微通道内两相流流型及液滴生成研究
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摘要
近年来,微流体技术发展迅速,多相流作为其研究和应用的基础,受到人们极大关注。本文研究了微通道内两相流流型及液滴的生成。
采用激光影像放大技术,观测了截面尺寸为40×160μm的竖直矩形微通道内空气-水两相流的流型,主要有弹状流、液环流和平行流。以两相流速为坐标绘制了流型图,得出了流型转换线,并与文献中的结果进行了对比。
利用高速摄像仪观察了对流T型、Y型微通道内液液两相流流型。油相为环己烷,水相为加入0.3%表面活性剂十二烷基硫酸钠(sodium dodecyl sulfate, SDS)的水溶液。观测到了滴状流、弹状流和平行流三种流型,实验发现流型转换线受微通道尺寸和进口方式的影响。以两相流的表观速度为坐标轴绘制了流型图,并与已有报道进行了对比。
利用高速摄像仪研究了对流T型和垂直型微通道内液滴的生成过程及机理。考察了微通道结构和尺寸、两相流率、流体物理性质(黏度、界面张力)等对液滴生成的影响。对于弹状流流型中的液滴,其生成主要是由两端压力降(积压)控制,液滴生成尺寸与两相流量比呈正比关系;对于滴状流中的小液滴,其破裂主要受剪切力和界面张力控制,液滴的生成尺寸与毛细管数呈指数关系。基于两端压力降和剪切力的共同作用机理,用毛细管数Ca和两相流量比φ对不同进口方式的微通道内液滴生成尺寸进行了关联和预测,预测值与实验结果吻合良好。
In recent years, microfluidic technology has developed rapidly and been widely used. The multiphase flow, as the basis for research and application of microfluidics, has been attracted much attention. In this paper, two-phase flow patterns and droplet formation in microchannels were studied.
The air-water two-phase flow patterns, including slug, annular and stratified flow, in vertical rectangle microchannels with the dimension of 40×160μm were investigated by means of laser image magnifying technique. A flow patterns map was constructed to obtain the transitions lines with the flow rates of both phases as the coordinates, and was compared with the results in the literature.
A high-speed camera was used to observe the liquid-liquid two-phase flow patterns in the T and Y-junction microchannels. Cyclohexane and demonized water with 0.3% surfactant sodium dodecyl sulfate (SDS), were employed as the oil and water phase, respectively. Three main flow patterns were observed: droplet, slug and parallel flow. The transition lines of flow patterns were affected by microchannel size and the way of feeding. A flow patterns map was constructed with the apparent flow rates of both phases as the coordinates, and was compared with the existing reports.
The processes and the mechanisms of droplet formation in the microchannels with head-on T-junctions and vertical-junction were studied using the high-speed camera. The effects of the geometry and size of microchannels, flow rates of both phases and physical properties (viscosity and interfacial tension) of fluids on droplet formation were investigated. In the slug flow regime, the droplet formation is mainly dominated by the accumulated pressure drop across the thread of the dispersed phase, and the size of formed droplet is proportional to the ratio of flow rates of dispersed/continuous phases. In the drop flow regime, the break-up of the droplet is mainly dominated by the shear force and interfacial tension, and the size of formed droplet has an exponential relation with capillary number. On the basis of interplay of the accumulated pressure drop and shear force, the correlations were proposed for predicting the size of formed droplet with different feeding ways, taking into account the capillary number Ca and the ratio of oil/water flow ratesφ, and the predicted values agreed well with the experimental data.
