气液界面传质机理与强化
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摘要
气液传质在化工过程中普遍存在,由于目前的研究大多局限于宏观的表面现象,尚难揭示其内在的传质特性及传质机理。现有的经典传质理论均是在经验或半经验基础上发展起来的,无法从微观上揭示相际传质机理,因而只适用于某些特定的情况,局限性较大。因此,从微观上进一步深入研究气液传质过程,建立精确的以界面非平衡机理为基础的非线性传质模型是非常必要的。
本文利用实时激光全息干涉系统,结合显微放大技术,对不同主体流速下甲醇-CO_2、乙醇-CO_2、正丙醇-CO_2、正丁醇-CO_2气液传质过程及不同浓度十二烷基硫酸钠(SDS)、十二烷基苯磺酸钠(SDBS)、十六烷基三甲基溴化铵(CTAB)、聚丙烯酸(PAA)四种表面活性剂对乙醇-CO_2传质过程的影响进行了研究。得到了气液界面附近液相侧的浓度场分布及界面浓度、浓度边界层厚度。
对于气体吸收过程,以分子热力学为基础,结合普遍化的化学势推动力通量方程,提出界面非平衡理论,推导出传质存在时两相界面处的浓度关系,并对静止和运动气泡两种情况分别进行了求解。针对气体组分被吸收进入静态小液滴的传质过程,分别采用平衡模型和非平衡模型对具有较低溶解度的物理吸收过程进行了分析,并对吸收过程中不同时间液滴内的浓度分布进行了求解。另外以对流扩散方程为基础,考虑了界面阻力对传质的影响,得到气泡周围近界面附近的浓度场分布模型,模型计算值和实验值进行了比较,结果吻合较好。
气液两相传质强化是化工过程研究的一个重要内容,在恒温反应釜内,对CO_2在不同搅拌速率下、不同浓度活性炭-水浆料体系中的吸收强化进行了实验研究,计算得到不同情况下的增强因子。基于膜模型和界面非平衡原理,提出了一个新的预测增强因子的模型,能很好地解释粒子浓度及搅拌强度对增强因子的影响,并且模型预测值与实验值吻合良好。
Gas-liquid mass transfer is often encountered in chemical engineering process. However, up to now, most researches in the field are based on macro phenomenon. The classic mass transfer theories and hypothesis are developed on the basis of some empirical and semi-empirical correlations. Therefore, the inherent mass transfer characteristic and mechanism have not yet been well known. It is of virtual significance to deeply investigate the micro mechanism of interfacial mass transfer and develop accuracy non-linear mass transfer pattern taking into account the interfacial non-equilibrium principle.
The mass transfer process of methanol-CO2, ethanol-CO2, n-propanol- CO2, n-butanol-CO2 and influence of various concentrations sodium dodecyl sulfate (SDS), sodium dodecyl benzene sulfonate (SDBS), cetyl trimethyl ammonium bromide (CTAB), polyacrylic acid (PAA) on mass transfer at different body velocities were studied respectively using micro holographic interferometer, and the concentration distribution near the interface, interfacial concentration and concentration boundary layer thickness on liquid side were determined.
On the basis of molecule thermodynamics, combining the general chemical potential driving force equation of mass transfer flux, the non-equilibrium principle at the interface was proposed and a concentration correlation between two phases at the interface is derived and solved under both quiescent and mobile conditions in the absorption processes of bubble,respectively, good agreements have been achieved between the calculated data and experimental data. For the absorption process of gaseous species into stationary droplets, equilibrium relation and non-equilibrium relations at the interface were used to analyze and predict the absorption time for a physical absorption at a relatively low solubility of gas, and the concentration distribution within the droplet at different times is solved. In addition, based on convection-diffusion equation, considering the effect of interfacial resistance on mass transfer, concentration field near the interface around bubble in liquid phase was solved, and the results were at good agreement with the experimental data.
The enhancement of gas-liquid mass transfer is very important in the intensification of chemical engineering process. CO_2 absorption in the slurries containing different concentration activated carbon particles and water at various stirrer speeds were studied experimentally in a thermostatic reactor, and the enhancement factors were determined. A quantitative model for predicting enhancement factor was proposed based on film model and non-equilibrium principle, which could well explain the effect of particles concentration and stirring intensity on enhancement factor, and the prediction value of present model are at considerable agreement with experimental data.
本文利用实时激光全息干涉系统,结合显微放大技术,对不同主体流速下甲醇-CO_2、乙醇-CO_2、正丙醇-CO_2、正丁醇-CO_2气液传质过程及不同浓度十二烷基硫酸钠(SDS)、十二烷基苯磺酸钠(SDBS)、十六烷基三甲基溴化铵(CTAB)、聚丙烯酸(PAA)四种表面活性剂对乙醇-CO_2传质过程的影响进行了研究。得到了气液界面附近液相侧的浓度场分布及界面浓度、浓度边界层厚度。
对于气体吸收过程,以分子热力学为基础,结合普遍化的化学势推动力通量方程,提出界面非平衡理论,推导出传质存在时两相界面处的浓度关系,并对静止和运动气泡两种情况分别进行了求解。针对气体组分被吸收进入静态小液滴的传质过程,分别采用平衡模型和非平衡模型对具有较低溶解度的物理吸收过程进行了分析,并对吸收过程中不同时间液滴内的浓度分布进行了求解。另外以对流扩散方程为基础,考虑了界面阻力对传质的影响,得到气泡周围近界面附近的浓度场分布模型,模型计算值和实验值进行了比较,结果吻合较好。
气液两相传质强化是化工过程研究的一个重要内容,在恒温反应釜内,对CO_2在不同搅拌速率下、不同浓度活性炭-水浆料体系中的吸收强化进行了实验研究,计算得到不同情况下的增强因子。基于膜模型和界面非平衡原理,提出了一个新的预测增强因子的模型,能很好地解释粒子浓度及搅拌强度对增强因子的影响,并且模型预测值与实验值吻合良好。
Gas-liquid mass transfer is often encountered in chemical engineering process. However, up to now, most researches in the field are based on macro phenomenon. The classic mass transfer theories and hypothesis are developed on the basis of some empirical and semi-empirical correlations. Therefore, the inherent mass transfer characteristic and mechanism have not yet been well known. It is of virtual significance to deeply investigate the micro mechanism of interfacial mass transfer and develop accuracy non-linear mass transfer pattern taking into account the interfacial non-equilibrium principle.
The mass transfer process of methanol-CO2, ethanol-CO2, n-propanol- CO2, n-butanol-CO2 and influence of various concentrations sodium dodecyl sulfate (SDS), sodium dodecyl benzene sulfonate (SDBS), cetyl trimethyl ammonium bromide (CTAB), polyacrylic acid (PAA) on mass transfer at different body velocities were studied respectively using micro holographic interferometer, and the concentration distribution near the interface, interfacial concentration and concentration boundary layer thickness on liquid side were determined.
On the basis of molecule thermodynamics, combining the general chemical potential driving force equation of mass transfer flux, the non-equilibrium principle at the interface was proposed and a concentration correlation between two phases at the interface is derived and solved under both quiescent and mobile conditions in the absorption processes of bubble,respectively, good agreements have been achieved between the calculated data and experimental data. For the absorption process of gaseous species into stationary droplets, equilibrium relation and non-equilibrium relations at the interface were used to analyze and predict the absorption time for a physical absorption at a relatively low solubility of gas, and the concentration distribution within the droplet at different times is solved. In addition, based on convection-diffusion equation, considering the effect of interfacial resistance on mass transfer, concentration field near the interface around bubble in liquid phase was solved, and the results were at good agreement with the experimental data.
