Solute movement analysis

Exanqile 18-2. Linear solute movement analysis of elution chromatography... 

There is an analogy that may be useful in understanding this solute movement analysis. The problems are similar to algebra problems where two trains start to leave a station at the same time, but with different velocities (u and Ug in chromatography). You want to calculate when each train arrives at a second station (a distance L away) and when the tail end of each train (analogous to the feed time, tp) leaves the second station. 

To study TSA systems with the solute movement analysis we must determine the effect of tenperature changes on the solute waves, the rate at which a tenperature wave moves in the column, and the effect of temperature changes on concentration. The first of these is easy. As tenperature increases the equilibrium constants, and K, both decrease, often following an Arrhenius type relationship as shown in Eq. fl8-7). If the effect of temperature on the equilibrium constants is known, new values of the equilibrium constants can be calculated and new solute velocities can be determined. 

The SMB system shown in Figure 18-14B is quite a conplicated system, particularly if conpared to the sinple elution chromatographic system shown in Figure 18-5B. The SMB is used in industry for high purity separations of binary feeds since much less desorbent and adsorbent are required. The solute movement analysis helps to explain how this conplicated process works. 

The solute movement analysis is thus a physically based analysis that can be derived rigorously with appropriate limiting assumptions. If mass transfer is slow and the velocity is high or the column is short, the solute may not have sufficient residence time in the column to diffuse into the solid. The solute then skips the separation mechanism (equilibrium between solid and fluid) and exits with the void volume of the fluid. In this situation the predictions of solute movement are not useful. Basmadjian (1997) states that one of the following conditions must be satisfied to avoid this instantaneous breakthrough, ... 

In general, we cannot obtain analytical solutions of the complete mass and energy balances for nonlinear systems. One exception to this is for isothermal systems when a constant pattern wave occurs. Constant pattern waves are concentration waves that do not change shape as they move down the column. They occur when the solute movement analysis predicts a shock wave. 

Skopp, J. 1984. Analysis of solute movement in structured soils, p. 220-227. In J. Bouma and P.A.C. Raats (ed.) Proc. ISSS Symp. Water Solute Movement in Heavy Clay Soils, Wageningen, The Netherlands. 27-31 August. ILRI, Wageningen, the Netherlands. 

In analysis of osmotic flow and net solute movement, the two basic equations... 

Eqn. 24 predicts that if bulk water flow exerts any influence on the movement of a substance (i.e. presence of solvent drag) then the natural logarithm of the flux ratio which can be experimentally measured should vary as a function of the rate of volume flow of water J. Moreover, this variation should be linear and the slope of the line determine the degree of coupling between bulk water flow and solute movement (i.e. the larger the slope the greater the coupling). Similar analysis can be used in the case of tracer water (THO) movement. 

Since purge cycles use large amounts of solvent, other regeneration methods have been developed. These methods and their analysis with the solute movement theory is the topic of this section. 

Figure 18-16. Diffuse wave analysis (A) solute movement graph for Example 18-6. (B) predicted...

Figure 18-17. Shock wave analysis (A) inlet concentration (B) shock wave following Eq. (18-341 (C) outlet concentrations with solid line predicted by solute movement theoiy, and dashed line representing experimental result (modified from Wankat. 19861.

Figure 18-18. Analysis and results forExanyle 18-7 (A) solute movement diagram showing intersection of two shock waves, (B) outlet concentration profile...

Experimental results (Figure 18-IS) and the shockwave analysis showed that the wave shape for constant pattern waves is independent of the distance traveled. This allows us to decouple the analysis into two parts. First, the center of the wave can be determined by analyzing the shock wave with solute movement theory. Second, the partial differential equations for the column mass balance can be sirtplified to an ordinary differential equation by using a variable = t - z/u jj that defines the deviation from the center of the wave. This approach is detailed in more advanced sources (e.g., Ruthven. 1984 Sherwood et al.. 1975 Wankat. 19901. 

The ideal solution to microanalysis would be simply to freeze the plant material rapidly to the temperature of liquid nitrogen and then section it while it is still frozen on a cryotome. The frozen sections would then be transferred to a cold stage in a TEM and analyzed. In theory, no ion movement will take place and analysis at the high resolution of TEM should be possible. Indeed, this is a useful technique for liver, kidney, and soft animal tissues, but unfortunately it is almost impossible to cut tough plant material, and maintain the sections in a reasonable state for analysis (2). Even if this problem could be overcome unstained tissues will be difficult to visualize in TEM. 

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