采用激光影像放大技术,观测了截面尺寸为40×160μm的竖直矩形微通道内空气-水两相流的流型,主要有弹状流、液环流和平行流。以两相流速为坐标绘制了流型图,得出了流型转换线,并与文献中的结果进行了对比。
利用高速摄像仪观察了对流T型、Y型微通道内液液两相流流型。油相为环己烷,水相为加入0.3%表面活性剂十二烷基硫酸钠(sodium dodecyl sulfate, SDS)的水溶液。观测到了滴状流、弹状流和平行流三种流型,实验发现流型转换线受微通道尺寸和进口方式的影响。以两相流的表观速度为坐标轴绘制了流型图,并与已有报道进行了对比。
利用高速摄像仪研究了对流T型和垂直型微通道内液滴的生成过程及机理。考察了微通道结构和尺寸、两相流率、流体物理性质(黏度、界面张力)等对液滴生成的影响。对于弹状流流型中的液滴,其生成主要是由两端压力降(积压)控制,液滴生成尺寸与两相流量比呈正比关系;对于滴状流中的小液滴,其破裂主要受剪切力和界面张力控制,液滴的生成尺寸与毛细管数呈指数关系。基于两端压力降和剪切力的共同作用机理,用毛细管数Ca和两相流量比φ对不同进口方式的微通道内液滴生成尺寸进行了关联和预测,预测值与实验结果吻合良好。
In recent years, microfluidic technology has developed rapidly and been widely used. The multiphase flow, as the basis for research and application of microfluidics, has been attracted much attention. In this paper, two-phase flow patterns and droplet formation in microchannels were studied.
The air-water two-phase flow patterns, including slug, annular and stratified flow, in vertical rectangle microchannels with the dimension of 40×160μm were investigated by means of laser image magnifying technique. A flow patterns map was constructed to obtain the transitions lines with the flow rates of both phases as the coordinates, and was compared with the results in the literature.
A high-speed camera was used to observe the liquid-liquid two-phase flow patterns in the T and Y-junction microchannels. Cyclohexane and demonized water with 0.3% surfactant sodium dodecyl sulfate (SDS), were employed as the oil and water phase, respectively. Three main flow patterns were observed: droplet, slug and parallel flow. The transition lines of flow patterns were affected by microchannel size and the way of feeding. A flow patterns map was constructed with the apparent flow rates of both phases as the coordinates, and was compared with the existing reports.
The processes and the mechanisms of droplet formation in the microchannels with head-on T-junctions and vertical-junction were studied using the high-speed camera. The effects of the geometry and size of microchannels, flow rates of both phases and physical properties (viscosity and interfacial tension) of fluids on droplet formation were investigated. In the slug flow regime, the droplet formation is mainly dominated by the accumulated pressure drop across the thread of the dispersed phase, and the size of formed droplet is proportional to the ratio of flow rates of dispersed/continuous phases. In the drop flow regime, the break-up of the droplet is mainly dominated by the shear force and interfacial tension, and the size of formed droplet has an exponential relation with capillary number. On the basis of interplay of the accumulated pressure drop and shear force, the correlations were proposed for predicting the size of formed droplet with different feeding ways, taking into account the capillary number Ca and the ratio of oil/water flow ratesφ, and the predicted values agreed well with the experimental data.
引文
[1] Ehrfeld W, Hessel V, Lowe H, Microreactor, NewYork: Weinheim:Wiley/VCH, 2000.
[2] Jensen K F, Microreaction engineering—is small better?, Chemical Engineering Science, 2001, 56(2): 293~303
[3] J?hnisch K, Hessel V, Lowe H, et al., Chemistry in microstructured reactors, Angewandte Chemie International Edition, 2004, 43(4): 406~446
[4] Chen G W, Yuan Q, Li H Q, et al., CO selective oxidation in a microchannel reactor for PEM fuel cell, Chemical Engineering Journal, 2004, 101(1-3): 101~106
[5] Utada A S, Lorenceau E, Link D R, et al., Monodisperse double emulsions generated from a microcapillary device, Science, 2005, 308(5721): 537~541
[6] Cristin V, Tan Y C, Theory and numerical simulation of droplet dynamics in complex flows-a review, Lab on a Chip, 2004, 4(4): 257~264
[7] Tabeling P, A brief introduction to slippage, droplets and mixing in microfluidic systems, Lab on a Chip, 2009, 9(17): 2428~2436
[8] Tonkovich A Y, Perry S, Wang Y, et al., Microchannel process technology for compact methane steam reforming, Chemical Engineering Science, 2004, 59(22-23): 4819~4824
[9] Song H, Chen D L, Ismagilov R F, Reactions in droplets in microflulidic channels, Angewandte Chemie-International Edition, 2006, 45(44): 7336~7356
[10] Stone H A, Kim S, Microfluidics: basic issues, applications, and challenges, AIChE Journal, 2001, 47(6): 1250~1254
[11] Tonkovich A, Kuhlmann D, Rogers A, et al., Microchannel technology scale-up to commercial capacity, Chemical Engineering Research and Design, 2005, 83(6): 634~639
[12]陈光文,袁权,微化工技术,化工学报, 2003, 54(4): 427~439
[13] Hessel V, L?we H, Sch?nfeld F, Micromixers-a review on passive and active mixing principles, Chemical Engineering Science, 2005, 60(8-9): 2479~2501
[14] Charpentier J C, Process intensification by miniaturization, Chemical Engineering & Technology, 2005, 28(3): 255~258.