The enhancement of gas-liquid mass transfer is very important in the intensification of chemical engineering process. CO_2 absorption in the slurries containing different concentration activated carbon particles and water at various stirrer speeds were studied experimentally in a thermostatic reactor, and the enhancement factors were determined. A quantitative model for predicting enhancement factor was proposed based on film model and non-equilibrium principle, which could well explain the effect of particles concentration and stirring intensity on enhancement factor, and the prediction value of present model are at considerable agreement with experimental data.
引文
[1] Nernst W, Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen[J]. Z Phys Chem, 1904, 47: 52–55
[2] Whitman W G. The two-film theory of gas absorption[J]. Chem Met Eng, 1923, 29(4): 146-148
[3] Lewis W K, Whitman W G, Principles of gas absorption[J]. Ind Eng Chem, 1924, 16(3):1215–1220
[4] Hansen E, Mollerup J. Application of the two-film theory to the determination of mass transfer coefficients for bovine serun albumin on anion-exchange columns[J]. J Chrom: A, 1998, 827(2): 259-267
[5] Rashid K A, Gavril D, Kasanos N A, Karaiskakis G. Flux of gases across the air-water interface studied by reversed-flow gas chromatography[J]. J Chrom: A, 2001, 934(1-2): 31-49
[6] Wang Maw-Ling, Tseng Yao-Hsuan. Kinetic model for synthesizing 4,4’- diethanoxy biphenyl by phase transfer catalysis[J]. J Mole Cata A: Chemical, 2002, 188(1-2): 51-61
[7] Markus B N, Friedl A, Koss U, Tork T. Modelling selective H2S absorption and desorption in an aqueous MDEA-solution using a rate-based non-equilibrium approach[J]. Chem Eng Process, 2004, 43(6): 701-715
[8] Higbie R. The rate of absorption of a pure gas into a still liquid during short periods of exposure[J]. Trans Am Inst Chem Eng, 1935, 31: 365-389
[9] Jeong J H, No H C. Mass transfer coefficient model for the analysis of volatile species transport between two phases[J]. Int Commun Heat Mass Transf, 1997, 24(7): 907-918
[10] Mandal B P, Guha M, Biswas A K, Bandyopadhyay S S. Removal of carbon dioxide by absorption in mixed amines: modeling of absorption in aqueous MDEA/MEA and AMP/MEA solution[J]. Chem Eng Sci, 2001, 56 (21-22): 6217-6224
[11] Félix F G, Gomez E. Theoretical prediction of gas–liquid mass transfer coefficient, specific area and hold-up in sparged stirred tanks[J]. Chem Eng Sci, 2004, 59(12): 2489-2501
[12] Mandal B P, Bandyopadhyay S S. Simultaneous absorption of carbon dioxide and hydrogen sulfide into aqueous blends of 2-amino-2-methyl-1-propanol and diethanolamine[J]. Chem Eng Sci, 2005, 60(22): 6438-6451
[13] Danckwerts P V. Significance of liquid-film coefficients in gas absorption[J]. Ind Eng Chem, 1951, 43(6): 1460-1467
[14] Maucci E, Briens C L, Martinuzzi R J, Wild G. Modeling of transient particle–liquid mass transfer in liquid and liquid–solid systems[J]. Chem Eng Sci, 2001, 56(15): 4555-4570
[15] Hanratty T J, Turbulent exchange of mass and momentum with a boundary[J]. AIChE J, 1956, 2(3), 359–363
[16] Toor H L, Marchello J M. Film-penetration model for mass and heat transfer[J]. AIChE J, 1958, 4(1): 97- 101
[17] Dobbin W E, BOD and oxygen relationships in streams[J]. J San Engng Div Proc A S C E, 1964, 90(3): 53–78
[18] Perlmutter D D. Surface-renewal models in mass transfer[J]. Chem Eng Sci, 1961, 16(3-4): 287-296
[19]沈自求,徐维勤,丁杰,相际传质(I)一个修正的表面膜更新模型[J].化工学报,1980,31(4):23-36
[20] Ruckenstein E. A note concerning turbulent exchange of heat or mass with a boundary. Chem Eng Sci, 1958, 7(4): 265–268.
[21] Ruckenstein E, Some remarks on renewal models[J]. Chem Eng Sci, 1963, 18(4): 233–241
[22] Koppel L B, Patel R D, Holmes J T, Statistical models for surface renewal in heat and mass transfer : partⅠ. Dependence pf average transport coefficients on age distribution[J]. AIChE J, 1966, 12(5): 941–946
[23] Nijsing R, Predictions on momentum, heat and mass transfer in turbulent channel flow with the aid of a boundary layer growth-breakdown model[J]. Warmeund Stoffiibertragung, 1969, 2(1):65–86
[24] Pinczewski W V, Sideman S, A model for mass (heat) transfer in turbulent tube flow. Moderate and high Schmidt (Prandtl) numbers[J]. Chem Eng Sci, 1974, 29(9): 1969–1976
[25] Hart J, Single-phase and two-phase pipe flow, PhD thesis. University of Amsterdam, The Netherlands, 1988
[26] Vignes A, Concentration dependence of the binary diffusion coeffcient[J].Ind Eng Chem Fundam, 1966, 5(2):281–283
[27] Kubaczka A, Bandrowski J, Solutions of a system of multicomponent mass transport equation for mixtures of real fluids[J]. Chem Eng Sci, 1991, 46(2): 539–556
[28] Krishna R, Ternary mass transfer in a wetted-wall column significance of diffusional interactions. I. Stefan diffusion[J]. Trans Inst Chem Eng, 1981, 59(1): 35–43
[29] Wang J, Langenann H, Unsteady two-film model for mass transfer[J]. Chem Eng Technol, 1994, 17(4): 280–284
[30] Wang J, Langenann H, Unsteady two-film model for mass transfer accompanied by chemical reaction[J]. Chem Eng Sci, 1994, 49(20):3457–3463
[31] Zhao B, Wang J, Yang W, Jin Y, Gas–liquid mass transfer in slurry bubble systems I. Mathematical modeling based on a single bubble mechanism[J]. Chem Eng J, 2003, 96(1-3): 23–27
[32] Levich V G. physicochemical hyrodynamics, Prentice-Hall Englewood Cliffs, 1962
[33] King C J. Turbulent liquid phase mass transfer at a free gas-liquid interface[J]. I & E C Fundamentals, 1966, 5(1):1-8
[34] Fortescue G E, Pearson J R A. On gas absorption into a turbulent liquid[J]. Chem Eng Sci, 1967,22(9):1163-1176
