Book contents
- Frontmatter
- Contents
- Preface and acknowledgments
- 1 Our approach to modeling chromatographic processes
- 2 Linear chromatography: the Russian Lego
- 3 Non-linear chromatography: equilibrium theory
- 4 Fluid–solid phase equilibria
- 5 Mass transfer
- 6 Hydrodynamics of chromatographic columns
- 7 Simulating chromatographic columns
- 8 Counter-current systems
- 9 Chromatographic modes and their optimization
- 10 Addressing a few industrial problems
- 11 Conclusion
- Appendix A Some important properties of the Laplace transform
- Appendix B Inlet and outlet boundary conditions
- Appendix C Equilibrium theory: single-solute chromatograms
- Appendix D Equilibrium theory: binary chromatograms
- Appendix E The influence of the porosity determination on chromatographic modeling
- Appendix F Useful physico-chemical data and orders of magnitude
- Appendix G Fick and Maxwell–Stefan approaches to diffusion
- Appendix H Non-linear LDF for multi-solute systems
- Appendix I Situations that make the use of the MC model problematic
- Appendix J Typical industrial chromatographic processes
- Notation
- Index
- References
4 - Fluid–solid phase equilibria
Published online by Cambridge University Press: 05 April 2015
- Frontmatter
- Contents
- Preface and acknowledgments
- 1 Our approach to modeling chromatographic processes
- 2 Linear chromatography: the Russian Lego
- 3 Non-linear chromatography: equilibrium theory
- 4 Fluid–solid phase equilibria
- 5 Mass transfer
- 6 Hydrodynamics of chromatographic columns
- 7 Simulating chromatographic columns
- 8 Counter-current systems
- 9 Chromatographic modes and their optimization
- 10 Addressing a few industrial problems
- 11 Conclusion
- Appendix A Some important properties of the Laplace transform
- Appendix B Inlet and outlet boundary conditions
- Appendix C Equilibrium theory: single-solute chromatograms
- Appendix D Equilibrium theory: binary chromatograms
- Appendix E The influence of the porosity determination on chromatographic modeling
- Appendix F Useful physico-chemical data and orders of magnitude
- Appendix G Fick and Maxwell–Stefan approaches to diffusion
- Appendix H Non-linear LDF for multi-solute systems
- Appendix I Situations that make the use of the MC model problematic
- Appendix J Typical industrial chromatographic processes
- Notation
- Index
- References
Summary
The roots …
Introduction
With the expression “fluid–solid phase equilibria”, we refer to what is often designated in chromatography as “adsorption isotherms”. The latter term is so widely used that it can easily be used in an inappropriate way. In a chromatographic process, the interactions of solutes between fluid and solid phases can include mechanisms that can be different from adsorption, including ion exchange, ion or size exclusion, chemical equilibria in the fluid phase and complexation on the surface. In order to avoid confusion, we will use the general term “fluid–solid phase equilibria” and restrict the use of “adsorption isotherm” to situations where an adsorption mechanism is likely to be the predominant factor.
In addition, “adsorption isotherm” suggests that a single univariate function relates the fluid-phase concentration to the solid-phase concentration (lumped or not) of a given solute, provided that temperature is kept constant. This can be misleading. Certainly temperature must be kept constant, but pressure must be kept constant as well when working with supercritical fluids. The same applies to normality in ion exchange, as explained in Section 4.5. Additionally, when working with multi-solute mixtures, relating a given solute concentration in the solid phase (lumped or not) to solute concentration in the fluid phase requires that all other concentrations, not only temperature, must be kept constant.
In Chapter 1 we presented basic concepts for describing chromatographic systems as well as simple considerations for relating concentrations of solutes located in the fluid mobile phase and in the particles. Recall that the qualifier mobile is important, to make clear that the intragranular fluid is not part of the mobile fluid.
An important assumption that was made in Chapter 1 and that, unless otherwise specified, will be made throughout this book is the rigidity of solute molecules and the absence of conformational changes during their interaction with the chromatographic medium. Similarly, we assume that the chromatographic medium is not subject to structural changes upon interaction with the solutes.
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- Chromatographic ProcessesModeling, Simulation, and Design, pp. 139 - 215Publisher: Cambridge University PressPrint publication year: 2015
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