利用动电模型分析黏土渗流的耦合动力学性状
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摘要
从水头-诱导电位耦合驱动的角度,探讨分析黏土-水溶液体系的流体动力学性状。为此,借助动电输运原理,耦合Poisson-Boltzmann、Nernst-Planck、Navier-Stokes方程,建立了"广义力"驱动"广义流"的耦合关系。模型从黏土代表性单元体入手,计算确定各项耦合系数,用以定量考察离子迁移、流体运动的耦合性状。计算表明:采用Debye-Huckel近似计算黏土双电层电位将引起显著的误差;诱导电位产生的原因在于维持体系的电中性,其梯度大小正比于正负离子间因水头迁移性的差异而产生的潜在分离程度;诱导电位作用于离子迁移的方式在于阻滞正离子迁移,助推负离子迁移,而作用于流体运动的方式在于引起反向电渗,进而削弱水头驱动下的正向渗流;高表面带电密度的黏土矿物(如蒙脱土)处于低孔隙率的状态时,诱导电位对于渗流的削弱程度有可能异常显著。因此,建议相应的水头渗透系数的测定需要充分考虑诱导电位的影响,否则将导致较为显著的误差。
This paper attempts an in-depth analysis on the hydrodynamic behavior of clays considering the multiple driving forces of pressure and induced electrical potential(IEP). Electrokinetics is employed to quantify the processes of ion migration, fluid motion,and potential distribution, which are described by the coupled equations of the Nernst-Planck(NP), the Navier-Stokes(NS), and the Poisson-Boltzmann(PB), respectively. The numerical investigation shows that employment of Debye-Huckel approximation may be inappropriate for clays in calculation of double layer potential since their relatively high surface charge density. IEP is caused by the requirement of electroneutrality for the clay-water system, and is directly proportional to the separation of cation-anion resulting from the differential hydraulic migratability between them. IEP contributes to decelerating cation, accelerating anion, and producing a negative electroosmosis that counteracts in partial the positive flow driven by pressure. At those conditions including low concentration, small porosity, and high surface charge density, double layer effects may be enhanced, leading to significant effects both in IEP and its flow reduction.
This paper attempts an in-depth analysis on the hydrodynamic behavior of clays considering the multiple driving forces of pressure and induced electrical potential(IEP). Electrokinetics is employed to quantify the processes of ion migration, fluid motion,and potential distribution, which are described by the coupled equations of the Nernst-Planck(NP), the Navier-Stokes(NS), and the Poisson-Boltzmann(PB), respectively. The numerical investigation shows that employment of Debye-Huckel approximation may be inappropriate for clays in calculation of double layer potential since their relatively high surface charge density. IEP is caused by the requirement of electroneutrality for the clay-water system, and is directly proportional to the separation of cation-anion resulting from the differential hydraulic migratability between them. IEP contributes to decelerating cation, accelerating anion, and producing a negative electroosmosis that counteracts in partial the positive flow driven by pressure. At those conditions including low concentration, small porosity, and high surface charge density, double layer effects may be enhanced, leading to significant effects both in IEP and its flow reduction.
引文
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[14]TANG X W,CHENG G C,CHEN Y M.An easy-to-implement multi-scale computation of permeability coefficient for porous materials[J].Microporous and Mesoporous Materials,2010,130(1-3):274-279.
[15]REN X W,ZHAO Y,DENG Y L.A relation of hydraulic conductivity-void ratio for soils based on Kozeny-Carman equation[J].Engineering Geology,2016,213(4):89-97.
[16]HUNTER R.Zeta potential in colloid science:principles and applications[M].New York:Academic Press,1981.
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[18]YANG C,LI D Q.Analysis of electrokinetic effects on the liquid flow in rectangular microchannels[J].Colloids and Surfaces A:Physicochemical and Engineering Aspects,1998,143:339-353.