[35] Lamont J C , Scott D S. Eddy cell model of mass transfer into the surface of a turbulent liquid[J]. AIChE J, 1970, 16(4): 513-519
[36] Luk S, Lee Y H, Mass transfer in eddies close to air-water interface. AIChE J, 1986,32(9): 1546-1554
[37]苗容生.两相流气泡界面附近湍流场和浓度场的激光测量及局部传质理论研究,学位论文,天津:天津大学,1993
[38] Austin L J, Banczyk L, Sawistowski H. Effect of electric field on mass transfer across a plane interface [J]. Chem Eng Sci. 1971,26(12): 2120-2121
[39]罗耀明,张秋香,陈晓祥.液液传质界面扰动现象的实时全息记录[J].高校化学工程学报,1995,9(2): 149-154
[40]戴干策,陈敏恒,化工流体力学,北京:化学工业出版社,1988,678-726
[41] Berg J C, Morig C R. Density effects in interfacial convection [J]. Chem Eng Sci, 1969,24(6): 937-946
[42] Sternling L V, Scriven L E. Interfacial Turbulence: Hydrodynamic instability and the Marangoni effect[J]. AIChE J, 1959, 5(4): 514-523
[43] Vazquez G, Antorrena G, Navaza J M. Estimation of the turbulence induced by the Marangoni effect at a gas-liquid interface[J]. Int Chem Eng, 1990, 30(2): 228-235
[44] Golovin A A. Mass transfer under interfacial turbulence: Kinetic regularities[J]. Chem Eng Sci, 1992,47(8): 2069-2080
[45] Zuiderweg F J. Marangoni effect in distillation of alcohol-water mixtures[J]. Chem Eng Res Des, 1983,61(6): 388-390
[46] Dijkstra H A, Drinkenburg A A H. Enlargement of wetted area and mass transfer due to surface tension gradients: The creeping film phenomenon[J]. Chem Eng Sci,1990,45(4): 1079-108
[47] Pertler M, Haeberl M, Rommel W, Blass E. Mass transfer across liquid-phase boundaries[J]. Chem Eng Proc,1995,34(3): 269-277
[48] Semkov K R. Liquid flow distribution in packed beds by multipoint liquid distributors[J]. Chem Eng Sci,1991,46(6): 1393-1399
[49] Proctor S J, Biddulph M W, Krishnamurthy K R. Effects of Marangoni surface tension forces on modern distillation packings[J]. AIChE J, 1998, 44(4): 831-835
[50] Martin A M, Perez A C. The influence of surgace tension on the bolumetric mass transfer coefficient in rectification[J]. Int Chem Eng, 1994, 34(1): 76-81
[51] Cullen E J, Davidson J F. Absorption of gases in liquid jets[J]. Trans Faraday Soc, 1957,53(1): 113-120
[52] Harvey E A, Smith W. The absorption of carbon dioxide by a quiescent liquid[J]. Chem Eng Sci, 1959,10(4): 274-280
[53] Thomas G S, Robert L P. Influence of surface turbulence and surfactants on gas transport through liquid interfaces[J]. Ind Eng Chem Fundam, 1970,9(3): 458-465
[54] Burnett J C, Himmelblau D M. The effect of surface active agents on interphase[J]. AIChE J, 1970,16(2): 185-193
[55] Ramirez J A, Davies R H. Mass transfer to a surfactant-covered bubble or drop[J]. AIChE J, 1999,45(6): 1355-1358
[56] Kang K H, Choi C K. Onset of solutal Marangoni convection in a suddenly desorbing liquid layer[J]. AIChE J, 2000,46(1): 15-23
[57] Stoica A G, Kurzeluk M, Floarea O. Experiment study of Marangoni effection a liquid-liquid system[J]. Chem Eng Sci, 2000,55: 3813- 3816
[58] Li X, Mao Z, Fei W. Effects of surface-active agents on mass transfer of a solute into single buoyancy driven drops in solvent extraction systems[J]. Chem Eng Sci, 2003, 58(16): 3793-3806
[59] Hanwright J, Zhou J, Evans G M, Galvin K P. Influence of surfactant on gas bubble stability[J]. Langmuir, 2005, 21(11): 4912-4920
[60] Liu Y, Dong X, Sun Y. Equilibria and kinetics of protein transfer to and from affinity-based reverse micelles of Span 85 modified with Cibacron Blue F-3GA[J]. Biochem Eng J, 2006,28(3): 281-288
[61] Oh S G, Shah D O. Effect of micellar lifetime on the rate of solubilization and detergency in sodium dodecyl sulfate solutions[J]. JAOCS, 1993, 70(7): 673-678
[62] Larson R S, Lam D K. Interfacial mass transfer resistance in nonideal systems[J]. Ind Eng Chem Fundam, 1986, 25(1): 148-152
[63] Shah R, Neogi P. Interfacial resistance in solubilization kinetics[J]., J Colloid Interface Sci, 2002, 253(2): 443-454
[64] Neogi P. A model for interfacial resistance observed during solubilization with micellar solution[J]. J Colloid Interface Sci, 2003, 261(2): 542-546
[65] Chang C Y, Liu L H, Chang I C et al. Film model for sulfur dioxide absorption into quiescent water with interfacial resistance[J]. Chemosphere, 1994, 28(6): 1217
[66] Higbie R, Rate of absorption of pure gas into a still liquid during short periods of exposure[J]. Trans, AIChE, 1935, 31(2):365-389
[67] Chiang S H,Toor H L, Interfacial resistance in the absorption of oxygen by water[J]. AIChE J, 1959, 5(2):165
[68] Mcmanamey W J, Interfacial resistances in the liquid extraction of inorganic nitrates[J]. Chem Eng Sci, 1961, 15(1): 210-219
[69] Cable M, Cardew G E, The kinetics of desorption with an interfacial resistance and concentration-dependent diffusicity[J]. Chem Eng Sci, 1977, 32(2): 535-541
[70] Shah R, Neogi P, Interfacial resistance in solubilization kinetcs[J]. J Colloid Interface Sci, 2002, 253(2): 443-454
[71] Gupta R K, Sridhar T, Effect of interfacial resistance on quiescent gas-liquid absorption[J]. Chem Eng Sci, 1984, 39(3): 471-477
[72] Shankar V, Influence of interfacial resistance on kinetics of sorption[J]. Polymer, 1981, 22(6): 748-752
[73] Cable M, Cabdew G E, The kinetics of desorption with an interfacial resistance and concentration-dependent diffusivity[J]. Chem Eng Sci, 1977, 32(5):535-541
[74] Alper E, Wichtendahl B, Deckwer W D. Gas absorption mechanism in catalytic slurry reactors [J]. Chem Eng Sci, 1980, 35(1-2): 217-222
[75] Tinge J T, Drinkenburg A A H. The enhancement of the physical absorption of gases in aqueous activated carbon slurries[J]. Chem Eng Sci,1995,50(6):937- 942.
