Method of Burghardt and Krupiczka

Burghardt and Krupiczka (1975) developed an approximate explicit solution to Eqs. 8.5.3 for the special case of diffusion of m species through n - m stagnant gases. We develop their method below for the case of diffusion in the presence of a single stagnant gas identified as 

For the special case of Stefan diffusion we may relate the n — 1 independent molar fluxes Ni to the n — 1 independent composition gradients as follows  

Burghardt and Krupiczka (1975) did not assume [ 4] to be constant. Instead, they assumed the matrix was constant over the film. To develop the solution of 

The subscript av serves to remind us that [yl] and are evaluated at the arithmetic average composition. To solve Eq. 8.5.11 we need an expression for the variation of over the film. The required equation is provided by the last of the set of n Maxwell-Stefan relations (Eq. 8.3.2), which simplifies to give 

In view of the assumptions underlying the film model, is constant. Equation 8.5.12 is easily integrated to give the variation through the film of the composition of species n 

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The method of Blanc [16] permits calculation of the gas-phase effective multicomponent diffusion coefficients based on binary diffusion coefficients. A conversion of binary diffusivities into effective diffusion coefficients can be also performed with the equation of Wilke [54]. The latter equation is frequently used in spite of the fact that it has been deduced only for the special case of an inert component. Furthermore, it is possible to estimate the effective diffusion coefficient of a multicomponent solution using a method of Burghardt and Krupiczka [55]. The Vignes approach [56] can be used in order to recalculate the binary diffusion coefficients at infinite dilution into the Maxwell-Stefan diffusion coefficients. An alternative method is suggested by Koijman and Taylor [57]. 

The method of Taylor and Smith (1982) is a generalization of the method of Burghardt and Krupiczka for Stefan diffusion. We use the determinacy condition (Eq. 7.2.10) to eliminate the nth flux from the Maxwell-Stefan relations (Eq. 2.1.16) and combine the first n-1 equations in matrix form as... 

The generalization of the method of Burghardt and Krupiczka is based on the assumption that the matrix [A] divided by the mole fraction weighted sum of the... 

Estimate the rate of evaporation of ethyl propionate(l) into mixtures of air(2) and hydro-gen(3) using the method of Burghardt and Krupiczka. This problem is based on experiments conducted by Fairbanks and Wilke (1950) with a view to assessing the validity of Wilke s effective diffusivity formula (Eq. 6.1.14). 

SOLUTION For diffusion of a single species into a mixture of inert gases all matrices in the Burghardt-Krupiczka method are scalars and the flux of species 1 is given by... 

One especially good use for the Taylor-Smith/Burghardt-Krupiczka method is to generate initial estimates of the fluxes for use with the Krishna-Standart or Toor-Stewart-Prober methods. It is a very rare problem that requires more than two or three iterations if Eq. 8.5.26 is used to generate initial estimates of the fluxes (Step 3 in Algorithm 8.2) (Krishnamurthy and Taylor, 1982). 

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