[15] Liu D S, Wang S D, Flow pattern and pressure drop of upward two-phase flow in vertical capillaries, Industrial & Engineering Chemistry Research, 2008, 47(1): 243~255
[16] Zhao T S, Bi Q C, Co-current air–water two-phase flow patterns in vertical triangular microchannels, International Journal of Multiphase Flow, 2001, 27(5): 765~782
[17] Liu H, Vandu C O, Krishna R, Hydrodynamics of taylor flow in vertical capillaries: Flow regimes, bubble rise velocity, liquid slug length, and pressure drop, Industrial & Engineering Chemistry Research, 2005, 44(14): 4884~4897
[18] Fu X, Qi S L, Zhang P, et al., Visualization of flow boiling of liquid nitrogen in a vertical mini-tube, International Journal of Multiphase Flow, 2008, 34(4): 333~351
[19] Xu J, Experimental study on gas-liquid two-phase flow regimes in rectangular channels with mini gaps, International Journal of Heat and Fluid Flow, 1999, 20(4): 422~428
[20] Zhang P, Fu X, Two-phase flow characteristics of liquid nitrogen in vertically upward 0.5 and 1.0 mm micro-tubes: Visualization studies, Cryogenics, 2009, 49(10): 565~575
[21] Triplett K A, Ghiaasiaan S M, Abdel-Khalik S I, et al., Gas-liquid two-phase flow in microchannels-Part I: two-phase flow patterns, International Journal of Multiphase Flow, 1999, 25(3): 377~394
[22] Chen W L, Twu M C, Pan C, Gas–liquid two-phase flow in micro-channels, International Journal of Multiphase Flow, 2002, 28(7): 1235~1247
[23] Serizawa A, Feng Z, Kawara Z, Two-phase flow in microchannels, Experimental Thermal and Fluid Science, 2002, 26(6-7): 703~714
[24] Saisorn S, Wongwises S, Flow pattern, void fraction and pressure drop of two-phase air–water flow in a horizontal circular micro-channel, Experimental Thermal and Fluid Science, 2007, 32(3): 748~760
[25] Ide H, Kariyasaki A, Fukano T, Fundamental data on the gas -liquid two-phase flow in minichannels, International Journal of Thermal Sciences, 2007, 46(6): 519~530
[26] Kawahara A, Chung P M Y, Kawaji M, Investigation of two-phase flow pattern, void fraction and pressure drop in a microchannel, International Journal of Multiphase Flow, 2002, 28(9): 1411~1435
[27] Saisorn S, Wongwises S, The effects of channel diameter on flow pattern, void fraction and pressure drop of two-phase air-water flow in circular micro-channels, Experimental Thermal and Fluid Science, 2008, 32(3): 748~760
[28] Pehlivan K, Hassan I, Vaillancourt M, Experimental study on two-phase flow and pressure drop in millimeter-size channels, Applied Thermal Engineering, 2006, 26(14-15): 1506~1514
[29]宋静,微通道内气液两相流动特性研究,青岛科技大学学报,2006,27(4):299~303
[30] Pohorecki R, Sobieszuk P, Kula K, et al., Hydrodynamic regimes of gas-liquid flow in a microreactor channel, Chemical Engineering Journal, 2008, 135(1): 185~190
[31] Cubaud T, Ho C M, Transport of bubbles in square microchannels, Physics of Fluids, 2004, 16(12): 4575~4585
[32] Akbar M K, Plummer D A, Ghiaasiaan S M, On gas-liquid two-phase flow regimes in microchannels, International Journal of Multiphase Flow, 2003, 29(5): 855~865