[76] Ruthiya K C, Schaaf van der, Kuster B F M, Schouten J C. Mechanisms of physical and reaction enhancement of mass transfer in a gas inducing stirred slurry reactor[J]. Chem Eng J, 2003, 96(1-3):55-69
[77] Dumont E, Delmas H. Mass transfer enhancement of gas absorption in oil-in- water systems: a review[J]. Chem Eng Process, 2003, 42(6): 419-438
[78] Zhang G D, Cai W F, Xu C J, Zhou M. A general enhancement factor model of the physical absorption of gases in multiphase system[J]. Chem Eng Sci, 2006, 61(2): 558-568
[79] Kaya A , Schumpe A. Surfactant adsorption rather than shuttle effect[J]. Chem Eng Sci, 2005, 60(22): 6504-6510
[80] KordaěM, Linek V, Mechanism of enhanced gas absorption in presence of fine solid particles. Effect of molecular diffusivity on mass transfer coefficient in stirred cell[J]. Chem Eng Sci, 2006, 61(21):7125-7132
[81] Rosu M, Schumpe A, Influence of surfactants on gas absorption into aqueous suspensions of activated carbon[J]. Chem Eng Sci, 2007, 62(18-20): 5458-5463
[82]成弘,周明,余国琮.强化气液两相传质的研究进展[J].化工进展, 2001,13(4) :315-322
[83] Mehra A,Sharma M M. Absorption with reaction:effect of emulsified second liquid phase[J]. Chem Eng Sci, 1985, 40(12): 2382-2385
[84] Vinke H, Hamersma P J, Fortuin J M H. Enhancement of the gas absorption rate in agitated slurry reactors by gas-adsorbing particles adhering to gas bubbles[J]. Chem Eng Sci, 1993,48(12): 2197-2210
[85] Joly-Vuillemin C, De Bellefon C, Delmas H. Solid effects on gas-liquid mass transfer in three-phase slurry catalytic hydrogenation of adiponitrile over raney nickel[J]. Chem Eng Sci, 1996, 51(10): 2149-2158
[86] Bruining W J, Joosten G E H, Beenackers A A C M, Hofman H. Enhancement of gas-liquid mass transfer by a dispersed second liquid phase[J]. Chem Eng Sci, 1986,41(7):1873-1877
[87] Holstvoogd R D,van Swaaij W P M,van Dierendonck L L. The absorption of gases in aqueous activated carbon slurries enhanced by adsorbing or catalytic particles[J]. Chem Eng Sci, 1988, 43(8) : 2181-2187
[88] Holstvoogd R D, van Swaaij W P M. The influence of adsorption capacity on enhanced gas absorption activated carbon slurries[J]. Chem Eng Sci, 1990, 45(1): 151-162
[89] Mehra A. Gas absorption in reactive slurries:particle dissolution near gas-liquid interface[J]. Chem Eng Sci,1996,51(3):461-477
[90] Brilman D W F, van Swaaij W P M, Versteeg G F. A one- dimensional instationary heterogeneous mass transfer model for gas absorption in multiphase systems[J]. Chem Eng Process.1998,37(6):471-488
[91] Mehra A. Intensification of multiphase reactions through the use of a microphase-I.theoretical[J]. Chem Eng Sci, 1988, 43(4): 899-912
[92] Lekhal A, Chaudhari R V, Wilhelm A M, Delmas H. Gas-liquid mass transfer in gas-liquid-liquid dispersions[J]. Chem Eng Sci, 1997,52(21-22): 4069-4077
[93] Dagaonkar MV, Heeres H J,Beenackers A A C M, Pangarkar V G. The application of fine TiO2 particles for enhanced gas absorption[J]. Chem Eng J, 2003, 92(1-3):151-159
[94] Nagy E. Three-phase mass transfer:one dimensional heterogeneous model[J]. Chem Eng Sci, 1994,50(5) :827-836
[95] Lin C, Zhou M,Xu C J. Axisymmetrical two-dimensional heterogeneous mass transfer model for the absorption of gas into liquid-liquid dispersions[J]. Chem Eng Sci, 1999, 54 (3): 389-399
[96] Brilman D W F, Goldschmidt M J V, Versteeg G F, van Swaaij W P M. Heterogeneous mass transfer models for gas absorption in multiphase systems[J]. Chem Eng Sci, 2000, 55 (15): 2793-2812
[97] Wimmers O J, Fortuin J M H. The use of adhesion of catalyst particles to gas bubbles to achieve enhancement of gas absorption in slurry reactors I. Investigation of particle-to-bubble adhesion using the bubble pick-up method[J]. Chem Eng Sci, 1988,43(2) : 303-312
[98] Akbar M K, Ghiaasiaan S M. Modeling the gas absorption in a spray scrubber with dissolving reactive particles[J]. Chem Eng Sci, 2004, 59(5): 967-976
[99] Cents A H G,Brilman D W F,Versteeg G F. Gas absorption in an agitated gas-liquid-liquid system[J]. Chem Eng Sci, 2001, 56(3): 1075-1083
[100] Linek V,Moucha T,Kordac M. Mechanism of mass transfer from bubbles in dispersions Part I.Danckwerts,plot method with sulphite solutions in the presence of viscosity and surface tension changing agents[J]. Chem Eng Process, 2005, 44 (3) : 353-361
[101] Linek V,Kordac M,Moucha T. Mechanism of mass transfer from bubbles in dispersions Part II: Mass transfer coefficients in stirred gas-liquid reactor and bubble column[J]. Chem Eng Process, 2005, 44 (1): 121-130
[102] Higbie R. The rate of absorption of a pure gas into a still liquid during short periods of exposure[J]. Transactions of the American Institute of Chemical Engineers , 1935, 31(2): 365ˉ377
[103] Danckwerts P V. Significance of liquid-film coefficients in gas absorption[J]. Ind Eng Chem, 1951, 43(6): 1460ˉ1468
[104] Toor H L, Marchello J M. Film-penetration model for mass and heat transfer[J]. AIChE J, 1958, 4(1): 97–101
[105] Lamont J C, Scott D S. An eddy cell model of mass transfer into the surface of a turbulent liquid[J]. AIChE J , 1970, 16(3): 513–519
[106] Levich V G. Physicochem Hydrodyn, Prentice-Hall, New York., 1962
[107] Lochiel A C, Calderbank P H. Mass transfer in the continuous phase around axisymmetric bodies of revolution[J] . Chem Eng Sci, 1964, 19(7): 471-484
[108] Petera J, Weatherley L R. Modelling of mass transfer from falling droplets[J]. Chem Eng Sci,2001,56(16): 4929- 4947
[109] Tom P. Oxygen absorption into moving water and tenside solutions[J]. Water Research, 2000, 34(9): 2569-2581
[110] Khan A R, Dimitrios G, Nicholas A K, George K. Flux of gases across the air- water interface studied by reversed-flow gas chromatography[J]. J Chroma A, 2001, 934: 31-49
[111] Pierotti R A. The solubility of gases in liquids[J] . J Phys Chem, 1963, 67 : 1840-1846
[112] Bennett C O, Myers J E, Momentum, heat and mass transfer, third ed., McGraw-Hill Book Company, New York,1982, pp.495-498
[113] Paterson W R, Hayhurst A N, Mass or heat transfer from a sphere to a flowing fluid[J]. Chem Eng Sci 2000,55(4): 1925-1927
[114] Bennett C O, .Myers J E, Momentum, Heat and Mass Transfer, McGraw-Hill Book Company, Inc, New York, USA, 1962
[115] Sherwood T K, Pigford R L, Wilke C R, Mass Transfer, McGraw-Hill, New York , 1975
[116] Yong S W, Dong K C, Anthony F M. Density, viscosity, surface tension, and carbon dioxide solubility and diffusivity of methanol. Ethanol, aqueous propanol, and aqueous ethylene glycol at 25℃[J]. J Chem Eng Data, 1981, 26(2): 140-141
