Diffusion of A through stagnant

Equations (2-2) and (2-3) can be manipulated algebraically, in a manner similar to that applied to equations (1-80) and (1-82), to yield 

Since concentrations may be defined in a number of equivalent ways, other definitions of mass-transfer coefficients for this case (NB - 0 dilute solutions) are frequently used, such as 

Notice that in the case of diffusion of A through stagnant B there is a bulk-motion contribution to the total flux that results in a logarithmic form of the concentration driving force. For that reason, the newly defined k-type mass-transfer coefficients are not constant, but usually depend on the concentration driving force. For very dilute solutions, the bulk-motion contibution is negligible and the driving force becomes approximately linear. In mathematical terms, this follows from the fact that for very dilute solutions yB M = xB M = 1.0. 

Therefore, for diffusion of A through stagnant B, equations (2-4), (2-5), (2-7), and (2-8) in terms of the -type mass-transfer coefficients are recommended only for very dilute solutions, otherwise, equations (2-2) and (2-3) should be used. 

Example 2.1 Mass-Transfer Coefficients in a Blood Oxygenator (Cussler, 1997) 

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For the diffusion of A through stagnant B in a constant-pressure, constant-temperature, ideal-gas system, Eq. (49) may be written in a number of forms ... 

Calculate molar fluxes for steady-state gaseous diffusion of A through stagnant B, and for equimolar counterdiffusion. 

Example 1.15 Steady-State Diffusion of A Through Stagnant B... 

Figure 1.6 shows schematically the concentration profiles for diffusion of A through stagnant B. Substance A diffuses by virtue of its concentration gradient, -dyA/dz. Substance B is also diffusing relative to the average molar velocity at a flux JB which depends upon -dy dz, but like a fish which swims upstream at the same velocity as the water flows downstream, NB = 0 relative to a fixed place in space. 

The two situations noted in Chapter 1, equimolar counterdiffusion and diffusion of A through stagnant B, occur so frequently that special mass-transfer coefficients are usually defined for them. These are defined by equations of the form... 

The mass-transfer conditions prevailing in the boundary layer described so far correspond to diffusion of A through stagnant B in dilute solutions. Therefore, the flux can be written in terms of a -type mass-transfer coefficient, as described by equation (2-7), using the difference in surface and bulk concentrations as the driving force ... 

KG overall convective mass-transfer coefficient for diffusion of A through stagnant B in dilute solutions with driving force in terms of partial pressures mol/m2-s-Pa. 

Figure 6.2.-2. Diffusion of A through stagnant, nondiffusing B (a) benzene evaporating into air, (b) ammonia in air being absorbed into water.

Equimolar counterdiffusion Diffusion of A through stagnant B, Z = A Units of transfer coefficient Relation between the two transfer coefficients... 

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