[33] Waelchli S, Rudolf von Rohr P, Two-phase flow characteristics in gas-liquid microreactors, International Journal of Multiphase Flow, 2006, 32(7): 791~806
[34] Lee C Y, Lee S Y, Influence of surface wettability on transition of two-phase flow pattern in round mini-channels, International Journal of Multiphase Flow, 2008, 34(7): 706~711
[35] Shao N, Gavriilidis A, Angeli P, Flow regimes for adiabatic gas-liquid flow in microchannels, Chemical Engineering Science, 2009, 64(11): 2749~2761
[36]骆广生,徐建鸿,李少伟等,微结构设备内液液两相流行为研究及其进展,现代化工,2006,26(3): 19~23
[37] Guillot P, Colin A, Stability of parallel flows in a microchannel after a T junction, Physical Review E, 2005, 72(6): 066301
[38] Zhao Y, Chen G, Yuan Q, Liquid-liquid two-phase flow patterns in a rectangular microchannel, AIChE Journal, 2006, 52(12): 4052~4046
[39] Dessimoz A-L, Cavin L, Renken A, et al., Liquid liquid two phase flow patterns and mass transfer characteristics in rectangular glass microreactors, Chemical Engineering Science, 2008, 63(16): 4035~4044
[40] Salim A, Fourar M, Pironon J, et al., Oil–water two-phase flow in microchannels: flow patterns and pressure drop measurements, The Canadian Journal of Chemical Engineering, 2008, 86(6): 978~988
[41] Xu J H, Luo G S, Li S W, et al., Shear force induced monodisperse droplet formation in a microfluidic device by controlling wetting properties, Lab on a Chip, 2006, 6(1): 131~136
[42] Cubaud T, Mason T G, Capillary thread and viscous droplets in square microchannels, Physics of Fluids, 2008, 20(5): 053302
[43] Galbiati L, Andreini P, Flow pattern transition for vertical downward two-phase flow in capillary tubes, Inlet mixing effects, International Communications in Heat and Mass Transfer, 1992, 19(6): 791~799
[44] Peng S J, Williams R A, Controlled production of emulsions using a crossflow membrane,partⅰ: droplet formation from a single pore. Transaction of IChemE, 1998, 76(8): 894~901
[45] van der Graaf S, Nisisako T, Schro?n C G P H, et al., Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel, Langmuir, 2006, 22(9): 4144~4152
[46] Steegmans M L J, Schro?n C G P H, Boom R M, Generalised insights in droplet formation at T-junctions through statistical analysis, Chemical Engineering Science, 2009, 64(13): 3042~3050
[47] Steegmans M L J, Schro?n K G P H, Boom R M, Characterization of Emulsification at Flat Microchannel Y Junctions, Langmuir, 2009, 25(6): 3396~3401
[48] Shui L, Mugele F, Berg A, et al., Geometry-controlled droplet generation in head-on microfluidic devices, Applied Physics Letters, 2008, 93(15): 153113
[49] Thorsen T, Roberts R W, Arnold F H, et al., Dynamic pattern formation in a vesicle-generating microfluidic device, Physical Review Letters, 2001, 86(18): 4163~4166
[50] De Menech M, Garstecki P, Jousse F, et al., Transition from squeezing to dripping in a microfluidic T-shaped junction, Journal of Fluid Mechanics, 2008, 595: 141~161
[51] Xu J H, Li S W, Tan J, et al., Preparation of Highly Monodisperse Droplet in a T-Junction Microfluidic Device, American Institute of Chemical Engineers Journal, 2006, 52(9): 3005~3010