[117] Taflin D C, and Davis E J. Mass transfer from an aerosol droplet at intermediate Peclet numbers[J]. Chem Eng Commun, 1987, 55: 199-210
[118] Widmann J F and Davis E J. Analysis of mass transfer between a sequence of drops and a surrounding gas[J]. J Aerosol Sci, 1997, 28: 1233-1249
[119] Chen W H. An analysis of absorption by a liquid aerosol in a stationary environment[J]. Atmos Environ, 2002, 36: 3671-3683
[120] Brogren C and Karlsson H T. Modeling the absorption of SO2 in a spray scrubber using the penetration theory[J]. Chem Eng Sci, 1997, 52: 3085-3099
[121] Adewuyi Y G and Carmichael G R. A theoretical investigation of gaseous absorption by water droplets from SO2-HNO3-CO2-HCl mixture[J]. Atmos Environ, 1982, 16: 719-729
[122] Clift R, Grace J R Weber M E, Bubbles, drops and particles. New York : Academic, 1978
[123] Zhang S H and Davis E J. Mass transfer from a single micro-droplet to a gas flowing at low Reynolds number[J]. Chem Eng Commun, 1987, 55: 51-67
[124] Piarah W H, Paschedag A. and Kraume M. Numerical simulation of mass transfer between a single droplet and an ambiant flow[J]. AIChE J, 2001, 47: 1701-1704
[125] Pedersen T. Oxygen absorption into moving water and tenside solution[J]. Water Research, 2000, 34: 2569-2581
[126] Ma Youguang , Cheng Hong and Yu Guocong. Measurement of concentration fields near the interface of a rising bubble by holographic interference technique[J]. Chinese J. Chem. Eng, 1999, 7: 363-367
[127] Ma Youguang , Yu Guocong, Huai Z Li, Note on the Mechanism of Interfacial Mass Transfer of Absorption Processes[J]. Int J Heat and Mass Transf, 2005, 48(16): 3454-3460
[128] Ferrell R T. and Himmelblau D M. Diffusion coefficients of nitrogen and oxygen in water[J]. J Chem Eng Data, 1967, 12, 111-115
[129] Milne-Thomson L M, Theoretical Hydrodynamics, 5th ed., Macmillan, London, 1972
[130] Parlange J Y. Spherical-Cap bubble with laminar wakes. J Fluid Mech ,1969, 37: 257-284
[131] Coppus J H C, Rietema K. Theoretical derivation of the mass transfer coefficient at the front of a spherical cap bubble[J]. Chem Eng Sci, 1980, 35(6): 1497-1499
[132] Johnson A I, Besik F, Hamielec A E, Mass transfer from a single rising bubble[J]. Canad J Chem Eng, 1969, 47(6): 559-564
[133] Abdullan A K, Theory of convective heat and mass transfer to Spherical-Cap bubbles[J]. AIChE J, 1994, 40(9): 1440-1448
[134] Joosten G E H, Schilder J G M, Janssen J J, The influence of suspended solid material on the gas–liquid mass transfer in stirred gas–liquid contactors[J]. Chem Eng Sci, 1977,32 (5): 563-566
[135] Kars R L, Best R J, Drinkenburg A A H, The sorption of propane in slurries of active carbon in water[J]. Chem Eng J, 1979,17: 201-210
[136] Quicker G, Alper E, Deckwer W D, Effect of fine activated carbon particles on the rate of CO2 absorption[J]. AIChE J, 1987, 33 (5): 871-875
[137] Beenackers A A C M, van Swaaij W P M, Mass transfer in gas–liquid slurry reactors[J]. Chem Eng Sci 1993,48 (18): 3109-3139
[138] Alper E, Wichtendahl B, Deckwer W D, Gas absorption mechanism in catalytic slurry reactors[J]. Chem Eng Sci, 1980,35 (1): 217-222
[139] Alper E, Ozturk S, Effect of fine solid particles on gas–liquid mass transfer rate in a slurry reactor[J]. Chem Eng Commun, 1986, 46 (1): 147-158
[140] Mehra A, Gas absorption in slurries of finite-capacity microphases[J]. Chem Engng Sci, 1990, 45(6): 1525–1538
[141] Demmink J F, Mehra A, Beenackers A A C M, Gas absorption in the presence of particles showing interfacial affinity: case of fine sulfur precipitates[J]. Chem Eng Sci, 1998, 53 (16): 2885-2902
[2] Whitman W G. The two-film theory of gas absorption[J]. Chem Met Eng, 1923, 29(4): 146-148
[3] Lewis W K, Whitman W G, Principles of gas absorption[J]. Ind Eng Chem, 1924, 16(3):1215–1220
[4] Hansen E, Mollerup J. Application of the two-film theory to the determination of mass transfer coefficients for bovine serun albumin on anion-exchange columns[J]. J Chrom: A, 1998, 827(2): 259-267
[5] Rashid K A, Gavril D, Kasanos N A, Karaiskakis G. Flux of gases across the air-water interface studied by reversed-flow gas chromatography[J]. J Chrom: A, 2001, 934(1-2): 31-49
[6] Wang Maw-Ling, Tseng Yao-Hsuan. Kinetic model for synthesizing 4,4’- diethanoxy biphenyl by phase transfer catalysis[J]. J Mole Cata A: Chemical, 2002, 188(1-2): 51-61
[7] Markus B N, Friedl A, Koss U, Tork T. Modelling selective H2S absorption and desorption in an aqueous MDEA-solution using a rate-based non-equilibrium approach[J]. Chem Eng Process, 2004, 43(6): 701-715
[8] Higbie R. The rate of absorption of a pure gas into a still liquid during short periods of exposure[J]. Trans Am Inst Chem Eng, 1935, 31: 365-389
[9] Jeong J H, No H C. Mass transfer coefficient model for the analysis of volatile species transport between two phases[J]. Int Commun Heat Mass Transf, 1997, 24(7): 907-918
[10] Mandal B P, Guha M, Biswas A K, Bandyopadhyay S S. Removal of carbon dioxide by absorption in mixed amines: modeling of absorption in aqueous MDEA/MEA and AMP/MEA solution[J]. Chem Eng Sci, 2001, 56 (21-22): 6217-6224
[11] Félix F G, Gomez E. Theoretical prediction of gas–liquid mass transfer coefficient, specific area and hold-up in sparged stirred tanks[J]. Chem Eng Sci, 2004, 59(12): 2489-2501
[12] Mandal B P, Bandyopadhyay S S. Simultaneous absorption of carbon dioxide and hydrogen sulfide into aqueous blends of 2-amino-2-methyl-1-propanol and diethanolamine[J]. Chem Eng Sci, 2005, 60(22): 6438-6451
[13] Danckwerts P V. Significance of liquid-film coefficients in gas absorption[J]. Ind Eng Chem, 1951, 43(6): 1460-1467
[14] Maucci E, Briens C L, Martinuzzi R J, Wild G. Modeling of transient particle–liquid mass transfer in liquid and liquid–solid systems[J]. Chem Eng Sci, 2001, 56(15): 4555-4570
[15] Hanratty T J, Turbulent exchange of mass and momentum with a boundary[J]. AIChE J, 1956, 2(3), 359–363
[16] Toor H L, Marchello J M. Film-penetration model for mass and heat transfer[J]. AIChE J, 1958, 4(1): 97- 101
[17] Dobbin W E, BOD and oxygen relationships in streams[J]. J San Engng Div Proc A S C E, 1964, 90(3): 53–78
[18] Perlmutter D D. Surface-renewal models in mass transfer[J]. Chem Eng Sci, 1961, 16(3-4): 287-296
[19]沈自求,徐维勤,丁杰,相际传质(I)一个修正的表面膜更新模型[J].化工学报,1980,31(4):23-36
[20] Ruckenstein E. A note concerning turbulent exchange of heat or mass with a boundary. Chem Eng Sci, 1958, 7(4): 265–268.
