膜分离理论和技术

1、关于膜分离理论与技术第一张，PPT共一百零二页，创作于2022年6月第二张，PPT共一百零二页，创作于2022年6月4.1.1: 膜及膜分离的定义:膜:狭义:如果在一个流体相或两个流体相之间有一薄层凝聚相(polymer phase, made from polyolefin)把流体分开,用于实现分离目的,这中间的凝聚相就叫膜. 广义:一个相或多个相中间的一个不连续区间(discrete margin),用于实现分离目的. A synthetic membrane is an interphase that separates two phases and restricts the tran

2、sport of chemical species in a specific manner.4.1: 膜分离技术概述第三张，PPT共一百零二页，创作于2022年6月膜的特点:A membrane must be Semi-permeable:A membrane can be: homogeneous or heterogeneous, symmetric or asymmetric in structure; solid or liquid; neutral, carry either positive or negative charges, or have functional gro

3、ups with specific binding or complexing abilities. Membrane thickness ranges from less than 100nm to more than 1cm. Mass transport through a membrane can occur via diffusion of individual molecules or convection induced by a concentration, pressure, 第四张，PPT共一百零二页，创作于2022年6月temperature, Or electrical

4、 potential gradient.被膜分离的物质:Liquid, gaseous.膜分离的定义: Membrane separation involves partially separating a feed containing a mixture of two or more components by use of a semipermeable barrier (the membrane) through which one or more of the species moves faster than another or other species. 第五张，PPT共一百

5、零二页，创作于2022年6月1:按膜性质分:生物膜:细胞膜,线粒体膜,液泡膜.合成膜:有机膜,无机膜.2:按结构分:Although synthetic membranes vary widely in physical structure and function, they can be classified conveniently in five groups:microporous membranes,Non-Porous Membranes (homogeneous membranes), asymmetric membranesCarrier Membranes,Liquid e

6、mulsion membrane or with selective carrierelectrically charged barriers,4.1.2:膜的分类第六张，PPT共一百零二页，创作于2022年6月Non-Porous MembranesCarrier Membranesmicroporous Membranes第七张，PPT共一百零二页，创作于2022年6月3:按分离过程分:Reverse osmosis membrane(ORM),Ultra-filtration membrane(UFM),Micro-filtration membrane(MFM),Nano-filtra

7、tion membrane(NFM),Dialysis membrane(DM),Electric dialysis membrane(EDM).4.1.3:膜过程的推动力1: Pressure driven(Pressure gap)Reverse osmosis (OR),Ultra-filtration (UF),Micro-filtration (MF),Nano-filtration (NF).Vapourization permeation(VP).第八张，PPT共一百零二页，创作于2022年6月2: Non-pressure drivenConcentration gradien

8、t(chemical potential gradient): Dialysis (D),Potential gradient: Electric dialysis (ED)Concentration gradient(chemical potential gradient, active transfer): Liquid emulsion dialysis(LED). 4.1.4:膜分离过程中膜的作用选择性透过:过滤;溶解-扩散;优先吸附;氢键结合;主动运输.第九张，PPT共一百零二页，创作于2022年6月第十张，PPT共一百零二页，创作于2022年6月Schematic diagram

9、illustrating the modes of mass transport in synthetic membranes separating two homogeneous phases:A) Passive transport; B) Facilitated transport; C) Active transportA=component to be transported; B=carrier; m= chemical potential; superscripts () and (“) indicate the two phases on the different sides

10、 of the membrane.第十一张，PPT共一百零二页，创作于2022年6月4.1.5:膜分离过程的特点及适用性1:特点:无相变,不存在平衡关系,过程简单,常温操作,能耗低,无污染,同样的过程可以解决不同的分离问题.2:适用性:化学或物理性质相似,但分子量不同的组分,如蛋白质和多肽.同分异构体,热敏性成分,酶,茶多酚,香气成分.大分子.第十二张，PPT共一百零二页，创作于2022年6月4.2:膜及膜分离技术的发展渗透和半渗透的发现(1748年，Nollet)扩散定律(Fick),1855渗析现象(1861,Graham)渗透现象和渗透压(Vant Hoff)微孔过滤,超滤和反渗透190

