marcel-mulder-basic-principles-of-membrane-technology-

MODULE AND PROCESS DESIGN 339 TABLE VIII - 5. Design data for a single stage seawater desalination plant permeate flow rate ~ : 1000 m3/day pIl!Ssure difference .1P: 55 bar flux J : 1.3 m3/ m2 day (at 15 bar, T = 16'C and 1500 ppm NaCl) rejection R: 99.5 % salt concentration cf : 35,000 ppm NaCI recovery S : 0.3 pump efficiency 11pump : 0.65 turbine efficiency 11turbine: 0.75 membrane area per module A module: 3 m2 As can be seen from table VIII - 6, the flux is given at 15 bar, 16'C and 1500 ppm NaCl so that the water permeability coefficient A must be calculated under these conditions. The volume flux is given by eq. VIn - 5 as: =J A (M> - ~1t) with ~1t =RT ~c nJM =(2400 1500 2) / 58.5 = 1.23 105 Pa = 1.23 bar and A = 54.2 / (15 - 1.23) = 3.9 1m -2 h -1 bar-1 The retentate concentration cr can be calculated using eq. VIII - 23, i.e. cr = cf (1 - S) - R while the average penneate concentration cp may be obtained from eq. VIII - 27, i.e. Cp = ~ [1 - (1 - S) 1-R] => Cp =208 ppm and cr = 49,910 ppm. indicating that the desired product quality ( cp < 250 ppm) is obtained. From the retentate and feed concentrations, the average osmotic pressure on the feed side can be calculated: ~1tf = 28.7 bar ~1tr = 40.9 bar

340 CHAPTER VIII Using an average osmotic pressure Ll1t :::: 34.8 bar, the flux at 55 bar can now be calculated: => J:::: 79 1 m -2 h-1 while the module flux is => Jmodule =2371 I h =5.7 m3 I day This means that 1000 I 5.7 '\" 176 modules with a total membrane area of 528 m2 are required. Energy consumption The energy consumption is mainly determined by the high-pressure feed pump. The flow rate to be pumped is: qf = qp I S = 3300 m3/day => ~ump =LlP . qf I 'TIpump = 323 103 J/s = 323 kW Part of this energy is recovered by means of a turbine (the pressure losses that actually occur are not considered here): => Ewrbine =LlP . qr/'TIturbine = 195 kW VIII. 16.2 Concentration of a colloidal solution by ultrafiltration Ultrafiltration is used in a wide range of applications, mainly in the food, dairy, textile, metallurgy and pharmaceutical industries. The feed is generally an aqueous solution containing macromolecular solutes, emulsions or suspended solids. Flux decline due to concentration polarisation and fouling presents a serious problem. To reduce this phenomenon, high cross-flow velocities are required. The concentration of aqueous feed solutions is a typical ultrafiltration application and recirculation systems are generally used. An example of concentrating a colloidal solution with a solute concentration of 50 kg/m3 to 200 kglm3 will be given. The required membrane area and pump energy will be calculated both for a single-stage recirculation process and a two-stage recirculation process with cross-flow velocities of 1, 2 and 3 mis, respectively. Membrane rejection is assumed to be 100% whilst osmotic pressures are neglected. Furthermore, the flux can be described as: where cg is the gel concentration (see chapter VII). The mass transfer coefficient of the solutes are related to the velocities by k = 2 10 - 5 v 0.75. The design data are listed in table VIII - 6

MODULE AND PROCESS DESIGN 341 TABLE VIII - 6. Relevant data for the calculations feed solute conc. cf 50 kg/m3 retentate solute conc. cr 200 kg/m3 rejection R 100% feed flow rate <If 3.6 m3/h (10 - 3 m3/s) pure water permeability gel concentration A 7.5 10-6 mls bar cg 300 kg/m3 Single-stage recirculation system The schematic flow diagram for the single-stage unit is given in figure VIII - 28. qf: 3.6m3/h cr : 200kg/m 3 cf .·50kg/m3 cp : 0 kg/m 3 Figure VIII - 28. Flow diagram for a single-stage unit. The required membrane area (AareJ can be calculated from with the penneate flow rate (qp) and the retentate flow rate (qr) being obtained from the volume balance and mass balance. Mass balance Volume balance