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[20]ZHU Q Y,XIE M H,YANG J,et al.Analytical determination of permeability of porous fibrous media with consideration of electrokinetic phenomena[J].International Journal of Heat and Mass Transfer,2012,55(5-6):1716-1723.
[21]ALLAIRE G,MIKELIC A,PIATNITSKI A.Homogenizationi of the linearized ionic transport equations in rigid periodic porous media[J].Journal of Mathematical Physics,2010,51:123103.
[22]PLAZA I,ONTIVEROS-ORTEGA A,CALERO J,et al.Implication of zeta potential and surface free energy in the description of agricultural soil quality:effect of different cations and humic acids on degraded soils[J].Soil and Tillage Research,2015,146(B):148-158.
[23]潘慧,蓝咏,吴锐钊,等.CTAB与SDS对膨润土改性的界面性质研究[J].华南师范大学学报(自然科学版),2008(1):88-92.PAN Hui,LAN Yong,WU Rui-zhao,et al.Interfacial characterization of organic bentonite with cetyltrimethyle ammonium brom ide and sodium dodecyl sulfate[J].Journal of South China Normal University(Natural Science Edition),2008(1):88-92.
[24]LI D Q.Electro-viscous effects on pressure-driven liquid flow in microchannels[J].Colloids and Surfaces A:Physicochemical and Engineering Aspects,2001,195:35-57.
[25]TOURNASSAT C,STEEFEL C I.Ionic transport in nano-porous clays with consideration of electrostatic effects[J].Reviews in Mineralogy and Geochemistry,2015,80(1):287-329.
[26]ONSAGER L.Reciprocal relations in irreversible processes.I[J].Physical Review,1931,37:405-426.
[27]GRIM R E.Clay mineralogy:the clay mineral composition of soils and clays is providing an understanding of their properties[J].Science,1962,135(3507):890-8.
[28]DULLIEN F A.Porous media:fluid transport and pore structure[M].New York:Academic Press,1991.
[29]FAIR J C,OSTERLE J F.Reverse electrodialysis in charged capillary membranes[J].The Journal of Chemical Physics,1971,54:3307-3316.
[30]DONNAN F.The theory of membrane equilibria[J].Chemical Reviews,1924,1(1):73-90.
[31]BABCOCK K L.Some characteristics of model Donnan system[J].Soil Science,1960,90:245-252.
[32]NEWMAN J,THOMAS A.Electrochemical Systems[M].New York:John Wiley&Sons,2004.
[33]MASLIYAH J H,BHATTACHARJEE S.Electrokinetic and Colloid Transport Phenomena[M].Hoboken:John Wiley&Sons,2007.
[34]OLPHEN H V.An introduction to clay colloid chemistry:for clay technologists,geologists,and soil scientists[M].New York:John Wiley&Sons,1963.
[35]BAILEY L,LEKKERKERKER H N W,MAITLAND GC.Smectite clay-inorganic nanoparticle mixed suspensions:Phase behaviour and rheology[J].Soft Matter,2015,11(2):222-236.
[36]MITCHELL J K,SOGA K.Fundamentals of Soil Behavior[M].2nd ed.New York:John Wiley&Sons,2005.
[37]ELRICK D E,SMILES D E,BAUMGARTNER N,et al.Coupling phenomena in saturated homo-ionic montmorillonite:I.Experimental[J].Soil Science Society of America Journal,1976,40(4):490-491.
[38]梁建伟,房营光,谷任国.极细颗粒黏土渗流的微电场效应分析[J].岩土力学,2010,31(10):3043-3050.LIANG Jian-wei,FANG Ying-guang,GU Ren-guo.Analysis of microelectric field effect of seepage in tiny-particle clay[J].Rock and Soil Mechanics,2010,31(10):3043-3050.
[39]MITCHELL J K.Conduction phenomena:from theory to geotechnical practice[J].Geotechnique,1991,41(3):299-340.
[2]TOURNASSAT C,STEEFEL C I,BOURG I C,et al.Natural and engineered clay barriers[M].Amsterdam:Elsevier,2015.