11、7,Backman)Donnan平衡(1911)电解质和非电解质的反渗透,1920s,Mangold膜电势1930s人工肾的发明,1940s电渗析脱盐,血液透析电渗析技术,1950sSourirajan对膜的制备苦咸水淡化技术,1960s膜分离的工业化应用1970s新型膜及膜技术的开发第十三张，PPT共一百零二页，创作于2022年6月第十四张，PPT共一百零二页，创作于2022年6月4.3:膜分离技术的分类4.3.1: Pressure driven(Pressure gap)1: Reverse osmosis (OR),去除具有高渗透压的小分子,需高压(4000-8000KPa)2: Ul

12、tra-filtration (UF),去除小分子,截留大分子(300-500,000)需压力(200-2000KPa)3: Nano-filtration (NF).在RO和UF的中间状态,去除分子量大于200-500的有机分子.4: Vapourization permeation(VP).气体渗透的推动力为分压差，常应用于空气中氧气的分离、富集.5: Micro-filtration (MF).从液体或气体中去除0.01-10m的粒子:空气除菌.微孔过滤Dead end MF,过滤方向与压力方向相同, build-up, batch process, A: Depth filtratio

13、n.B: Surface-filtration第十五张，PPT共一百零二页，创作于2022年6月第十六张，PPT共一百零二页，创作于2022年6月第十七张，PPT共一百零二页，创作于2022年6月第十八张，PPT共一百零二页，创作于2022年6月Schematic diagram illustrating pressure-driven membrane separation processesa) Particles; b) Macromolecules; c) Low molecular mass solutes (microsolutes); d) Solvent; e) Gas.第十九

14、张，PPT共一百零二页，创作于2022年6月Dead-end MF:depth filtrationA：微孔过滤Dead end MF,过滤方向与压力方向相同, build-up, batch process, A: Depth filtration.B: Surface-filtration第二十张，PPT共一百零二页，创作于2022年6月Dead end MF: surface filtration第二十一张，PPT共一百零二页，创作于2022年6月Cross MFB:微孔过滤Cross MF（错流微孔过滤）, no build-up, continuous process, high f

15、lux rate for long period of time.过滤方向与压力方向垂直.第二十二张，PPT共一百零二页，创作于2022年6月6: Gas-exchange and separation:Porous membrane, 根据气体分子量不同而实现分离: Gases can be separated in microporous as well as in homogeneous membranes. The selectivity of microporous membranes is generally rather low because of the Knudsen di

16、ffusion transport mechanism; 第二十三张，PPT共一百零二页，创作于2022年6月Schematic diagram illustrating gas separationp=pressureNon-porous membrane.根据气体过膜时对膜的溶解和扩散的差异而进行分离.Under the driving force of a hydrostatic pressure difference, some components permeate the membrane, and the feed stream is split into a permeate

17、and a retentate stream. If the membrane has a higher permeability for one of the components in the feed mixture than for others, this component is enriched in the permeate and depleted in the retentate.第二十四张，PPT共一百零二页，创作于2022年6月Significantly higher selectivities can be obtained in homogeneous membra

18、nes where transport is based on the solution and diffusion of the components in the membrane phase. Mass transport in a solutiondiffusion membrane is illustrated in Figure and consists of three steps: 1. sorption of the components from a feed mixture according to their partition coefficients between

19、 the gas and polymer phases;2. diffusion of the individual components within the membrane phase according to their activity gradients; and3. desorption of the components from the membrane in the permeable gas phase.第二十五张，PPT共一百零二页，创作于2022年6月Schematic diagram illustrating three idealized feed and per

