Solute movement analysis shock waves

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. 

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. 

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See also in sourсe #XX -- [ , , , , , , ]

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