342 CHAPTER VIII We can now calculate k. J and A for various cross-flow velocities (see table VIII - 7). TABLE VIII - 7. Calculated values of the membrane area A, flux] and mass transfer coefficient k for various cross-flow velocities v (m/s) k 105 (m/s) J lOS (m/s) 1 2.0 0.8 94 1.4 54 2 3.4 l.9 39 3 4.6 Two-stage recirculation system The flow diagram for the two-stage unit is given in figure VIII - 29. qf: 3.6 m_3/h_~ cr : 200kg/m 3 cf ·.50kg/m3 Figure VIII - 29. Flow diagram of a two-stage recirculation unit From this diagram we can write the volume balances as: and since qr,l = qf.2 and cr.} = cf.2' one obtains (cp. 1 = Cp.2 = 0)

MODULE AND PROCESS DESIGN 343 If we assume that the permeate flow in both stages is the same, then ~ qp,1 = qp,2 = 1.35 m3Jh = 3.75 . 10 - 4 m3/s The required membrane area for the two-stage process is given in table VIII - 8. Energy consumption. Some simple calculations will be carried out to estimate the energy consumption for a single-stage and a two-stage process. The type of membrane configuration (or module configuration) is not involved in calculations of the required membrane area. However, the membrane configuration has to be taken into account in calculating the energy consumption. Here we consider tubular membranes with a diameter of 1 cm.The power consumption to maintain a certain cross-flow velocity is then given by: where Tleff is the pump efficiency and ~p the pressure drop over the tubes. The latter is given by [7]: where dh, the hydraulic diameter, is for a tube simply its diameter d. The friction factor in the turbulent region can be obtained from the Blasius relationship [7]: 4f = 0.316 Re - 0.25 with the Reynolds number being given by Re = p v d/Tl The retentate flow qr is given by where Ad is tile cross-sectional area of the tube. Because there is not a single (very long) tube but a number of parallel tubes (n), then and the membrane area is equal to Aarea = n 1t dL

344 CHAPTER VIII Combination of all these equations gives the power consumption as: P = 0.06 Re - 0.25 A P v3 /1l eff (Note that the energy consumption is related to the third power of the velocity, P\", f v3, where f is a friction factor). The membrane area and power consumption are listed in table VIII - 8 for both the single-stage and the two-stage process. TABLE VIII - 8. Membrane area and power consumption for the single-stage and two-stage process single-stage process two-stage process v (m/s) Re.1O-3 Aarea (m2) P(kW) Aarea (m2) P(kW) 1 15 94 0.5 60 0.3 2 30 54 2.0 36 1.3 3 45 39 4.5 27 2.9 This example shows that both the membrane area required and the power consumption are lower for the two-stage process. On the other hand, the capital cost will be higher for the two-stage process. Furthermore, by increasing the cross-flow velocity from 1 to 3 mis, the membrane area is reduced by more than a factor of two, whereas the energy consumption increases by one order of magnitude. These data can be used to calculate the actual process costs, where power consumption and membrane area are important parameters. VIII. 16.3 Oxygen/nitrogen separation in a single-stage process. A very interesting application of air separation is the production of oxygen-enriched air as well as nitrogen-enriched air. Most of the oxygen and nitrogen produced nowadays is obtained via cryogenic techniques, but membrane processes (and also pressure swing adsorption) show very good prospects especially for small applications. A major application for oxygen-enriched air is for enhancing combustion. Other applications are in the medical and biotechnological field. Nitrogen-enriched air is used as an inert gas for blanketing flammable liquids. Another application is as a sealant gas to prevent the oxidation of foods (fruits, vegetables, etc.). The process design and membrane choice are different for both applications as will be shown by the following examples. The driving force across the membranes can be established either by pressurising the feed or applying a vacuum on the permeate side. VIII . 16.3.1 Oxygen enrichment in a single-stage process Oxygen with an enrichment of 25 - 40 % is generally of interest for enhanced combustion. To obtain concentrations of this order a proper membrane must be chosen on the basis of selectivity and permeation rate. Another factor of interest is the pressure ratio across the membrane.