[3]蔡武军,凌道盛,徐泽龙,等.单一裂隙优势渗流对黏土层防渗性能的影响分析[J].岩土力学,2014,35(10):2838-2844.CAI Wu-jun,LING Dao-sheng,XU Ze-long,et al.Influence of preferential flow induced by a single crack on anti-seepage performance of clay barrier[J].Rock and Soil Mechanics,2014,35(10):2838-2844.
[4]叶剑,兰吉武,陈云敏,等.垃圾填埋场中水平导排盲沟渗流模型及间距设计[J].岩土工程学报,2016,38(10):1923-1929.YE Jian,LAN Ji-wu,CHEN Yun-min,et al.Seepage model and spacing design of horizontal trench in landfills[J].Chinese Journal of Geotechnical Engineering,2016,38(10):1923-1929.
[5]王志良,申林方,李邵军,等.基于格子Boltzmann方法的岩体单裂隙面渗流特性研究[J].岩土力学,2017,38(4):1203-1210.WANG Zhi-liang,SHEN Lin-fang,LI Shao-jun,et al.Seepage characteristics of a single fracture based on lattice Boltzmann method[J].Rock and Soil Mechanics,2017,38(4):1203-1210.
[6]HAPPEL J,BRENNER H.Low Reynolds number hydrodynamics:with special applications to particulate media[M].Boston:Kluwer Academic Publishers,1983.
[7]BEAR J.Dynamics of fluids in porous media[M].New York:Dover Publication,1988.
[8]薛禹群.地下水动力学[M].北京:地质出版社,1997.XUE Yu-qun.Groundwater dynamics[M].Beijing:Geological Publishing House,1997.
[9]CHAPUIS R P,AUBERTIN M.On the use of the Kozeny-Carman equation to predict the hydraulic conductivity of soils[J].Canadian Geotechnical Journal,2003,40(3):616-628.
[10]CARMAN P C.Fluid flow through granular beds[J].Transactions of the Institution of Chemical Engineers,1937,15:150-166.
[11]ZUNKER F.Zeitschrift fur Pflanzeneraehrung[J].Duengung und Bodenkunde,1932,A25:1.
[12]MICHAELS A S,LIN C S.Effects of counterelectro-osmosis and sodium ion exchange on permeability of kaolinite[J].Industrial&Engineering Chemistry,1955,47(6):1249-1253.
[13]CARMAN P C.Permeability of saturated sands,soils and clays[J].The Journal of Agricultural Science,1939,29(2):262-273.
[14]TANG X W,CHENG G C,CHEN Y M.An easy-to-implement multi-scale computation of permeability coefficient for porous materials[J].Microporous and Mesoporous Materials,2010,130(1-3):274-279.
[15]REN X W,ZHAO Y,DENG Y L.A relation of hydraulic conductivity-void ratio for soils based on Kozeny-Carman equation[J].Engineering Geology,2016,213(4):89-97.
[16]HUNTER R.Zeta potential in colloid science:principles and applications[M].New York:Academic Press,1981.
[17]刘伟,龚玲艳,朱育丹,等.嵌有离子选择性膜的微通道内增强电渗流及除盐效应分析[J].中国科学(技术科学),2018,48(1):17-24.LIU Wei,GONG Ling-yan,ZHU Yu-dan,et al.Augmented electroosmotic flow and simultaneous desalination in microchannels embedded with permselective membranes[J].Scientia Sinica(Technologica),2018,48(1):17-24.
[18]YANG C,LI D Q.Analysis of electrokinetic effects on the liquid flow in rectangular microchannels[J].Colloids and Surfaces A:Physicochemical and Engineering Aspects,1998,143:339-353.
[19]吴健康,龚磊,陈波,等.微/纳流控系统电渗研究进展[J].力学进展,2009,39(5):555-565.WU Jian-kang,GONG Lei,CHEN Bo,et al.Advances in the research of electroosmotic flows in micro/nanofluidic systems[J].Advances in Mechanics,2009,39(5):555-565.