20、meate flow patterns used in gas separation systemsA) perpendicular plug of feed and permeate; B) Cocurrent plug flow of feed and permeate; C) Countercurrent plug flow of feed and permeate第二十六张，PPT共一百零二页，创作于2022年6月*4.3.2: Non-pressure driven process:Electrodialysis: electrical potentialLiquid emulsio

21、n separation(LEM), Concentration gradient and active carrier.Membrane reactor:Enzyme-membrane reactor(EMR)Catalyst membrane reactor(CMR)第二十七张，PPT共一百零二页，创作于2022年6月Schematic diagram of electrodialysisa) Cation-exchange membrane; b) Anion-exchange membrane第二十八张，PPT共一百零二页，创作于2022年6月Schematic diagram ill

22、ustrating preparation of an emulsion-type liquid membranea) Liquid membrane phase; b) Stripping solution; c) Feed solution第二十九张，PPT共一百零二页，创作于2022年6月第三十张，PPT共一百零二页，创作于2022年6月4.4:膜技术的应用领域水处理:海水,苦咸水淡化,纯水的生产.医药工业:药剂浓缩,提纯,人工肝,人工肾,人工肺的制备.食品工业:果蔬汁浓缩,饮料除菌及澄清,大豆分离蛋白的制备,乳制品处理,食品废水处理.石油化工.环境保护.第三十一张，PPT共一百零二页，

23、创作于2022年6月4.5:膜的制备4.5.1:与膜过程有关的因素:待分离物质的性质,膜的孔径,形状,梳密膜的分子结构,膜-组分之间的相互作用,膜的荷电性质.第三十二张，PPT共一百零二页，创作于2022年6月4.5.2:按结构分类的膜Membrane must have a high permeability to certain types of molecules. Membrane structures consist of the following basic types:microporous membranes,Non-Porous Membranes (homogeneous

24、 membranes), Symmetric and asymmetric membranesCarrier Membranes,Liquid emulsion membrane or with selective carrierelectrically charged barriers,第三十三张，PPT共一百零二页，创作于2022年6月4.5.3:Porous Membranes用途: Porous membranes are used in microfiltration and ultrafiltration. 孔径大小: The dimension of the pores (0.1

25、10m). 空隙率:80%, 107个/cm2. 分离效果主要取决与膜孔及组分的分子大小. High selectivities can be obtained when the size of the solute is large relative to the pore size in the membrane. Porous Membranes第三十四张，PPT共一百零二页，创作于2022年6月4.5.3.1:微孔膜的制备制膜材料:溶质:高分子聚合物,如乙酸纤维素,聚烯烃类,壳聚糖等.溶剂:甲酸,乙酸,丙酸,甲醇,乙醇多种有机酸.添加剂:PEG,PVP,NaCl,酶,催化剂.制膜方法:

26、烧结法:氧化铝、氮化硅、碳、钨、镍、铝及多种有机高分子等微细粉末在高温下烧结而成。孔径越过1m，可用于气体、液体中微粒分离. 相转化法:溶解 浇铸 凝胶化 相转化 (获得非对称性膜) 拉伸均相法: 熔融 挤出成膜 延伸退火 拉伸痕迹刻蚀法: 均相聚合成膜 U235 辐射 刻蚀 洗涤成膜.膜组织膜孔第三十五张，PPT共一百零二页，创作于2022年6月Schematic diagram illustrating preparation of capillary pore membranes by track etchinga) Radiation source; b) Polymer film;

27、c) Radiation track第三十六张，PPT共一百零二页，创作于2022年6月Scanning electron micrograph of a sintered(烧结) membrane prepared from aluminum oxide powder第三十七张，PPT共一百零二页，创作于2022年6月Schematic diagram of the filtration characteristics of symmetric (A) and asymmetric (B) membranes第三十八张，PPT共一百零二页，创作于2022年6月Schematic drawin