MODULE AND PROCESS DESIGN 345 Since the cost of air is negligible, the process will be carried out with low recoveries (or, in other words, the composition does not change on the feed side, xf\"\" xr) using a vacuum pump on the permeate side. Figure VIII - 30 shows a simplified flow scheme. vacuum oxygen pump enriched air Figure VIII - 30. Process scheme for oxygen enriched air. At zero recovery the composition in the permeate depends on the selectivity (PoJPNz) and on the pressure ratio across the membrane (Ph/PC). Table VIII - 9 shows the oxygen concentration in the permeate calculated via eq. VIII - 38, using a pressure ratio of 5 (Ph = 1 bar and Pc = 0.2 bar). Now let us calculate the membrane area required and the energy consumption for a product stream of 10 m3/h of air enriched to 30% oxygen. Composite membranes are available with polydimethylsiloxane (silicone rubber) top layer of thickness 1 j.l.m: polydimethylsiloxane has a POz value of 600 Barrer and a selectivity factor (J..02/Nz of 2.2. TABLE VIII - 9. Oxygen concentration in the permeate for various separation factors (a = Po/PNz). Pressure ratio (Pi/pc) =5. % 02 in permeate 2 31 2.2 33 3 38 4 43 5 46 10 57 Assuming that the process operates at constant feed composition, xf\"\" xr., the relevant data are summarised in table VIII - 10. It can be seen from table VIII - 10 that the membranes selected are capable of producing 30% oxygen-enriched air. In fact a permeate concentration of 33% is obtained which means that the pressure ratio can be reduced (saving power requirement) or air can be

346 CHAPTER VIII added as a diluent. TABLE VIII - 10. Relevant data necessary for the calculations oxygen feed conc. Xf: 0.21 oxygen permeate conc. ~: 0.3 selectivity <X 02/N2: 2.2 permeate flow rate '\\l: 10 m3jh oxygen permeability P02 : 600 Barrer membrane thickness upstream pressure t:1Jlm downstream pressure Ph : 1 bar Pe. : 0.2 bar A flow diagram of this single-stage membrane process is given in figure VITI - 31. Xf: 0.21 02 Figure VIII - 31. Single-stage membrane process for oxygen enrichment. The oxygen flux can be calculated through the use of eq. VITI - 35 as => J02 == 0.235 m3 m-2 h-1 which means that a membrane area of about 14 m2 is required: - when the thickness of the silicone rubber layer is reduced from 1 f.lm to 0.1 f.lm, then the membrane area reduces to\"\" 1.4 m2. - when a more selective membrane of lower permeability is used, the pressure ratio can be decreased or air can be added as a diluent to obtain 30% oxygen-enriched air. However, high permeabilities are preferred in the system design with a vacuum pump.

MODULE AND PROCESS DESIGN 347 Energy consumption The energy consumption is determined by the power consumption of the vacuum pump and the blower. The power requirement (assuming isothermal compression or expansion) can be calculated using the following equation: n RT Ph P In- 11 Pe where 11 is the pump efficiency, n the number of moles to be pumped per second and Pw'Pl the pressure ratio. It is assumed that the blower efficiency is 60%, the vacuum pump efficiency 50% and the pressure ratio across the blower Pw'Pe = 1.05, while the feed flow rate may be estimate as qf: 200 m3Jh (qf I qp = 20). The power consumption of vacuum pump and blower at 25CC can now be calculated, i.e. vacuum pump: =>P 988 Jls \"\" 1.0 kW blower: =>P 599 Jls \"\" 0.6 kW VIII . 16.3.2 Nitrogen enrichment in a single-stage process Another application of air separation is nitrogen-enriched air with 95 - 99.9% N2 being the range of interest since the minimum nitrogen concentration for blanketing is about 95%. In contrast to oxygen-enrichment, nitrogen-enrichment systems (where the retentate stream is the product) operate with pressure applied on the feed side as shown in figure VIII - 32. i---air o.-oA-m-~I~~rt --- ]-1---1.-- nitrogen ~ enriched W< Figure VIII - 32. Flow scheme for the production of nitrogen-enriched air. The membranes used in this application have a higher selectivity than those used for oxygen enrichment. The following example estimates the membrane area required and power consumption necessary to produce 10 m3/h of 95% N2. For this application, a modified asymmetric poly(phenylene oxide) membrane is used. The characteristics of the membrane and the process data are given in table VIII - 11. A flow diagram is depicted in figure VIII - 33, where the mole fractions of oxygen are given.

