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With the uncertainty of correspondence in mind note that the expression derived by direct integration of a differential equation for rate constants in Model A is ft = q« , **, K K ob ba (e-x-'-e-"*»') (10) Although kba appears to be the gx and kob the g2 of Eq. (9), their identical position in the equations does not in itself prove numerical identity. It so happens that these two equations give the same numerical result because of the compensatory effect of the algebraic signs. Equation (10) is the classical equation for radioactive transformation where the decay of mother substance (a) produces daughter product (b).

Explicit calculations will be based on the curve for pool a because the labeled pool is most likely to be available for sampling. As was emphasized in Chapter 2, paragraph 2, although material in a chemical pool is of a particular molecular species, sizes and rates are in terms of tracee atoms. See also Chapter 2, paragraph 27, in connection with nonuniform labeling. THE CURVE FOR POOL a 2. In all models of Figure 20, save J and K, a curve of SA or quantity of tracer in pool a will have three exponential components (as will curves for pools b and c).

A three-pool system possessing all possible routes of interchange, ingress, and egress for each pool is shown in Figure 20A. This unrestricted version is the basis for the general equations of Appendix II. For explicit mathematical solution based on a time curve for tracer obtained from one of the pools, considerable restriction in number of flow channels is required (Models B-K). Calculations for such models are simplified when some of the terms of the general equations become zero and drop out.

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Characterization of Porous Materials Using Molecular Theory and Simulation


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