materials to occur. 

Information about the size of molecules is also provided by the results of experiments on the rates of movement of the molecules in solution. Properties which depend on rates of movement are referred to as transport properties. If the motion occurs in aqueous solution, we can also speak of hydrodynamic properties. The most important transport properties are diffusion, viscosity, and sedimentation. The theory of transport properties will be dealt with in Chapter 11, after the treatment of chemical kinetics. 

Transport properties, including diffusion coefficients and viscosities, undergo changes in the critical region. As mentioned in Figure 1, these properties are useful in optimizing supercritical processes and the use of these properties should become more important as supercritical fluid process calculations develop. This discussion is presented to stress the density dependence of these properties. 

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). 

The stopping criterion depends on the specific properties to be fitted. For example, if the density deviates by less than 0.5 % from experiment, the corresponding force field is considered as optimal because the experiment is not more accurate either. The same holds for all other properties. However, the experimental accuracy is much lower for transport properties like diffusion coefficients or viscosity. 

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

A paiticularly attiactive and useful feature of supeicritical fluids is that these materials can have properties somewhere between those of a gas and a hquid (Table 2). A supercritical fluid has more hquid-hke densities, and subsequent solvation strengths, while possessiag transport properties, ie, viscosities and diffusivities, that are more like gases. Thus, an SCF may diffuse iato a matrix more quickly than a Hquid solvent, yet still possess a Hquid-like solvent strength for extracting a component from the matrix. 

Transport Properties Although the densities of supercritical fluids approach those of conventional hquids, their transport properties are closer to those of gases, as shown for a typical SCF such as CO9 in Table 22-12. For example, the viscosity is several orders of magnitude lower than at liquidlike conditions. The self-diffusion coefficient ranges between 10" and 10" em /s, and binaiy-diffusiou coefficients are similar [Liong, Wells, and Foster, J. Supercritical Fluids 4, 91 (1991) Catchpole and King, Ind. Eng. Chem. Research, 33,... 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

Since thermal agitation is the common origin of transport properties, it gives rise to several relationships among them, for example, the Nemst-Einstein relation between diffusion and conductivity, or the Stokes-Einstein relation between diffusion and viscosity. Although transport... 

Some 30 years ago, transport properties of molten salts were reviewed by Janz and Reeves, who described classical experimental techniques for measuring density, electrical conductance, viscosity, transport number, and self-diffusion coefficient. 

Transport Properties Although the densities of SCFs can approach those of conventional liquids, transport properties are more favorable because viscosities remain lower and diffusion coefficients remain higher. Furthermore, CO2 diffuses through condensed-liquid phases (e.g., adsorbents and polymers) faster than do typical solvents which have larger molecular sizes. For example, at 35°C the estimated pyrene diffusion coefficient in polymethylmethacrylate increases by 4 orders of magnitude when the CO2 content is increased from 8 to 17 wt % with pressure [Cao, Johnston, and Webber, Macromolecules, 38(4), 1335-1340 (2005)]. 

Using Eq. (2.6.18) the temperature dependence of various transport properties of polymers, such as diffusion coefficient D, ionic conductivity a and fluidity (reciprocal viscosity) 1/rj are described, since all these quantities are proportional to p. Except for fluidity, the proportionality constant (pre-exponential factor) also depends, however, on temperature,... 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

Transport Properties. Because the feed is primarily air and because substantial amounts of N2 and 02 are present in the effluent stream, we will assume that the fluid viscosity is that of air for purposes of pressure drop calculations. For the temperature range of interest, the fluid viscosity may be taken as equal to 320 micropoise. The pressure range of interest does not extend to levels where variations of viscosity with pressure need be considered. The effective diffusivities of naphthalene and phthalic anhydride in the catalyst pellet may be evaluated using the techniques developed in Section 12.2. 

TRANFIT A Fortran Computer Code Package for the Evolution of Gas-Phase Multicomponent Transport Properties, Kee, R. J., Dixon-Lewis, G., Wamatz, J., Coltrin, M. E. and Miller, J. A. Sandia National Laboratories, Livermore, CA, Sandia Report SAND86-8246, 1986. TRANFIT is a Fortran computer code (tranlib.f, tranfit.f, and trandatf) that allows for the evaluation and polynomial fitting of gas-phase multicomponent viscosities, thermal conductivities, and thermal diffusion coefficients. 

Hydrodynamic properties, such as the translational diffusion coefficient, or the shear viscosity, are very useful in the conformational study of chain molecules, and are routinely employed to characterize different types of polymers [15,20, 21]. One can consider the translational friction coefficient, fi, related to a transport property, the translational diffusion coefficient, D, through the Einstein equation, applicable for infinitely dilute solutions ... 

Key material properties for SOFC, such as the ionic conductivity as a function of temperature, are available in refs 36—39. In addition, Todd and Young ° compiled extensive data and presented estimation methods for the calculation of diffusion coefficients, thermal conductivities, and viscosities for both pure components and mixtures of a wide variety of gases commonly encountered in SOFCs. Another excellent source of transport properties for gases and mixtures involved in a SOFC is the CHEMKIN thermodynamic database. ... 

Table 10.4 gives critical data for the most common solvents used in high-pressure extraction. Table 10.5 illustrates the favorable mass transport properties that can be achieved in the supercritical area owing to a low viscosity and a high diffusivity, compared with the liquid phase. 

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... 

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. 

---