Effect of Component Numbering on the Fick Matrix

Example 4.2.4 Effect of Component Numbering on the Fick Matrix 

The preceding examples illustrated some of the ways in which the Fick matrix [D] depends on the composition of the mixture and on the binary (Maxwell-Stefan) diffusion coefficients. One further property of [D] is that both the sign and magnitude of the elements of [ ] depends on the order in which the components are numbered. Wesselingh (1985) provided a dramatic and elegant illustration of this fact for the system H2-N2-CCI2F2. At a temperature of 298 K and a pressure of 101.3 kPa the diffusion coefficients of the three binary pairs that make up the mixture are 

The ratio of the largest to the smallest of these coefficients is nearly an order of magnitude thus we may expect the Fick matrix [D] to show a strong composition dependency. 

SOLUTION For each of the three possible choices for component 3 there are two ways to order the components. We will calculate the elements of [D] for three ways of ordering the components obtained by rotating the component numbers in order. With the compo- 

Another aspect of the choice of component numbering relates to the accuracy of the calculations it is not a good idea to calculate small fluxes by subtracting two Targe numbers. Put another way, if the flux of component i is expected to be small, do not label this as solvent species n Include i as one of the first n - 1 species. Greater accuracy is obtained by choosing n to be the species with the highest concentration.  

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