348 CHAPTER VIII TABLE VIII - 11. Relevant data necessary for the calculations nitrogen feed conc. Xf: 0.79 nitrogen retentate conc. selectivity xr: 0.95 retentate flow rate a 02/N2: 4.2 oxygen permeability 'Ip : 10 m3/h membrane thickness P02 : 50 Barrer upstream pressure downstream pressure t:lllm Ph : 10 bar Pt : 1 bar x : 0.05 02 r .. ~: 10m3 /h Figure VIII - 33. Flow diagram for the production of nitrogen-enriched air. The equations given in section VIII - 12 cannot be applied directly because the difference between the oxygen feed composition and the retentate composition is too large (x/xf < 0.5). Hence the calculations must be performed in steps [2]. This example employs a two step calculation, i.e. 1st step: 21% 02 => 10% 02 2nd step: 10% O2 => 5% 02 ~ l Ozx r, 2: 0.05... .. -- - -- -- J Figure VIII - 34. Two-step calculation for a nitrogen enrichment system. The retentate flow rate in step I is the inlet flow rate of step 2 ( ~,! == xf,2 and qr,! == qr,2). Step 2 will be first considered since qr,2 is known.

MODULE AND PROCESS DESIGN 349 ~The log mean average oxygen feed concentration in step 2 is: => X2 = 0.072 and the oxygen permeate concentration ~,2 can be calculated from eq. VIII - 41. => xp,2 = 0.20 The feed and permeate flow rates can be determined from the material balance equations and consequently the membrane area can be calculated. qf,2 = qp,2 + 10 0.1 * qf,2 = 0.20 * qp,2 + 10 * 0.05 => J02 = 0.071 m3 m-2 h-1 This means that a membrane area A2 = 14 m2 is required in step 2. The log mean average oxygen feed concentration in step 1 is =>Xl =0.144 and the oxygen permeate concentration ~,l can be calculated from eq. VIII - 41 as: => xp,l = 0.36 Then

350 CHAP1ER VIII 0.21 * ~,l = 0.36 * qp,l + 0.1 * 15 => qf,l = 25 m3Jh and qp,l = 10 m3Jh => J02 = 0.148 m3 m-2 h-l => qaz = qp * 0.36 = 3.6 m3Jh =This means that a membrane area Al 24 m2 is required. Hence, the total membrane area required is Atotal =Al + A2 =38 m2. This example demonstrates that it is also possible to have two product streams, an oxygen-enriched stream in the first step and a nitrogen-enriched stream in the second step. This is shown schematically in figure VIII - 35. area: 14 m2 area: 24 m2 r---1---.. :n-air---l~~~ ~ ~.. -- - -- -- +c o m p r e s s o r . .r---\"1-----1~ nitrogen • [ -- -- - -- J • ched (95% N2) oxygen enriched air (36% 0 ) 2 Figure VIII - 35. Separation of air into two product streams, i.e. an oxygen-enriched stream and a nitrogen-enriched stream. Energy consumption The energy consumption is determined by the power requirement of the compressor. The latter can be calculated using the same equation as that for the vacuum pump. The efficiency of the compressor is assumed to be 70%. qf,l = 25 m3Jh => n =0.284 molls => P = 2313 Jls \"\" 2.3 kW VIII . 17 Literature 1. Saltonstall, C.W., and Lawrence, R.W., Desalination, 42 (1982) 247 2. Hogsett, J.E., and Mazur, W.H., Hydrocarbon Processing, 62, aug. 1983, p. 52 3. Spillman, W., Chemical Engineering Progress, January 1989, p.41 4. Hwang, S.T., and Kammermeyer, K., Membranes in separations, John Wiley,