[52] Xu J H, Li S W, Tan J, et al., Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping, Microfluidics and Nanofluidics, 2008, 5(6): 711~717
[53] Husny J, Cooper-White J J, The effect of elasticity on drop creation in T-shaped microchannels, Journal of Non-Newtonian Fluid Mechanics, 2006, 137(1-3): 121~136
[54]方肇伦,微流控分析芯片的制作及应用,北京:化学工业出版社,2005. 9~61
[55]林炳承,秦建华,微流控芯片实验室,北京:科学出版社,2006. 16~46
[56] BENJAMIN T B. Wave formation in laminar flow down an inclined plane, Journal of Fluid Mechanics, 1957, 2(6): 554~574
[57] Steinbrenner J E, Hidrovo C H, Wang F-M, et al., Measurement and modeling of liquid film thickness evolution in stratified two-phase microchannel flows, Applied Thermal Engineering, 2007, 27(10): 1722~1727
[58] Chung P M Y, Kawaji M, Kawahara A, et al., Two-phase flow through square and circular microchannels—effects of channel geometry, Journal of Fluids Engineering, 2004, 126(4): 546~552
[59] Garstecki P, Fuerstman M J, Stone H A, et al., Formation of droplets and bubbles in a microfluidic T-junction-Scaling and mechanism of break-up, Lab on a Chip, 2006, 6(3): 437~446
[60] Christopher G F, Noharuddin N N, Taylor J A, et al., Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions, Physical Review E, 2008, 78(3): 036317
[2] Jensen K F, Microreaction engineering—is small better?, Chemical Engineering Science, 2001, 56(2): 293~303
[3] J?hnisch K, Hessel V, Lowe H, et al., Chemistry in microstructured reactors, Angewandte Chemie International Edition, 2004, 43(4): 406~446
[4] Chen G W, Yuan Q, Li H Q, et al., CO selective oxidation in a microchannel reactor for PEM fuel cell, Chemical Engineering Journal, 2004, 101(1-3): 101~106
[5] Utada A S, Lorenceau E, Link D R, et al., Monodisperse double emulsions generated from a microcapillary device, Science, 2005, 308(5721): 537~541
[6] Cristin V, Tan Y C, Theory and numerical simulation of droplet dynamics in complex flows-a review, Lab on a Chip, 2004, 4(4): 257~264
[7] Tabeling P, A brief introduction to slippage, droplets and mixing in microfluidic systems, Lab on a Chip, 2009, 9(17): 2428~2436
[8] Tonkovich A Y, Perry S, Wang Y, et al., Microchannel process technology for compact methane steam reforming, Chemical Engineering Science, 2004, 59(22-23): 4819~4824
[9] Song H, Chen D L, Ismagilov R F, Reactions in droplets in microflulidic channels, Angewandte Chemie-International Edition, 2006, 45(44): 7336~7356
[10] Stone H A, Kim S, Microfluidics: basic issues, applications, and challenges, AIChE Journal, 2001, 47(6): 1250~1254
[11] Tonkovich A, Kuhlmann D, Rogers A, et al., Microchannel technology scale-up to commercial capacity, Chemical Engineering Research and Design, 2005, 83(6): 634~639
[12]陈光文,袁权,微化工技术,化工学报, 2003, 54(4): 427~439
[13] Hessel V, L?we H, Sch?nfeld F, Micromixers-a review on passive and active mixing principles, Chemical Engineering Science, 2005, 60(8-9): 2479~2501
[14] Charpentier J C, Process intensification by miniaturization, Chemical Engineering & Technology, 2005, 28(3): 255~258.