[21] Ruckenstein E, Some remarks on renewal models[J]. Chem Eng Sci, 1963, 18(4): 233–241
[22] Koppel L B, Patel R D, Holmes J T, Statistical models for surface renewal in heat and mass transfer : partⅠ. Dependence pf average transport coefficients on age distribution[J]. AIChE J, 1966, 12(5): 941–946
[23] Nijsing R, Predictions on momentum, heat and mass transfer in turbulent channel flow with the aid of a boundary layer growth-breakdown model[J]. Warmeund Stoffiibertragung, 1969, 2(1):65–86
[24] Pinczewski W V, Sideman S, A model for mass (heat) transfer in turbulent tube flow. Moderate and high Schmidt (Prandtl) numbers[J]. Chem Eng Sci, 1974, 29(9): 1969–1976
[25] Hart J, Single-phase and two-phase pipe flow, PhD thesis. University of Amsterdam, The Netherlands, 1988
[26] Vignes A, Concentration dependence of the binary diffusion coeffcient[J].Ind Eng Chem Fundam, 1966, 5(2):281–283
[27] Kubaczka A, Bandrowski J, Solutions of a system of multicomponent mass transport equation for mixtures of real fluids[J]. Chem Eng Sci, 1991, 46(2): 539–556
[28] Krishna R, Ternary mass transfer in a wetted-wall column significance of diffusional interactions. I. Stefan diffusion[J]. Trans Inst Chem Eng, 1981, 59(1): 35–43
[29] Wang J, Langenann H, Unsteady two-film model for mass transfer[J]. Chem Eng Technol, 1994, 17(4): 280–284
[30] Wang J, Langenann H, Unsteady two-film model for mass transfer accompanied by chemical reaction[J]. Chem Eng Sci, 1994, 49(20):3457–3463
[31] Zhao B, Wang J, Yang W, Jin Y, Gas–liquid mass transfer in slurry bubble systems I. Mathematical modeling based on a single bubble mechanism[J]. Chem Eng J, 2003, 96(1-3): 23–27
[32] Levich V G. physicochemical hyrodynamics, Prentice-Hall Englewood Cliffs, 1962
[33] King C J. Turbulent liquid phase mass transfer at a free gas-liquid interface[J]. I & E C Fundamentals, 1966, 5(1):1-8
[34] Fortescue G E, Pearson J R A. On gas absorption into a turbulent liquid[J]. Chem Eng Sci, 1967,22(9):1163-1176
[35] Lamont J C , Scott D S. Eddy cell model of mass transfer into the surface of a turbulent liquid[J]. AIChE J, 1970, 16(4): 513-519
[36] Luk S, Lee Y H, Mass transfer in eddies close to air-water interface. AIChE J, 1986,32(9): 1546-1554
[37]苗容生.两相流气泡界面附近湍流场和浓度场的激光测量及局部传质理论研究,学位论文,天津:天津大学,1993
[38] Austin L J, Banczyk L, Sawistowski H. Effect of electric field on mass transfer across a plane interface [J]. Chem Eng Sci. 1971,26(12): 2120-2121
[39]罗耀明,张秋香,陈晓祥.液液传质界面扰动现象的实时全息记录[J].高校化学工程学报,1995,9(2): 149-154
[40]戴干策,陈敏恒,化工流体力学,北京:化学工业出版社,1988,678-726
[41] Berg J C, Morig C R. Density effects in interfacial convection [J]. Chem Eng Sci, 1969,24(6): 937-946
[42] Sternling L V, Scriven L E. Interfacial Turbulence: Hydrodynamic instability and the Marangoni effect[J]. AIChE J, 1959, 5(4): 514-523
[43] Vazquez G, Antorrena G, Navaza J M. Estimation of the turbulence induced by the Marangoni effect at a gas-liquid interface[J]. Int Chem Eng, 1990, 30(2): 228-235
[44] Golovin A A. Mass transfer under interfacial turbulence: Kinetic regularities[J]. Chem Eng Sci, 1992,47(8): 2069-2080
[45] Zuiderweg F J. Marangoni effect in distillation of alcohol-water mixtures[J]. Chem Eng Res Des, 1983,61(6): 388-390
[46] Dijkstra H A, Drinkenburg A A H. Enlargement of wetted area and mass transfer due to surface tension gradients: The creeping film phenomenon[J]. Chem Eng Sci,1990,45(4): 1079-108
[47] Pertler M, Haeberl M, Rommel W, Blass E. Mass transfer across liquid-phase boundaries[J]. Chem Eng Proc,1995,34(3): 269-277
[48] Semkov K R. Liquid flow distribution in packed beds by multipoint liquid distributors[J]. Chem Eng Sci,1991,46(6): 1393-1399
[49] Proctor S J, Biddulph M W, Krishnamurthy K R. Effects of Marangoni surface tension forces on modern distillation packings[J]. AIChE J, 1998, 44(4): 831-835
[50] Martin A M, Perez A C. The influence of surgace tension on the bolumetric mass transfer coefficient in rectification[J]. Int Chem Eng, 1994, 34(1): 76-81
[51] Cullen E J, Davidson J F. Absorption of gases in liquid jets[J]. Trans Faraday Soc, 1957,53(1): 113-120
[52] Harvey E A, Smith W. The absorption of carbon dioxide by a quiescent liquid[J]. Chem Eng Sci, 1959,10(4): 274-280
[53] Thomas G S, Robert L P. Influence of surface turbulence and surfactants on gas transport through liquid interfaces[J]. Ind Eng Chem Fundam, 1970,9(3): 458-465
[54] Burnett J C, Himmelblau D M. The effect of surface active agents on interphase[J]. AIChE J, 1970,16(2): 185-193
[55] Ramirez J A, Davies R H. Mass transfer to a surfactant-covered bubble or drop[J]. AIChE J, 1999,45(6): 1355-1358
[56] Kang K H, Choi C K. Onset of solutal Marangoni convection in a suddenly desorbing liquid layer[J]. AIChE J, 2000,46(1): 15-23
[57] Stoica A G, Kurzeluk M, Floarea O. Experiment study of Marangoni effection a liquid-liquid system[J]. Chem Eng Sci, 2000,55: 3813- 3816
[58] Li X, Mao Z, Fei W. Effects of surface-active agents on mass transfer of a solute into single buoyancy driven drops in solvent extraction systems[J]. Chem Eng Sci, 2003, 58(16): 3793-3806
[59] Hanwright J, Zhou J, Evans G M, Galvin K P. Influence of surfactant on gas bubble stability[J]. Langmuir, 2005, 21(11): 4912-4920
[60] Liu Y, Dong X, Sun Y. Equilibria and kinetics of protein transfer to and from affinity-based reverse micelles of Span 85 modified with Cibacron Blue F-3GA[J]. Biochem Eng J, 2006,28(3): 281-288
[61] Oh S G, Shah D O. Effect of micellar lifetime on the rate of solubilization and detergency in sodium dodecyl sulfate solutions[J]. JAOCS, 1993, 70(7): 673-678
[62] Larson R S, Lam D K. Interfacial mass transfer resistance in nonideal systems[J]. Ind Eng Chem Fundam, 1986, 25(1): 148-152
[63] Shah R, Neogi P. Interfacial resistance in solubilization kinetics[J]., J Colloid Interface Sci, 2002, 253(2): 443-454
