By Zaks J.

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Coupled solutes with shock and diffuse waves. (A) Characteristic diagram for ternary ion exchange; (B) outlet concentration profiles for coupled adsorption for input of large pulse. region contains no A + . This plateau is separated from pure eluant by a slow diffuse wave across which the B + concentration drops to zero. 485-486 If given a long enough period, coupled species will always order themselves according to affinity. Binary systems with two adsorbed species in a carrier will show a similar coupling.

Substituting in the linear isotherm (Equation 2-29) and rearranging, we have the ordinary differential equation: d c c u = dV u-i ~ cu (2 8 3 ) V VM + k, Ms For a pulse of F1 moles of feed into stage 0, the solution is the Poisson distribution: e~vi vi F- where the dimensionless cumulative flow of mobile phase, vi9 is <2 85) *> " ^TW, - TT ' where Equation 2-30 and the height of a stage (Equation 2-91) have been used to relate the solute velocity to the staged terms. The outlet concentration is found by setting j = N.

6C are quite accurate except at the corners. At very low concentrations the Langmuir isotherm becomes linear and thus the solute movement theory underpredicts zone spreading. At very high concentrations the Langmuir isotherm approaches an asymptote and thus also underpredicts zone spreading. For nonlinear systems where the solute movement theory predicts shock waves, a constant pattern is generated. There is zone spreading around the shock wave (see Figure 2-9), but once developed it does not change shape.

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