[20]ZHU Q Y,XIE M H,YANG J,et al.Analytical determination of permeability of porous fibrous media with consideration of electrokinetic phenomena[J].International Journal of Heat and Mass Transfer,2012,55(5-6):1716-1723.
[21]ALLAIRE G,MIKELIC A,PIATNITSKI A.Homogenizationi of the linearized ionic transport equations in rigid periodic porous media[J].Journal of Mathematical Physics,2010,51:123103.
[22]PLAZA I,ONTIVEROS-ORTEGA A,CALERO J,et al.Implication of zeta potential and surface free energy in the description of agricultural soil quality:effect of different cations and humic acids on degraded soils[J].Soil and Tillage Research,2015,146(B):148-158.
[23]潘慧,蓝咏,吴锐钊,等.CTAB与SDS对膨润土改性的界面性质研究[J].华南师范大学学报(自然科学版),2008(1):88-92.PAN Hui,LAN Yong,WU Rui-zhao,et al.Interfacial characterization of organic bentonite with cetyltrimethyle ammonium brom ide and sodium dodecyl sulfate[J].Journal of South China Normal University(Natural Science Edition),2008(1):88-92.
[24]LI D Q.Electro-viscous effects on pressure-driven liquid flow in microchannels[J].Colloids and Surfaces A:Physicochemical and Engineering Aspects,2001,195:35-57.
[25]TOURNASSAT C,STEEFEL C I.Ionic transport in nano-porous clays with consideration of electrostatic effects[J].Reviews in Mineralogy and Geochemistry,2015,80(1):287-329.
[26]ONSAGER L.Reciprocal relations in irreversible processes.I[J].Physical Review,1931,37:405-426.
[27]GRIM R E.Clay mineralogy:the clay mineral composition of soils and clays is providing an understanding of their properties[J].Science,1962,135(3507):890-8.
[28]DULLIEN F A.Porous media:fluid transport and pore structure[M].New York:Academic Press,1991.
[29]FAIR J C,OSTERLE J F.Reverse electrodialysis in charged capillary membranes[J].The Journal of Chemical Physics,1971,54:3307-3316.
[30]DONNAN F.The theory of membrane equilibria[J].Chemical Reviews,1924,1(1):73-90.
[31]BABCOCK K L.Some characteristics of model Donnan system[J].Soil Science,1960,90:245-252.
[32]NEWMAN J,THOMAS A.Electrochemical Systems[M].New York:John Wiley&Sons,2004.
[33]MASLIYAH J H,BHATTACHARJEE S.Electrokinetic and Colloid Transport Phenomena[M].Hoboken:John Wiley&Sons,2007.
[34]OLPHEN H V.An introduction to clay colloid chemistry:for clay technologists,geologists,and soil scientists[M].New York:John Wiley&Sons,1963.
[35]BAILEY L,LEKKERKERKER H N W,MAITLAND GC.Smectite clay-inorganic nanoparticle mixed suspensions:Phase behaviour and rheology[J].Soft Matter,2015,11(2):222-236.
[36]MITCHELL J K,SOGA K.Fundamentals of Soil Behavior[M].2nd ed.New York:John Wiley&Sons,2005.
[37]ELRICK D E,SMILES D E,BAUMGARTNER N,et al.Coupling phenomena in saturated homo-ionic montmorillonite:I.Experimental[J].Soil Science Society of America Journal,1976,40(4):490-491.
[38]梁建伟,房营光,谷任国.极细颗粒黏土渗流的微电场效应分析[J].岩土力学,2010,31(10):3043-3050.LIANG Jian-wei,FANG Ying-guang,GU Ren-guo.Analysis of microelectric field effect of seepage in tiny-particle clay[J].Rock and Soil Mechanics,2010,31(10):3043-3050.
[39]MITCHELL J K.Conduction phenomena:from theory to geotechnical practice[J].Geotechnique,1991,41(3):299-340.