28、g of the cross section of an asymmetric membrane第三十九张，PPT共一百零二页，创作于2022年6月Scanning electron micrographs of cross sections of asymmetric membranes showing typical “finger” structure (A, polysulfone), a “sponge” structure with graded pore size distribution (B, polyamide) and a structure with uniform p

29、ore size distribution (C, polyamide)第四十张，PPT共一百零二页，创作于2022年6月Schematic diagram showing the structure of an asymmetric composite membrane第四十一张，PPT共一百零二页，创作于2022年6月Scanning electron micrograph showing an asymmetric composite membrane with polydimethylsiloxane（聚二甲基硅氧烷） as the selective layer deposited

30、on a polysulfone support第四十二张，PPT共一百零二页，创作于2022年6月Scanning electron micrograph of the surface of a microporous polypropylene（聚丙烯）membrane precipitated by thermal gelation from a hot homogeneous polymer solution.第四十三张，PPT共一百零二页，创作于2022年6月Scanning electron micrograph of the surface of a microporous ce

31、llulose nitrate membrane prepared from a homogeneous polymer solution by precipitation with water vapor.第四十四张，PPT共一百零二页，创作于2022年6月Scanning electron micrograph of a membrane prepared by stretching an extruded polytetrafluoroethylene（PTFE，聚四氟乙烯）film perpendicular to the direction of extrusion。第四十五张，PP

32、T共一百零二页，创作于2022年6月Scanning electron micrograph of the surface of a capillary pore polycarbonate（聚碳酸酯）membrane第四十六张，PPT共一百零二页，创作于2022年6月Membrane material*Pore size, mManufacturing processApplicationCeramic, metal, or polymer powder0.120pressing and sintering of powdermicrofiltrationHomogeneous polyme

33、r sheets (PE, PTFE)0.510stretching of extruded polymer sheetsmicrofiltration, burn dressings, artificial blood vesselsHomogeneous polymer sheets (PC)0.0210track etchingmicrofiltrationPolymer solution (CN, CA)0.0015phase inversionmicrofiltration, ultrafiltration, sterilizationTable2.Microporous membr

34、anes, their preparation and applicationPE=polyethylene; PTFE=polytetrafluoroethylene; PC=polycarbonate; CN=cellulose nitrate; CA=cellulose acetate.第四十七张，PPT共一百零二页，创作于2022年6月4.5.4:Non-Porous MembranesThese membranes are capable of separating molecules of the same size, gases as well as liquids. 用途: N

35、on-porous membranes are mainly used in RO process,UF.孔径大小: The dimension of the pores (510). 孔结构用电子显微镜难以观察.空隙率:10%. 厚薄:50-50000 . 由结晶部分与非定型部分组成.The transport is determined by the solution-diffusion mechanism, which means that components first must dissolve into the membrane and then diffuse through

36、the membrane due to a driving force. Separation is due to differences in diffusivity and/or solubility. 第四十八张，PPT共一百零二页，创作于2022年6月 (1)将含有一定乙醚基值的乙酸纤维按比例加进溶剂和添加剂中，充分混合，配成浇注液。 (2)流延成膜配制好的注膜液经压滤和脱气泡后，在一定的温度与湿度下，以流延法在平滑的玻璃板表面上刮制成具有一定形状和厚度的液膜 (3)蒸发使制成的液膜在上操择作条件下，静置一定时间，让溶剂蒸发第四十九张，PPT共一百零二页，创作于2022年6月第五十张，

37、PPT共一百零二页，创作于2022年6月Non-Porous Membranes H2O or solvent salt or other minerals第五十一张，PPT共一百零二页，创作于2022年6月The representative membrane materials and applications are listed in following table. polyacrylonitrile 聚丙烯腈，polyimide 聚酰亚胺第五十二张，PPT共一百零二页，创作于2022年6月4.5.5:Ion exchange membrane离子交换膜:阳离子（cation-exc