[64] Neogi P. A model for interfacial resistance observed during solubilization with micellar solution[J]. J Colloid Interface Sci, 2003, 261(2): 542-546
[65] Chang C Y, Liu L H, Chang I C et al. Film model for sulfur dioxide absorption into quiescent water with interfacial resistance[J]. Chemosphere, 1994, 28(6): 1217
[66] Higbie R, Rate of absorption of pure gas into a still liquid during short periods of exposure[J]. Trans, AIChE, 1935, 31(2):365-389
[67] Chiang S H,Toor H L, Interfacial resistance in the absorption of oxygen by water[J]. AIChE J, 1959, 5(2):165
[68] Mcmanamey W J, Interfacial resistances in the liquid extraction of inorganic nitrates[J]. Chem Eng Sci, 1961, 15(1): 210-219
[69] Cable M, Cardew G E, The kinetics of desorption with an interfacial resistance and concentration-dependent diffusicity[J]. Chem Eng Sci, 1977, 32(2): 535-541
[70] Shah R, Neogi P, Interfacial resistance in solubilization kinetcs[J]. J Colloid Interface Sci, 2002, 253(2): 443-454
[71] Gupta R K, Sridhar T, Effect of interfacial resistance on quiescent gas-liquid absorption[J]. Chem Eng Sci, 1984, 39(3): 471-477
[72] Shankar V, Influence of interfacial resistance on kinetics of sorption[J]. Polymer, 1981, 22(6): 748-752
[73] Cable M, Cabdew G E, The kinetics of desorption with an interfacial resistance and concentration-dependent diffusivity[J]. Chem Eng Sci, 1977, 32(5):535-541
[74] Alper E, Wichtendahl B, Deckwer W D. Gas absorption mechanism in catalytic slurry reactors [J]. Chem Eng Sci, 1980, 35(1-2): 217-222
[75] Tinge J T, Drinkenburg A A H. The enhancement of the physical absorption of gases in aqueous activated carbon slurries[J]. Chem Eng Sci,1995,50(6):937- 942.
[76] Ruthiya K C, Schaaf van der, Kuster B F M, Schouten J C. Mechanisms of physical and reaction enhancement of mass transfer in a gas inducing stirred slurry reactor[J]. Chem Eng J, 2003, 96(1-3):55-69
[77] Dumont E, Delmas H. Mass transfer enhancement of gas absorption in oil-in- water systems: a review[J]. Chem Eng Process, 2003, 42(6): 419-438
[78] Zhang G D, Cai W F, Xu C J, Zhou M. A general enhancement factor model of the physical absorption of gases in multiphase system[J]. Chem Eng Sci, 2006, 61(2): 558-568
[79] Kaya A , Schumpe A. Surfactant adsorption rather than shuttle effect[J]. Chem Eng Sci, 2005, 60(22): 6504-6510
[80] KordaěM, Linek V, Mechanism of enhanced gas absorption in presence of fine solid particles. Effect of molecular diffusivity on mass transfer coefficient in stirred cell[J]. Chem Eng Sci, 2006, 61(21):7125-7132
[81] Rosu M, Schumpe A, Influence of surfactants on gas absorption into aqueous suspensions of activated carbon[J]. Chem Eng Sci, 2007, 62(18-20): 5458-5463
[82]成弘,周明,余国琮.强化气液两相传质的研究进展[J].化工进展, 2001,13(4) :315-322
[83] Mehra A,Sharma M M. Absorption with reaction:effect of emulsified second liquid phase[J]. Chem Eng Sci, 1985, 40(12): 2382-2385
[84] Vinke H, Hamersma P J, Fortuin J M H. Enhancement of the gas absorption rate in agitated slurry reactors by gas-adsorbing particles adhering to gas bubbles[J]. Chem Eng Sci, 1993,48(12): 2197-2210
[85] Joly-Vuillemin C, De Bellefon C, Delmas H. Solid effects on gas-liquid mass transfer in three-phase slurry catalytic hydrogenation of adiponitrile over raney nickel[J]. Chem Eng Sci, 1996, 51(10): 2149-2158
[86] Bruining W J, Joosten G E H, Beenackers A A C M, Hofman H. Enhancement of gas-liquid mass transfer by a dispersed second liquid phase[J]. Chem Eng Sci, 1986,41(7):1873-1877
[87] Holstvoogd R D,van Swaaij W P M,van Dierendonck L L. The absorption of gases in aqueous activated carbon slurries enhanced by adsorbing or catalytic particles[J]. Chem Eng Sci, 1988, 43(8) : 2181-2187
[88] Holstvoogd R D, van Swaaij W P M. The influence of adsorption capacity on enhanced gas absorption activated carbon slurries[J]. Chem Eng Sci, 1990, 45(1): 151-162
[89] Mehra A. Gas absorption in reactive slurries:particle dissolution near gas-liquid interface[J]. Chem Eng Sci,1996,51(3):461-477
[90] Brilman D W F, van Swaaij W P M, Versteeg G F. A one- dimensional instationary heterogeneous mass transfer model for gas absorption in multiphase systems[J]. Chem Eng Process.1998,37(6):471-488
[91] Mehra A. Intensification of multiphase reactions through the use of a microphase-I.theoretical[J]. Chem Eng Sci, 1988, 43(4): 899-912
[92] Lekhal A, Chaudhari R V, Wilhelm A M, Delmas H. Gas-liquid mass transfer in gas-liquid-liquid dispersions[J]. Chem Eng Sci, 1997,52(21-22): 4069-4077
[93] Dagaonkar MV, Heeres H J,Beenackers A A C M, Pangarkar V G. The application of fine TiO2 particles for enhanced gas absorption[J]. Chem Eng J, 2003, 92(1-3):151-159
[94] Nagy E. Three-phase mass transfer:one dimensional heterogeneous model[J]. Chem Eng Sci, 1994,50(5) :827-836
[95] Lin C, Zhou M,Xu C J. Axisymmetrical two-dimensional heterogeneous mass transfer model for the absorption of gas into liquid-liquid dispersions[J]. Chem Eng Sci, 1999, 54 (3): 389-399
[96] Brilman D W F, Goldschmidt M J V, Versteeg G F, van Swaaij W P M. Heterogeneous mass transfer models for gas absorption in multiphase systems[J]. Chem Eng Sci, 2000, 55 (15): 2793-2812
[97] Wimmers O J, Fortuin J M H. The use of adhesion of catalyst particles to gas bubbles to achieve enhancement of gas absorption in slurry reactors I. Investigation of particle-to-bubble adhesion using the bubble pick-up method[J]. Chem Eng Sci, 1988,43(2) : 303-312
[98] Akbar M K, Ghiaasiaan S M. Modeling the gas absorption in a spray scrubber with dissolving reactive particles[J]. Chem Eng Sci, 2004, 59(5): 967-976
[99] Cents A H G,Brilman D W F,Versteeg G F. Gas absorption in an agitated gas-liquid-liquid system[J]. Chem Eng Sci, 2001, 56(3): 1075-1083
[100] Linek V,Moucha T,Kordac M. Mechanism of mass transfer from bubbles in dispersions Part I.Danckwerts,plot method with sulphite solutions in the presence of viscosity and surface tension changing agents[J]. Chem Eng Process, 2005, 44 (3) : 353-361