MODULE AND PROCESS DESIGN 351 New York, 1975 5. Rautenbach, R., and Albrecht, R., Membrane Processes, John Wiley, New York, 1989 6. Nitto Denko Technical Report, The 70th Anniversary Special Issue, 1989 7. Beek, W.J., and Muttzall, K.M.K., Mass transport phenomena, John Wiley, New York,1977 8. Toray, Technical Bulletin

LIST OF SYMBOLS (-) (m2) a activity (m3/m2.s.bar) A surface area (-) A water permeability coefficient b friction factor (-) B constant B solute permeability coefficient (mls) (kg/m3) concentration of i (m3(STP)/m3) amount of sorbed gas per amount of polymer c' geometrical parameter (-) concentration in the bulk Langmuir capacity constant (kg/m3) c concentration (m3(STP)/m3) c average concentration (kg/m3) (kg/m3) ~ pore diameter (m) Djj diffusion coefficient of i in j Dj diffusivity of i in polymer fixed frame (m2/s) (m2/s) Dr thermodynamic diffusion coefficient (m2/s) (J/mole) E activation energy (V) E electrochemical potential (V) Edon Donnan potential f fraction free volume (-) fjj friction coefficient F Faraday constant (J.s/m2) Fj driving force (C/equiv) g concentration dependent interaction parameter (N) Gm Free energy of mixing (-) Hm Enthalpy of mixing current density (J/mole) flux of component i (J/mole) volume flux (C!cm2.s) mass transfer coefficient (mls) Planck constant (mls) rate constants (mls) Henry's law solubility coefficient (J.s) constant (l/s) 353 (m3(STP)/m3.atm) (m2)

354 thickness LIST OF SYMBOLS phenomenological coefficient t water permeability coefficient (m) mobility (kg.s/m) L1·J molecular weight (g/s.bar.m2) mass (mol.m/N.s) ~ number of moles (kg/kmol) exponent (kg) m number of pores (-) Mw A vogadro's number Mt pore radius (-) n vapour pressure n saturation vapour pressure (-) nk (hydraulic) pressure N av permeability constant of the pure component A (l/mole) ror rp differential heat of adsorption (m) p flow rate (Pa) po gas constant (Pa) resistance (Pa) P retention (m3/m2s.Pa.m) PA Reynolds number (J/mole) q friction coefficients (m3/s) q (pore) radi us (J/mole.K) R Kelvin radius (cm2.s.bar/cm3) R specific cake resistance (-) R Entropy of mixing Rc Surface area (-) R1·J solubility coefficient r Recovery (J.s/m2) rk Schmidt number (m) rc time (m) Sm temperature () S glass-rubber transition temperature (J/mole.K) S velocity of i in a membrane (m2/g) S average molecular velocity (m3/m3.Pa) Sc partial specific volume (-) fractional free volume (-) T molar volume Tg (s) (K) Uj (K) vA (m/s) Vj (m/s) (m 3/kg) vf V (-) (m3/mole)

LIST OF SYMBOLS 355 VR Volume reduction (-) xi (molar) fraction (-) X driving force (N/mole) Greek symbols: (-) a. selectivity (K-l) a. coefficient of thermal expansion (m) 0 thickness of the boundary layer (-) (Pa.s) E porosity (J/kg) (m) \" viscosity (kg/m3) (-) Il chemical potential (-) (-) A. mean free path of (gas)molecules (N/m) (-) p density (-) (Pa) 't tortuosity (-) y activity coefficient (-) y± mean ionic activity coefficient (s) y surface tension (-) y exponential factor (m/s) <Pi volume fraction of component i (-) 1t osmotic pressure 0\" reflection coefficient X Flory - Huggins' interaction parameter e time lag e contact angle ro permeability coefficient 'Pc fraction crystalline polymer subscripts and superscripts: b bulk bl boundary layer f feed componenti g gel h high (high pressure side; feed side) I low (low pressure side; permeate side) m membrane p permeate p polymer

