By Bessi U.
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Extra resources for An analytic counterexample to the KAM theorem
3-37) is dropped for that component. If no component is totally excluded, the addition of the size exclusion effect in the rate models is very simple. One only has to use E~Ppi to replace EpDpi in the expression of Bii and T/i' and E~i in EpCpi of Eq. (3-10). , E~i = 0 ) if one does not use Eq. (3-38) to replace Eqs. (3-9) and (3-10). It turns out that, for numerical calculation, there is no need to worry about this singularity if E~i is given a very small value below that of the tolerance of the ODE solver, which is set to 10-5 throughout this book.
3-10) to replace C;i' Instead, a second order kinetic expression can be used. It has been widely adopted to account for reaction kinetics in the study of affinity chromatography [32-38]. A rate model with second order kinetics was applied to affinity chromatography by Arve and Liapis . Second order kinetics assumes the following common reversible binding and dissociation reaction: where ~ is component i in the fluid and L represents immobilized ligands. k ai and kdi are the adsorption and desorption rate constants for component i, respectively.
In Eq. (4-1), eddy diffusivity is the dominant term in liquid chromatography, especially when the flow velocity is not low, thus Dbocy. This relationship has been acknowledged by some researchers [31, 67]. For simplicity in discussions, the multicomponent mixing effects on Dbj, Dpj and kj for multicomponent systems are ignored in this book. Thus, Dbjocy and PeLi is independent of Y for each component. The relationship between k j and Y can simply be expressed as k j oc y1I3 . It is in agreement with two different experimental correlations reported by Pfeffer and Happel , Wilson and Geankoplis  and Ruthven  for liquid systems at low Reynolds numbers (Re=2Rp yp/p-> that cover the range for liquid chromatography [70,71].