[101] Linek V,Kordac M,Moucha T. Mechanism of mass transfer from bubbles in dispersions Part II: Mass transfer coefficients in stirred gas-liquid reactor and bubble column[J]. Chem Eng Process, 2005, 44 (1): 121-130
[102] Higbie R. The rate of absorption of a pure gas into a still liquid during short periods of exposure[J]. Transactions of the American Institute of Chemical Engineers , 1935, 31(2): 365ˉ377
[103] Danckwerts P V. Significance of liquid-film coefficients in gas absorption[J]. Ind Eng Chem, 1951, 43(6): 1460ˉ1468
[104] Toor H L, Marchello J M. Film-penetration model for mass and heat transfer[J]. AIChE J, 1958, 4(1): 97–101
[105] Lamont J C, Scott D S. An eddy cell model of mass transfer into the surface of a turbulent liquid[J]. AIChE J , 1970, 16(3): 513–519
[106] Levich V G. Physicochem Hydrodyn, Prentice-Hall, New York., 1962
[107] Lochiel A C, Calderbank P H. Mass transfer in the continuous phase around axisymmetric bodies of revolution[J] . Chem Eng Sci, 1964, 19(7): 471-484
[108] Petera J, Weatherley L R. Modelling of mass transfer from falling droplets[J]. Chem Eng Sci,2001,56(16): 4929- 4947
[109] Tom P. Oxygen absorption into moving water and tenside solutions[J]. Water Research, 2000, 34(9): 2569-2581
[110] Khan A R, Dimitrios G, Nicholas A K, George K. Flux of gases across the air- water interface studied by reversed-flow gas chromatography[J]. J Chroma A, 2001, 934: 31-49
[111] Pierotti R A. The solubility of gases in liquids[J] . J Phys Chem, 1963, 67 : 1840-1846
[112] Bennett C O, Myers J E, Momentum, heat and mass transfer, third ed., McGraw-Hill Book Company, New York,1982, pp.495-498
[113] Paterson W R, Hayhurst A N, Mass or heat transfer from a sphere to a flowing fluid[J]. Chem Eng Sci 2000,55(4): 1925-1927
[114] Bennett C O, .Myers J E, Momentum, Heat and Mass Transfer, McGraw-Hill Book Company, Inc, New York, USA, 1962
[115] Sherwood T K, Pigford R L, Wilke C R, Mass Transfer, McGraw-Hill, New York , 1975
[116] Yong S W, Dong K C, Anthony F M. Density, viscosity, surface tension, and carbon dioxide solubility and diffusivity of methanol. Ethanol, aqueous propanol, and aqueous ethylene glycol at 25℃[J]. J Chem Eng Data, 1981, 26(2): 140-141
[117] Taflin D C, and Davis E J. Mass transfer from an aerosol droplet at intermediate Peclet numbers[J]. Chem Eng Commun, 1987, 55: 199-210
[118] Widmann J F and Davis E J. Analysis of mass transfer between a sequence of drops and a surrounding gas[J]. J Aerosol Sci, 1997, 28: 1233-1249
[119] Chen W H. An analysis of absorption by a liquid aerosol in a stationary environment[J]. Atmos Environ, 2002, 36: 3671-3683
[120] Brogren C and Karlsson H T. Modeling the absorption of SO2 in a spray scrubber using the penetration theory[J]. Chem Eng Sci, 1997, 52: 3085-3099
[121] Adewuyi Y G and Carmichael G R. A theoretical investigation of gaseous absorption by water droplets from SO2-HNO3-CO2-HCl mixture[J]. Atmos Environ, 1982, 16: 719-729
[122] Clift R, Grace J R Weber M E, Bubbles, drops and particles. New York : Academic, 1978
[123] Zhang S H and Davis E J. Mass transfer from a single micro-droplet to a gas flowing at low Reynolds number[J]. Chem Eng Commun, 1987, 55: 51-67
[124] Piarah W H, Paschedag A. and Kraume M. Numerical simulation of mass transfer between a single droplet and an ambiant flow[J]. AIChE J, 2001, 47: 1701-1704
[125] Pedersen T. Oxygen absorption into moving water and tenside solution[J]. Water Research, 2000, 34: 2569-2581
[126] Ma Youguang , Cheng Hong and Yu Guocong. Measurement of concentration fields near the interface of a rising bubble by holographic interference technique[J]. Chinese J. Chem. Eng, 1999, 7: 363-367
[127] Ma Youguang , Yu Guocong, Huai Z Li, Note on the Mechanism of Interfacial Mass Transfer of Absorption Processes[J]. Int J Heat and Mass Transf, 2005, 48(16): 3454-3460
[128] Ferrell R T. and Himmelblau D M. Diffusion coefficients of nitrogen and oxygen in water[J]. J Chem Eng Data, 1967, 12, 111-115
[129] Milne-Thomson L M, Theoretical Hydrodynamics, 5th ed., Macmillan, London, 1972
[130] Parlange J Y. Spherical-Cap bubble with laminar wakes. J Fluid Mech ,1969, 37: 257-284
[131] Coppus J H C, Rietema K. Theoretical derivation of the mass transfer coefficient at the front of a spherical cap bubble[J]. Chem Eng Sci, 1980, 35(6): 1497-1499
[132] Johnson A I, Besik F, Hamielec A E, Mass transfer from a single rising bubble[J]. Canad J Chem Eng, 1969, 47(6): 559-564
[133] Abdullan A K, Theory of convective heat and mass transfer to Spherical-Cap bubbles[J]. AIChE J, 1994, 40(9): 1440-1448
[134] Joosten G E H, Schilder J G M, Janssen J J, The influence of suspended solid material on the gas–liquid mass transfer in stirred gas–liquid contactors[J]. Chem Eng Sci, 1977,32 (5): 563-566
[135] Kars R L, Best R J, Drinkenburg A A H, The sorption of propane in slurries of active carbon in water[J]. Chem Eng J, 1979,17: 201-210
[136] Quicker G, Alper E, Deckwer W D, Effect of fine activated carbon particles on the rate of CO2 absorption[J]. AIChE J, 1987, 33 (5): 871-875
[137] Beenackers A A C M, van Swaaij W P M, Mass transfer in gas–liquid slurry reactors[J]. Chem Eng Sci 1993,48 (18): 3109-3139
[138] Alper E, Wichtendahl B, Deckwer W D, Gas absorption mechanism in catalytic slurry reactors[J]. Chem Eng Sci, 1980,35 (1): 217-222
[139] Alper E, Ozturk S, Effect of fine solid particles on gas–liquid mass transfer rate in a slurry reactor[J]. Chem Eng Commun, 1986, 46 (1): 147-158
[140] Mehra A, Gas absorption in slurries of finite-capacity microphases[J]. Chem Engng Sci, 1990, 45(6): 1525–1538
[141] Demmink J F, Mehra A, Beenackers A A C M, Gas absorption in the presence of particles showing interfacial affinity: case of fine sulfur precipitates[J]. Chem Eng Sci, 1998, 53 (16): 2885-2902