Mathematical Modeling and Scale-up of Liquid Chromatography

1 Introduction.- 2 Literature Review.- 2.1 Theories for Nonlinear Multicomponent Liquid Chromatography.- 2.1.1 Equilibrium Theory.- 2.1.2 Plate Models.- 2.1.3 Rate Models.- 2.1.3.1 Rate Expressions.- 2.1.3.2 Governing Equation for the Bulk-Fluid Phase.- 2.1.3.3 General Multicomponent Rate Models.- 2.1.3.4 Numerical Solutions.- 2.1.3.5 Solution to the ODE System.- 2.2 Scale-Up of Liquid Chromatography.- 3 A General Multicomponent Rate Model for Column Liquid Chromatography.- 3.1 Model Assumptions.- 3.2 Model Formulation.- 3.3 Finite Element Formulation for the Bulk-Fluid Phase Governing Equation.- 3.4 Orthogonal Collocation Formulation of the Particle Phase Governing Equation.- 3.5 Solution to the ODE System.- 3.6 Fortran 77 Code for the General Multicomponent Rate Model.- 3.7 CPU Time for the Simulation.- 3.8 Extension of the General Multicomponent Rate Model.- 3.8.1 Second Order Kinetics.- 3.8.2 Addition of Size Exclusion Effect to the Rate Model.- 3.9 The Question of Choosing Column Boundary Conditions.- 4 Mass Transfer Effects.- 4.1 Effects of Parameters PeLi, Bii and ?i.- 4.2 Effect of Flow Rate.- 4.3 Effect of Mass Transfer in a Case with Unfavorable Isotherm.- 5 Interference Effects in Multicomponent Chromatography.- 5.1 Introduction.- 5.2 Computer Simulation and Discussion.- 5.2.1 Displacement Mode.- 5.2.2 Frontal Adsorption Mode.- 5.2.3 Elution Mode.- 5.2.3.1 Adsorption Equilibrium Constants.- 5.2.3.2 Low Adsorption Saturation Capacity.- 5.2.3.3 High Sample Feed Concentration (Concentration Overload).- 5.2.3.4 Large Sample Size (Volume Overload).- 5.2.3.5 More Component(s).- 5.3 Summary.- 6 System Peaks In Multicomponent Elution.- 6.1 Introduction.- 6.2 Boundary Conditions for the General Rate Model.- 6.3 Results and Discussion.- 6.3.1 Modifier is Weaker than Sample Solutes.- 6.3.2 Modifier Affinity is Between those of Sample Solutes.- 6.3.3 Modifier is Stronger than Sample Solutes.- 6.3.4 Effect of Modifier Concentration on System Peak Patterns.- 6.3.5 Effect of Modifier on Sample Solutes.- 6.3.6 Effect of Sample Type.- 6.3.7 Effect of Sample Solutes on the Modifier.- 6.3.8 Summary of System Peak Patterns.- 6.3.9 Binary Elution with Two Different Modifiers.- 6.4 Concluding Remarks.- 7 Multicomponent Adsorption with Uneven Saturation Capacities.- 7.1 Introduction.- 7.2 Kinetic and Isotherm Models.- 7.3 Isotherm Crossover.- 7.4 Summary.- 8 Modeling of Affinity Chromatography.- 8.1 Introduction.- 8.2 Effect of Reaction Kinetics.- 8.3 Effect of Size Exclusion.- 8.4 Interaction Between Soluble Ligand and Macromolecule.- 8.4.1 Modeling of Reaction in the Fluid.- 8.4.2 Solution Strategy.- 8.5 Modeling of the Three Stages in Affinity Chromatography.- 8.6 How to Use the Fortran 77 Code AFFINITY.F.- 8.7 Summary.- 9 Modeling of Multicomponent Gradient Elution.- 9.1 Introduction.- 9.2 General Rate Model for Multicomponent Gradient Elution.- 9.3 Numerical Solution.- 9.4 How to Use the Fortran 77 Code GRADIENT.F.- 9.5 Summary.- 10 Multicomponent Radial Flow Chromatography.- 10.1 Introduction.- 10.2 General Multicomponent Rate Model for RFC.- 10.3 Numerical Solution.- 10.4 How to Use the Fortran 77 Code RATERFC.F.- 10.5 Extensions of the General Multicomponent Rate Model for RFC.- 10.6 Summary.- 11 Scale-Up of Liquid Chromatography using General Rate Models.- 11.1 Isotherms.- 11.1.1 Batch Adsorption Equilibrium Method.- 11.1.2 Column Method.- 11.1.3 Langmuir Isotherm.- 11.1.4 Other Isotherm Models.- 11.2 Mass Transfer Parameters.- 11.3 Evaluation of Pei, ?i, and Bii,.- 11.4 General Procedure for Scale-Up.- 12 References.- 13 Subject Index.