Coefficient mutual

Z) g = mutual coefficient of diffusion AB = mutual coefficient of diffusion calculated by Fuller s method... 

These two equations, (50) and (51), illustrate how the macrodynamic theory can give a kinematic framework, which may be of interest in connection with work on the molecular dynamics of diffusion. It is seen that on a fundamental basis it is not possible to express the mutual coefficient in terms of the two selfdiffusion coefficients (of component a) and D (of component b). As a matter of fact, self diffusion of a component in a mixture is a more complicated process than mutual diffusion, as far as frictions are concerned, because according to (50) it depends on two kinds of friction, viz., internal friction within this component... 

Generally, the experimentally measured rates of reaction of solvated electrons with uncharged oxidants are less than or equal to the rate of reaction calculated from the Smoluchowski expression (20) using independent estimates of the mutual coefficient of diffusion, D, and encounter distance, In a few cases, the measured rates are larger than predicted theoretically such cases can be explained by either inter-molecular forces (and are discussed in Chap. 3) or by long-range transfer (see Chap. 4). 

For a binary mixture of two components A and B in the gas phase, the mutual diffusion coefficient such as defined in 4.3.2.3, does not depend on composition. It can be calculated by the Fuller (1966) method ... 

A complication now arises. The surface tensions of A and B in Eq. IV-2 are those for the pure liquids. However, when two substances are in contact, they will become mutually saturated, so that 7a will change to 7a(B) and 7b to 7B(A). That is, the convention will be used that a given phase is saturated with respect to that substance or phase whose symbol follows in parentheses. The corresponding spreading coefficient is then written 5b(A)/a(B)-... 

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

Note the use of a script for the binary pair mutual diffusion coefficient, as distinct from the Roman D already used to represent Knudsen diffusion coefficients. This convention will be adhered to throughout. 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

Factory Mutual provides loss prevention data sheets that explain how to protect buildings from wind damage. Pressure coefficients that define increased uplift at corners and edges adjust the calculated uplift pressures. A laboratory uplift pressure test rates roofing assemblies. An uplift pressure of 2.9 kPa (0.42 psi) must be withstood under FM conditions to meet the Class 1-60 requirements. The FM approval guide is revised aimuaHy (37). 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient. 5-46... 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

In the special case that A and B are similar in molecular weight, polarity, and so on, the self-diffusion coefficients of pure A and B will be approximately equal to the mutual diffusivity, D g. Second, when A and B are the less mobile and more mobile components, respectively, their self-diffusion coefficients can be used as rough lower and upper bounds of the mutual diffusion coefficient. That is, < D g < Dg g. Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal AIChE]. 30, 641 (1984), Ertl and Dullien, AIChE J. 19, 1215 (1973), and Vadovic and Colver, AIChE J. 18, 1264 (1972)]. 

Note that some new engineering constants have been used. The new constants are called coefficients of mutual influence by Lekhnitskii [2-5] and are defined as... 

Lekhnitskii defines the coefficients of mutual influence and the Poisson s ratios with subscripts that are reversed from the present notation. The coefficients of mutual influence are not named very effectively because the Poisson s ratios could also be called coefficients of mutual influence. Instead, the rijjj and ri y are more appropriately called by the functional name shear-exitension coupling coefficients. 

Extension-extension coupling coefficients (Poisson s ratios) Shear-extension coupling coefficients (coefficients of mutual influence) Shear-shear coupling coefficients (Chentsov coefficients)... 

The description of mass transfer requires a separation of the contributions of convection and mutual diffusion. While convection means macroscopic motion of complete volume elements, mutual diffusion denotes the macroscopically perceptible relative motion of the individual particles due to concentration gradients. Hence, when measuring mutual diffusion coefficients, one has to avoid convection in the system or, at least has to take it into consideration. 

In a system with two components, one finds experimentally the same values for and D, because is not independent from J,. It follows that the system can be described with only one mutual diffusion coefficient D = Dj = D2. 

From the molecular point of view, the self-diffusion coefficient is more important than the mutual diffusion coefficient, because the different self-diffusion coefficients give a more detailed description of the single chemical species than the mutual diffusion coefficient, which characterizes the system with only one coefficient. Owing to its cooperative nature, a theoretical description of mutual diffusion is expected to be more complex than one of self-diffusion [5]. Besides that, self-diffusion measurements are determinable in pure ionic liquids, while mutual diffusion measurements require mixtures of liquids. 

From the applications point of view, mutual diffusion is far more important than self-diffusion, because the transport of matter plays a major role in many physical and chemical processes, such as crystallization, distillation or extraction. Knowledge of mutual diffusion coefficients is hence valuable for modeling and scaling-up of these processes. 

The need to predict mutual diffusion coefficients from self-diffusion coefficients often arises, and many efforts have been made to understand and predict mutual diffusion data, through approaches such as, for example, the following extension of the Darken equation [5j ... 

Since the prediction of mutual diffusion coefficients from self-diffusion coefficients is not accurate enough to be used for modeling of chemical processes, complete data sets of mutual and self-diffusion coefficients are necessary and valuable. 

Typical values of self-diffusion coefficients and mutual diffusion coefficients in aqueous solutions and in molten salt systems such as (K,Ag)N03 are of the order... 

Figure 4.4-3 Self-diffusion and mutual diffusion coefficients in the methanol/[BMIM][PFg] sys-...

Self-diffusion coefficients were measured with the NMR spin-echo method and mutual diffusion coefficients by digital image holography. As can be seen from Figure 4.4-3, the diffusion coefficients show the whole bandwidth of diffusion coeffi-... 

Examples of Values of L and AF°. As a first example we may evaluate both L and AF° for a moderately soluble salt in aqueous solution. At 25° a saturated solution of potassium perchlorate has a concentration of 0.148 mole of KCIO4 in a 1000 grams of water that is to say, y+ = y = 0.148/55.5. The activity coefficient in the saturated solution has been taken1 to be 0.70 + 0.05. Using this value, we can estimate the work required to take a pair of ions from the crystal surface to mutually distant points, when the crystal is in contact with pure solvent at 25°C ... 

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