356 LIST OF SYMBOLS r retentate s solvent w water v volume non solvent 2 solvent 3 polymer ave average sorp sorption obs observed int intrinsic

INDEX Carbon dioxide 234 Carrier A 258 - choice 246,258 Absorption 166 - sbUctures Active transpon 146 Carrier mediated transpon 247 Activity 147,198 Cascades 323 Activity coefficient 147,198 Cation-exchange membrane 38,274,301 Activity proflle 238 Cell pair 272 Adsorption 282 Cellulose 43,262 Adsorption-desorption 123 Cellulose acetate 207,210,261 Air separation 344 Cellulose esters 207,210,261 Alcohol 243 Cellulose triacetate 217 Alumina 207 Ceramics 47 Anion-exchange membranes 38,274 Chain Aromatic polyamide 35,44,215 - interaction 24 Argon 169 - flexibility 22 Artificial kidney 261 Cheese 212 Asymmetric membrane 11,210,215 Cheesewey 212 Azeotropic mixture 243 Chemical potential 72,198 Chemical stability 33,48 B Chlor-a1ka1i process 276 Chlorine resistance 215 Backflushing 310 Cleaning 309 Batch operation 321 Clustering 181 Benzene 240 Coating 57 Binary phase diagram Co-current flow 320 Binodal 77 Cohesive energy density 71 Biological membranes 78 Co-ion 196 Bipolar membrane 48 Colloidal suspensions 208,340 Blend 277 Compaction 311 Boundary layer 40 Composition path 93 Boundary layer resistance 251,284,301,303 Composite membrane 11,58,64 Blood 297 Concentration differerence 199,220 Bubble-point 261 Concentration polarisation 281 117 Concentration profile 238 Contact angle 264 C Convective transpon 158,204,209 Copolymer 19 Capillary membrane 312 Counter current flow 320 Capillary model (see Hagen-Poisseuille) 315 Counter-ion 38 Capillary module Coupled transport 247 Covalent binding 25 357

358 INDEX Critical temperature 172 E Crown ethers 246,258 Cross flow 208,319 Economics 328 Crosslinking Elastomer 38 Crystallinity 19,83 Electrical potential Crystallisation 134,185 Electrodialysis 147,199,270 Cut-off Electro-neutrality 270 30,83 Electron microscopy 195 131 Electro-osmosis 114 Emulsion liquid membrane 156 D Engineering aspects 245 Damk1lhler number 252 - boundary layer 251,284,301 - cascades 323 Dead-end mtration 208 - diafiltration 334 - gas separation Dehydration of solvents 327 - hyperfiltration 336,344 - multi-stage 330,338 Demixing - single-stage - ultrafiltration 323 - binary systems 78 Entanglement 323 Entropy 340 - binodal 78 Entropy production ESCA 24 - delayed 92 Etching 71 Ethylene 149,156 - diffusional aspects 87 Ethylene vinyl acetate 142 Ethylene vinyl alcohol 140 - instantaneous 92 Evaporation 17 18,261 - liquid-liquid 78 18,261 59 - spinodal 80 - ternary systems 81 Density 138 Desalination 326 Dextran 132 Diafiltration 334 Dialysis 192,260 Differential scanning calorimetry (DSC) 136 Differential thermal analysis (DTA) 136 Diffusion 167 Diffusion coefficient 167,174 F Dip-coating 66 Facilitated transport 247 Fick's law 13,167,222 Dissipation function 149 Fingerlike structures Fixed charge 106 Distillation 235 Flat membranes 38,194,270 Flory-Huggins thermodynamics Distribution coefficient 192 Flow pattern 60,312 73 Divinyl benzene 274 - co - cross 320 Donnan equilibrium 193 - counter 320 320 Double layers 38 Driving force 145,147 Dual sorption theory 166

