An exact solution of the ideal model of chromatography is derived in the case of a binary mixture, when the equilibrium isotherms of the two compounds between the stationary and the mobile phases are competitive Langmuir isotherms. The concentration profiles of the two compounds are derived. Each compound profile is composed of discontinuities and continuous parts. There are two discontinuities (or shocks). The first one separates the pure mobile phase from a solution containing only the lesser retained component of the mixture. The second shock separates this solution from a solution of the two components. The composition of these solutions varies continuously between the shocks and behind the second shock. Thus, the concentration profile of the first component has two discontinuities; one that jumps from the base line to the band maximum constitutes the first shock. The second one, on its rear, jumps between two finite values of the concentration. The concentration profile of the second component has a single discontinuity, on its front. These last two discontinuities constitute the second shock. The profiles Obtained as analytical solutions of the ideal model are compared to those obtained as numerical solutions of the semiideal model. It is shown that as long as the mass-transfer kinetics between the two phases of the chromatographic system is fast enough and the column efficiency remains larger than a few thousand theoretical plates, the difference between the profiles is small, the shocks are replaced by shock layers whose thickness is proportional to the column height equivalent to a theoretical plate, and the shock layers move at almost the same speed as the ideal shocks.
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