Gamma function concentration profile

As an alternative, equation 19.4-38 may be solved using the E-Z Solve software to obtain the concentration profiles. The gamma function can be evaluated by numerical integration using the user-defined functions gamma, fjrateqn, and rkint provided within the software. 

The Ei (f) can be approached as shown above with the incomplete Gamma function. Thus, the concentration profile along y will be for the firsts two terms ... 

Hence, the dimensionless concentration profile P(f) is given by the incomplete gamma function when the argument = 5 and the variable A =... 

Band broadening effects such as dispersion and mass transfer resistance are represented by the number of tanks (or stages) N. This can be explained by evaluating the moments of the analytical solution of Equation 6.98. For linear isotherms and the injection of an ideal Dirac pulse of one component, this equation yields a gamma density function for the concentration profile. With the retention time Ir lin.i of Equation 6.49 one obtains the elution profile as the time dependence of the concentration in the last tank (k= N) ... 

FIGURE 29.18 ESR depth profile of gamma-irradiated UHMWPE (GUR 4150). (A) Samples Cl-ClO from the surface to the core were prepared following postgamma aging for 120 days in air, bovine serum. Ringer solution, or ethyl alcohol. (B) Relative free radical concentration as a function of depth. (C) ESR spectrum of representative samples recorded immediately after they were prepared Oeft) and 10 months later (right). 

The numerator in this expression is the incomplete gamma function. We now know the concentration profile. 

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