INDEX 359 - laminar 286 Hyperfiltration 190,213,330 - mixed 320 - plug 320 I - turbulent 286 Flux Ideal separation factor 171 Fouling 6 Ideal solution 237 Fourier's law 305 Immersion precipitation 59,85 Fractionation Immobilised liquid membranes 244 Free enthalpy of mixing 13 Inorganic membranes 47 Free volume theory 334 Interfacial polymerisation 65 Friction resistance 71 Interaction parameter 89,92 Ff-IR 178 Ion-exchange 192,270 Fugacity 90,170 Isoelectric point 275 144 199 G K Gas adsorption 123 Kelvin relation 123 Gas desorption 123 Kinetic diameter 226 Gas permeation 135 Knudsen flow 160,221 Gas separation 192,221,336 Kozeny Carman equation 159,204 Gelation 83 Krypton 169 Gel layer 290 Glass 47 L Glass transition temperature 26,29,137 Glassy polymers 26 Laminar flow 286 Langmuir sorption 166 Grafting 70 LaPlace equation 117,119,264 Lecithine H Lennard-Jones diameter 49 Light transmission 174 Hagen-Poisseuille equation 58,204 Limiting current density 94 Helium 169 Limiting flux 302 Hemodialysis 261 Lipids 289 Henry's law 166 Liposomes 48 History 8 Liquid membranes 51 Hollow fiber 244 Homogeneous membranes 62,315 Hydrodynamic resistance model 11 M Hydrogen Hydrogen bonding 297 Macropores 112 Hydrophilic polymers 172,233 Macrovoid 106 Hydrophobic polymers Mass transfer coefficient 284 25 207 207

360 INDEX Mechanical properties 35,48 -design 312 - hollow fiber 316 Membrane - plate-and-frame 313 - spiral wound 314 asymmetric II - tubular 315 48 Molecular weight 22 - biological Molecular weight distribution 23 Mosaic membrane 219 - ceramic 128,205 characterisation 110 cleaning 309 N 312 - configuration 10 definition 262 305 - distillation - fouling fouling index (MFI) 306 NanofIltIation 209 69 Neon 169 - homogeneous 47 Nemst-Planck equation 196 NitIate removal 249 - inorganic Nitrogen 32,225,249 Nitrogen enrichment 347 - liquid 244 Non-equilibrium thermodynamics 149 Nonporous membranes - morphology 11,110 Nonsolvent 3 Nylon-6 59,81 - nonporous 47,134,164 44 - polymer 41 - porous 41,112,158 - preparation 54 - processes 12,198 - selectivity 7 0 - symmetric 11 - synthetic 17 Ohm's law 13 Mercury intrusion 119 Osmosis 199 Osmotic pressure 201,293 Mesopores 112 Osmotic pressure model 292 Oxygen 32,225,249 Metals 47 Oxygen enrichment 344 oxygen/nitrogen separation 344 Methane 234 MicrofIltIation 114,204 Micropores 112 Miscibility gap 77 Mobility 170 P Model - boundary layer resistance 297 Passive transport 146 Permeability coefficient 135,165 - capillary (see hagen-Poisseulille) Permeate Permporometry 5,329 - gel layer 290 Pervaporation 129 Phase diagram - osmotic pressure 292 Phase inversion 192,234 Phase separation 77 - resistance 230 58,82 Module 58,71 - capillary 315 - configuration 312