38、hange membranes ）交换膜,用于交换阳离子. 阴离子固定基团阳离子交换基团阴离子交换膜（anion-exchange membranes）,用于交换阴离子.阳离子固定基团阴离子交换基团R-SO3H+(Na+)R-N+(CH3)3-OH-(Cl-)固定基团解离离子解离离子固定基团磺酸型阳离子交换膜(阳膜)活性基团季胺型阴离子交换膜(阴膜)活性基团第五十三张，PPT共一百零二页，创作于2022年6月The type and concentration of fixed ionic charges determine the permselectivity and electrical

39、 resistance of the membrane and also influence its mechanical properties. The degree of swelling is affected by the concentration of fixed charges. The following groups are used as fixed charges in cation-exchange membranes: In anion-exchange membranes, fixed charges may be 第五十四张，PPT共一百零二页，创作于2022年6

40、月Homogeneous ion-exchange membranes can be prepared by three basic procedures: 1. Polymerization or polycondensation of monomers2. Introduction of anionic or cationic moieties into a preformed film3. Introduction of anionic or cationic moieties into a polymer, followed by film casting.第五十五张，PPT共一百零二

41、页，创作于2022年6月Structure of a cation-exchange membrane:a) Polymer matrix with negative fixed charges; b) Positive counterions; c) Negative co-ions.第五十六张，PPT共一百零二页，创作于2022年6月4.5.6:液膜(Liquid emulsion membrane,LEM)液膜构成:成膜溶剂,油溶性溶剂水溶性溶剂表面活性剂:促进膜过程乳化和选择性分离的作用.添加剂:提高膜的稳定性.载体:载体的作用是使分离组分与载体在液膜的一端形成结合体，然后在液膜中扩散

42、，及至扩散至液膜的另一侧时将分离组分释放，载体再返回与其他分离组分结合。成膜的方法：将成膜剂倒入分离液中，高速搅拌使之乳化，乳化液外层即为液膜,液膜分油包水型和水包油型两类。水溶性分离液采用油溶性成膜剂，乳化后形成油包水型液膜；油溶性分离液则采用水溶性成膜剂，形成水包油型液膜。液膜厚度约为110m,乳化液的液滴直径为0.05-0.2mm。第五十七张，PPT共一百零二页，创作于2022年6月Schematic drawing of supported (A) and unsupported (B) liquid membranesa) Aqueous phase; b) Porous suppo

43、rt; c) Liquid membrane第五十八张，PPT共一百零二页，创作于2022年6月Schematic diagram illustrating preparation of an emulsion-type liquid membranea) Liquid membrane phase; b) Stripping solution; c) Feed solution第五十九张，PPT共一百零二页，创作于2022年6月Carrier Membranes第六十张，PPT共一百零二页，创作于2022年6月第六十一张，PPT共一百零二页，创作于2022年6月第六十二张，PPT共一百零二页

44、，创作于2022年6月4.6:RO和UF的分离过程机理及工艺4.6.1:反渗透现象:平衡(equilibrium):C1=C2, P1=P2;1=2, 1 = 2渗透(osmosis)C1C2, P1=P2;1 2渗透平衡(osmotic equilibrium) C1C2, P1 P2;P= , 反渗透(reverse osmosis) C1 P2;P , H2O12P111222H2OC1=C2, P1=P2;1=2, 1 = 2C1C2, P1=P2;1 2C1C2, P1 2P= C1 P2;P , 1 2P 第六十三张，PPT共一百零二页，创作于2022年6月The osmotic

45、pressure is approximated by the following relation: where cs is solute concentration, R the gas constant, T the absolute temperature, and g the osmotic coefficient; g is a correction factor for the nonideal behavior of a solution, only for an ideal solution does g approach unity.反渗透的两个必要条件:1: 半透膜2:

46、操作压力渗透压.第六十四张，PPT共一百零二页，创作于2022年6月4.6.2: 膜过程中的几种传递现象:1:溶剂(水)在压力差的作用下通过膜的传导.2:溶质在压力差及浓度差的作用下通过膜的传导;3:膜的高压侧由于浓差极化现象,溶质由边界层向主体溶液的扩散现象.a) Particles; b) Macromolecules; c) Low molecular mass solutes (microsolutes); d) Solvent; 第六十五张，PPT共一百零二页，创作于2022年6月Schematic diagram illustrating the concentration pro

47、file of components retained by the membrane in the film model.第六十六张，PPT共一百零二页，创作于2022年6月Schematic diagram illustrating the transport mechanism of components retained by the membrane and accumulated in a gel layer from the membrane surface back into the bulk solution第六十七张，PPT共一百零二页，创作于2022年6月4.7:膜的透过

48、机理4.7.1:氢键理论及结合水空穴有序扩散模型(Ried等提出)1:膜材料必须是亲水性的，能与水形成氢键。如醋酸纤维素膜 (无孔)，由于氢键和范德华力的作用大分子之间是牢固结合的，形成晶相区域和非晶相区域。2:在非晶相区，水与醋酸纤维素羰基上的氧原子形成氢键，形成所谓的“结合水”。引起水分子熵值的极大下降，类似于冰的构造。3:在结合水中依靠氢键与膜保持紧密结合的称为一级结合水，保持较松散结合的称为二级结合水。4:一级结合水的介电常数很低，对离子无溶剂化作用，离子不能进入一级结合水透过膜。二级结合水的介电常数与普通水相同，离子可以进入并透过膜。理想的膜表面只存在一级结合水。5:与醋酸纤维不能形

49、成氢键的离子或分子不能透过结合水区域, 能和膜产生氢键结合的离子或分子(如水、酸等)可以进入结合水区域，并进行迁移，通过膜。第六十八张，PPT共一百零二页，创作于2022年6月6:在压力作用下，溶液中的水分子和醋酸纤维素的羰基上的原子形成氢键，而原来水分子间形成的氢键被断开，水分子解离出来和碳基上的原子形成新的氢键。这样连续的氢键形成与断开，使水分子进入膜的多孔层，由于多孔层含有大量的毛细管水水分子能畅通流出膜外。这种离子或分子的迁移称为孔穴扩散。但氢键理论忽略了溶质溶剂膜材料之间的相互作用力。另外盐的渗透与孔穴形成的几率有关,降低孔穴形成的几率，可减少盐的渗透性。4.7.2:优先吸附毛细孔流

50、理论(preferential sorption and pore flow model) 1963年sourirajan在Gibbs吸附方程的基础上提出了优先吸附毛细孔流理论:1:当溶液与高分子多孔膜接触时，膜对水优先吸附.2:在膜与溶液界面附近的溶质浓度会急剧下降？，在界面上形成被吸附的纯水层. 第六十九张，PPT共一百零二页，创作于2022年6月3:由于压力作用将使其通过膜表面的毛细孔，即可获得纯水。4:纯水层厚度约为1-2个水分子层，水分子的有效直径约5 ，则纯水层厚度约为5-10 。纯水层的厚度与溶液及膜的化学性质有关。5:当膜表面毛细孔孔径为纯水层厚度的2倍时，即10-20 ,每个

51、毛细孔就得到最大流量的纯水此时该毛细孔径称为“临界孔径”；如果孔径大于临界孔径，就会产生溶质的泄漏,小于临界孔径时则通量下降.6:但临界孔径可以比溶质与溶剂分子直径大几倍而溶质仍能进行分离。因此这种分离不是简单的筛分和超过滤作用，而是与孔的结构有关，包括:纯水层厚度、膜的厚度、孔径与孔分布、孔隙率、支撑层孔隙大小等。第七十张，PPT共一百零二页，创作于2022年6月7:膜材料对水要优先选择吸附，对溶质要选择排斥膜表面应具有尽可能多的有效直径的孔，这才能获得最佳的分离率和最高的透水速度。这个理论符合氢键理论的结合水和孔穴型扩散模型，说明能与膜产生氢键的溶质以有序扩散的方式迁移。但是用电子显微镜观

