VI CORRECI10N OF WALL CONCEN1RATION FOR VARIABLE VISCOSITY 69 6.1. Wall Concentrations for Variable Viscosity and Constant Flux 70 "Effect of Viscosity on Concentration Polarization in Ultrafiltration" 70 6.2. Wall Concentrations for Variable Viscosity and Variable Flux 75 VII CORRECI10N OF PRESSURE DROP FOR VARIABLE VISCOSITY 82 7.1. Modelling Concentration Profiles as a Function of Distance 82 7.1.1. Concentration Profiles in the Pressure Dependent Region 82 7.1.2. Concentration Profiles in

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... e Pressure Independent Region 83 7.2. Prediction of Frictional Pressure Drop as a Function of Distance 85 7.3. Prediction of Flux as a Function of Distance 92 7.4. The Relationship between Friction Factor and Reynolds Number 95 7.5. Implications for the Design of Ultrafiltration Modules 97 VIII CONCLUSIONS BffiLIOGRAPHY 106 APPENDIX I "Optimization of Module Design for Membrane Ultrafiltration" 115 APPENDIX II "Design Package for Ethanol Dehydration Column" 120 APPENDIX ill 'Water Purification with Membranes" APPENDIX IV Program listing ofDIMTEC.FOR APPENDIX V Program listing ofUF.FOR APPENDIX VI Program listing of CW.BAS APPENDIX Vll Program listing of CWBRIAN.BAS APPENDIX Vlli Program listing of PDEP.BAS APPENDIX IX Program listing of PIND.BAS APPENDIX X Program listing ofRECPLOT.FOR APPENDIX XI Program listing of TRIPLOT.FOR APPENDIX XII Program listing of PLOTID.FOR ADDENDUM I Spacer Geometry and the Optimal Design of Spiral Wound Membrane Systems ADDENDUM IT Sensitivity of the Optimal Design of Reverse Osmosis Units to Rejection ADDENDUM ill The Effect of Temperature on Optimal Designs 193 216 equations when variable solution properties are involved. Rather, a step-wise approach, which considers the accumulative effect on each of the important parameters, has been carried out Chapter V, therefore, describes the effects of flux and variable solution properties on the mass transfer coefficient. Of the solution properties which vary with concentration, the one which is of most concern in ultrafiltration is viscosity, as shown in chapter VI. This chapter describes the effect of variable viscosity on the wall concentration, while chapter Vll discusses the effect of variable viscosity and increased wall concentration on frictional pressure drop in membrane channels. Chapter VIll summarizes how results presented in the thesis affect the design and operation of ultrafiltration and reverse osmosis units.