INDEX 361 Phase transition 15,234,263 Polystyrene 20,32 Phenol 259 Polysulfone 207 Phenomenological equations Polytetrafluoroethylene Phospholipids 13,151 Polytrimethylsilylpropyne 35,43,207,265 Piezodialysis 49 Polyvinylalcohol 33 Piperazine Polyvinylidenefluoride Plasma-etching 219 Polyvinyltrimethylsilane 20,242 Plasmapheresis 216 Pore geometry 43,207,210,266 Plasmapolymerisation 140 Pore shape Plasma etching 208 Pore size 33 Plasticisation 68 Pore size distribution 114 Plate-and-frame systems 140 Porosity 114 Plugging 197,228,231 Precipitation 113,128 Poisseuille flow 313 113,126,128 Polarisation 282 - controlled evaporation 158,206 158,160 - immersion - concentration - vapour phase 59 - temperature 283 Preferential sorption 59 Polyacrylamide 303 Pressure retarded osmosis 59 Polyacrylonitrile 242 Pre-treatment 240 Polyamide 20,210,242 217 Polybenzimidazoles 44,207,210 309 Polybutadiene Polycarbonate 34 Q polychloroprene 37 Polycondensation 42,207 Quarternary amines 38 Polydimethylsiloxane 37 Polyelectrolyte 37 R Polyester 37,228 Polyether sulfone 38 Radiation 70 Polyether imide 35 Recirculation 321 Polyethylene 46,207,210 Recovery 329 Polyethyleneterephthalate 46,207,210 Reflection coefficient 153 Polyethyleneimine 18,266 Rejection coefficient Polyimides 29 Relaxation 7 Polyisoprene 66 Resistance model 166 Polymethylpentene 34,46,207,210 Retention 230 Polymers 21 Reverse Osmosis (see hyperfiltration) Polyoxadiazole 29,32 Reynolds number 7 Polyphenylene oxide 17 Rubbery state Polyphosphasenes 34 286 Polypropylene 128 26 35 20,43,207,266 S Scanning electron microscopy 114 Schmidt number 286

362 INDEX Seawater desalination 216,338 Streaming potential 156 Stress 36 Sedimentation 299 Sttetched membranes 56 Sublayer 11,229,241 Sedimentation coefficient 298 Surface 141 Selectivity 7 - analysis 265 -- energy 39 Selectivity coefficient 7 Sulfonated polyethylene 39 Semiconductor industry 217,324 Sulfonated polysulfone 244 Supported liquid membranes 169,221 Semi-crystalline 31,83,135 Swelling Symmetric membranes 11 Separation System - concentration dependent 175 - factor 7 - ideal 171 - gaseous mixtures 32,224 - liquid mixtures 242 Sherwood number 285 Sieving 54,111 Silicone rubber (see polydimethylsiloxane) Single pass 321,338 Sintering 56 T Skin 11 Solubility 181 Solubility coefficient 172,223 Tapered design 323 Solubility parameter 71 Tensile modulus 26,31 Solute rejection 131 Ternary phase diagram 82 Solution-diffusion model 165,223,235 Thermal stability 33,47 Sorption Thermal precipitation 59,85 - gases 227 Thermodynamics 71,181 - in glassy polymers 166,227 Thermo-osmosis 270 - in rubbery polymers 166 Thermoporometry 126 - liquids 169,221 Thin film composite 11,58,64 Spinodal demixing 80 Time lag 175 Spinneret 63 Tortuosity 158,204 Spinning hollow fibers 61 Track etching 56 Spiral wound configuration 314 Transport 145,204,213,222,236,250,260,271 Sponge ball cleaning 310 TubuUrrconfiguration 320 Stability Tubular membranes 61,64 - chemical 33,48 Tungsten 47 - mechanical 33,48 Turbulence promoters 309 - thermal Turbulent flow 286 35,47 State of the polymer 26 U Stefan-Maxwell 90 Stereoisomerism 19 Ultracentrifuge 122,298 Ultrafiltration 209 Stokes-Einstein 226,256 Ultra-pure water 324 Strain 36

INDEX 363 Uranium enrichment 47,222 v Vapour penneation 176,228 Vesicles 51 Volatile solvents 160,228 W Water 2,169,208,212,216,324 Wet dry spinning process 61 Wide angle X-ray scattering (WAXS) 139 X XPS 142 Y Yield 329 Z Zirconium oxide 207