Series Editors' Foreword; Preface; Acknowledgments; Contents; List of Figures; List of Tables; Nomenclature; 1 Membrane Processes; 1.1 Membrane Separation ; 1.1.1 Pore Sizes ; 1.1.2 Operation Modes ; 1.1.3 Modules; 1.1.4 Configurations ; 1.1.5 Fouling of Membranes ; 1.2 Mathematical Modelling of Membrane Processes; 1.3 Diafiltration Process ; 1.3.1 Process Model; 1.3.2 Fouling Models; 1.3.3 Operational Modes of Diafiltration; 1.3.4 Optimisation of Diafiltration Process; References; 2 Optimal Control Problem; 2.1 Objective Functional; 2.1.1 Typical Optimal Control Tasks; 2.2 Constraints.

2.3 Process Model2.3.1 Linear Time-Invariant System; 2.3.2 Input Affine System; 2.4 Summary of Problem Definition; References; 3 Solution of Optimal Control Problems; 3.1 Necessary Conditions for Optimality; 3.2 Analytical Methods; 3.2.1 Calculus of Variations; 3.2.2 Dynamic Programming; 3.2.3 Pontryagin's Minimum Principle; 3.3 Numerical Methods; 3.3.1 Control Vector Iteration; 3.3.2 Boundary Condition Iteration; 3.3.3 Complete Discretisation ; 3.3.4 Control Vector Parametrisation; 3.3.5 Direct Multiple Shooting; 3.4 Methods for Computing Gradients.

3.5 Feedback Strategies for Optimal ControlReferences; 4 Operation at Limiting Flux; 4.1 Process Model and Definition of Optimisation Problem; 4.1.1 Filtration Modes; 4.1.2 Optimisation Problem; 4.2 Optimal Operation; 4.2.1 Numerical Results; 4.2.2 Theoretical Results; 4.2.3 Discussion; 4.3 Case Studies; 4.3.1 Example 1; 4.3.2 Separation of Pectin from Sugar; 4.3.3 Purification of Soybean Water Extracts; 4.4 Models Derived from Limiting Flux; 4.4.1 Viscosity Dependent Mass Transfer Coefficient; 4.4.2 Osmotic Pressure Model; References; 5 Perfect Rejection of Both Solutes.

5.1 Optimal Operation5.2 Case Studies; 5.2.1 Separation of Lactose from Proteins; 5.2.2 Albumin
Ethanol Separation; References; 6 Perfect Rejection of Macro-Solute; 6.1 Optimal Operation; 6.2 Case Studies; 6.2.1 Dye
Salt Separation; 6.2.2 Radiopaque
Ethylene Glycol Separation; 6.2.3 Sucrose
Sodium Chloride Separation; References; 7 Constant Incomplete Rejection of Solutes; 7.1 Optimal Operation; 7.2 Case Studies; 7.2.1 Extended Limiting Flux Model; 7.2.2 Three Component Separation; References; 8 General Membrane Model; 8.1 Optimal Operation; 8.2 Case Studies.

8.2.1 Radiopaque
Ethylene Glycol Separation8.2.2 Separation of Peptide from Trifluoroacetic Acid; References; 9 Conclusions and Future Research; 9.1 Discussion; 9.2 Conclusions; References; Index.