Nonclassical Composition Fronts in Nonlinear Chromatography: Delta-Shock
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- 作者：Marco Mazzotti
- 刊名：Industrial & Engineering Chemistry Research
- 出版年：2009
- 出版时间：August 19, 2009
- 年：2009
- 卷：48
- 期：16
- 页码：7733-7752
- 全文大小：723K
- 年卷期：v.48,no.16(August 19, 2009)
- ISSN：1520-5045
文摘
The local equilibrium theory of chromatography is applied to study binary systems subject to the mixed generalized Langmuir isotherm, ni = Hici/(1 − K1c1 + K2c2) (i = 1, 2), where components 1 and 2 are anti-Langmuir-like and Langmuir-like, respectively. Riemann problems, where a stream of a given composition is fed to a column initially saturated at a different composition, are analyzed. Within the hyperbolic region of the hodograph plane close to the origin, it is shown that such Riemann problems admit not only classical solutions, consisting of constant states separated by simple wave and shock wave transitions, but also nonclassical solutions, namely including a continuous nonsimple wave transition and a delta-shock. The latter can be viewed as a traveling spike of growing strength superimposed to the discontinuity separating the initial and the feed states. Exact conditions for the occurrence of classical and nonclassical solutions are derived. Thus, this work adds two new types of composition fronts to the classical ones already known in nonlinear chromatography. In the case of the delta-shock, the most striking new transition, it is possible to derive exact relationships for its properties, including the slope of its image in the physical plane, i.e. the reciprocal of its propagation speed, dt/dz = {1/W}{1 + ν((H1K2[n2] − H2K1[n1])/(H1K2[c2] − H2K1[c2]))}, where the symbol [·] denotes the jump across the discontinuity of the quantity enclosed. These analytical expressions match the results obtained through numerical simulations. The physical legitimacy of the model considered in this work is demonstrated theoretically and is further supported by the experimental evidence of the existence of delta-shocks that has been recently provided [Mazzotti et al. J. Chromatogr., submitted].