By Phillip C. Wankat
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Extra info for Large-Scale Adsorption and Chromatography
The plateau z t Plateau Feed Cone ZL Plateau t FIGURE 2-16. 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.
The predicted outlet concentrations are shown in Figure 2-12C. Since the concentration wave takes less time to exit than to enter, it must have a higher concentration. The effect of the thermal wave on the solute concentration can be determined by a mass balance. This mass balance calculation is similar to the balance done for the shock wave. A column segment of length Az is selected. The thermal wave will pass through this segment in a time: TF t z t T0Ut t FIGURE 2-11. Movement of pure energy waves in a column.
In this case the nonlinear mass balance Equation 2-44 must be solved. An alternate way to heat or cool the column is to use a jacket or heating coils. This is called the direct mode. Now the entire length of the column is heated or cooled simultaneously. Thus, uth is essentially infinite, and Equation 2-45 becomes: c(Tc) us(Tc) l ; If the equilibrium constant k;(T) decreases as temperature increases, Equation 2-46 predicts that c(Th) > c(Tc). That is, as solute desorbs it diffuses into the fluid and increases the fluid concentration.