52、察，并没有看到所谓的临界孔径细孔及纯水层。 第七十一张，PPT共一百零二页，创作于2022年6月第七十二张，PPT共一百零二页，创作于2022年6月5.7.3:溶解扩散理论(solutiondiffusion):Lonsdale和Riley等认为:1:此模型是把半透膜看作是一种完全致密的中性界面水和溶质通过薄膜是分为两个阶段完成的2:溶剂与溶质透过膜的机理是由于溶剂与溶质在膜中的溶解。与膜孔的有无及性质关系不大.3:第一阶段是水和溶质被吸附溶解到膜材质表面上；4:第二阶段是水和溶质在膜中扩散传递，在压力和化学位差的推动力作用下，最后通过膜因此，溶解扩散模型不要求膜是有孔的5:在给定条件下，溶质

53、与溶剂在膜中的溶解度和扩散系数应恒定，过滤速率及分离率也应当恒定。由于溶质与溶剂在膜中的溶解度和扩散系数的差异而获得分离.溶解扩散理论认为膜可以是均质膜，或非均质多孔膜但表面具有致密活化层，或超薄膜。但这个理论忽略了膜结构性能的重要影响。同时还不能解释膜材料具有高度吸附性和对水、盐具有高渗透性的原因。5.7.4:筛网理论.第七十三张，PPT共一百零二页，创作于2022年6月5.8.1:Membrane Mass Transport in Ultrafiltration. In ultrafiltration the driving force again is a pressure gradi

54、ent, and mass transport is also dominated by the convective flux. However, solute retention by the membrane leads to a concentration difference for the retained components, which can cause osmotic pressure differences and diffusive fluxes of the solutes through the membrane. The volume flux in ultra

55、filtration can thus be expressed bywhere Lvv is phenomenological coefficient, the membrane porosity, r the pore radius, the dynamic viscosity, a tortuosity factor, p the pressure difference across the membrane, and z the membrane thickness. A factor, osmosis pressure difference. 5.8:传质的数学模型Jv=A( p -

56、 ) or第七十四张，PPT共一百零二页，创作于2022年6月the solute flux of a dilute solution through a membrane may be expressed bywhere is the diffusion coefficient and the concentration of the solutes in the solvent-filled pores of the ultrafiltration membrane.第七十五张，PPT共一百零二页，创作于2022年6月5.8.2:Membrane Mass Transport in Rev

57、erse Osmosis. In reverse osmosis the driving force is a hydrostatic pressure difference. Two models have been discussed for the transport mechanism. The model proposed by Sourirajan is based on the hypothesis of pore flow in reverse osmosis membranes.The second model, which is discussed in more deta

58、il here, is based on a solutiondiffusion mechanism that virtually excludes convective flow. The flux in reverse osmosis membranes can be expressed byWhere, D1M represents diffusion coefficient of the solvent the in the boundary layer of the membrane, and l the partial molar volume of the solvent.第七十

59、六张，PPT共一百零二页，创作于2022年6月For the solute flux in dilute solution , the solute flux can be described by where and are the diffusion coefficient and the concentration of the solute in the membrane phase, respectively.第七十七张，PPT共一百零二页，创作于2022年6月5.9:评价膜分离效果的指标The performance of a membrane in a pressure-driv

60、en separation process is determined by1: its filtration rate(透过速率)2: its mass separation properties (i.e., retention capability, Rejection Rate,截留率). 3: reduction constant of flux rate(通量衰减系数).5.9.1:Filtration rates: The filtration rates in microfiltration, ultrafiltration, and reverse osmosis are d