[15] Liu D S, Wang S D, Flow pattern and pressure drop of upward two-phase flow in vertical capillaries, Industrial & Engineering Chemistry Research, 2008, 47(1): 243~255
[16] Zhao T S, Bi Q C, Co-current air–water two-phase flow patterns in vertical triangular microchannels, International Journal of Multiphase Flow, 2001, 27(5): 765~782
[17] Liu H, Vandu C O, Krishna R, Hydrodynamics of taylor flow in vertical capillaries: Flow regimes, bubble rise velocity, liquid slug length, and pressure drop, Industrial & Engineering Chemistry Research, 2005, 44(14): 4884~4897
[18] Fu X, Qi S L, Zhang P, et al., Visualization of flow boiling of liquid nitrogen in a vertical mini-tube, International Journal of Multiphase Flow, 2008, 34(4): 333~351
[19] Xu J, Experimental study on gas-liquid two-phase flow regimes in rectangular channels with mini gaps, International Journal of Heat and Fluid Flow, 1999, 20(4): 422~428
[20] Zhang P, Fu X, Two-phase flow characteristics of liquid nitrogen in vertically upward 0.5 and 1.0 mm micro-tubes: Visualization studies, Cryogenics, 2009, 49(10): 565~575
[21] Triplett K A, Ghiaasiaan S M, Abdel-Khalik S I, et al., Gas-liquid two-phase flow in microchannels-Part I: two-phase flow patterns, International Journal of Multiphase Flow, 1999, 25(3): 377~394
[22] Chen W L, Twu M C, Pan C, Gas–liquid two-phase flow in micro-channels, International Journal of Multiphase Flow, 2002, 28(7): 1235~1247
[23] Serizawa A, Feng Z, Kawara Z, Two-phase flow in microchannels, Experimental Thermal and Fluid Science, 2002, 26(6-7): 703~714
[24] Saisorn S, Wongwises S, Flow pattern, void fraction and pressure drop of two-phase air–water flow in a horizontal circular micro-channel, Experimental Thermal and Fluid Science, 2007, 32(3): 748~760
[25] Ide H, Kariyasaki A, Fukano T, Fundamental data on the gas -liquid two-phase flow in minichannels, International Journal of Thermal Sciences, 2007, 46(6): 519~530
[26] Kawahara A, Chung P M Y, Kawaji M, Investigation of two-phase flow pattern, void fraction and pressure drop in a microchannel, International Journal of Multiphase Flow, 2002, 28(9): 1411~1435
[27] Saisorn S, Wongwises S, The effects of channel diameter on flow pattern, void fraction and pressure drop of two-phase air-water flow in circular micro-channels, Experimental Thermal and Fluid Science, 2008, 32(3): 748~760
[28] Pehlivan K, Hassan I, Vaillancourt M, Experimental study on two-phase flow and pressure drop in millimeter-size channels, Applied Thermal Engineering, 2006, 26(14-15): 1506~1514
[29]宋静,微通道内气液两相流动特性研究,青岛科技大学学报,2006,27(4):299~303
[30] Pohorecki R, Sobieszuk P, Kula K, et al., Hydrodynamic regimes of gas-liquid flow in a microreactor channel, Chemical Engineering Journal, 2008, 135(1): 185~190
[31] Cubaud T, Ho C M, Transport of bubbles in square microchannels, Physics of Fluids, 2004, 16(12): 4575~4585
[32] Akbar M K, Plummer D A, Ghiaasiaan S M, On gas-liquid two-phase flow regimes in microchannels, International Journal of Multiphase Flow, 2003, 29(5): 855~865
[33] Waelchli S, Rudolf von Rohr P, Two-phase flow characteristics in gas-liquid microreactors, International Journal of Multiphase Flow, 2006, 32(7): 791~806
[34] Lee C Y, Lee S Y, Influence of surface wettability on transition of two-phase flow pattern in round mini-channels, International Journal of Multiphase Flow, 2008, 34(7): 706~711
[35] Shao N, Gavriilidis A, Angeli P, Flow regimes for adiabatic gas-liquid flow in microchannels, Chemical Engineering Science, 2009, 64(11): 2749~2761
[36]骆广生,徐建鸿,李少伟等,微结构设备内液液两相流行为研究及其进展,现代化工,2006,26(3): 19~23
[37] Guillot P, Colin A, Stability of parallel flows in a microchannel after a T junction, Physical Review E, 2005, 72(6): 066301
[38] Zhao Y, Chen G, Yuan Q, Liquid-liquid two-phase flow patterns in a rectangular microchannel, AIChE Journal, 2006, 52(12): 4052~4046
[39] Dessimoz A-L, Cavin L, Renken A, et al., Liquid liquid two phase flow patterns and mass transfer characteristics in rectangular glass microreactors, Chemical Engineering Science, 2008, 63(16): 4035~4044
[40] Salim A, Fourar M, Pironon J, et al., Oil–water two-phase flow in microchannels: flow patterns and pressure drop measurements, The Canadian Journal of Chemical Engineering, 2008, 86(6): 978~988
[41] Xu J H, Luo G S, Li S W, et al., Shear force induced monodisperse droplet formation in a microfluidic device by controlling wetting properties, Lab on a Chip, 2006, 6(1): 131~136
[42] Cubaud T, Mason T G, Capillary thread and viscous droplets in square microchannels, Physics of Fluids, 2008, 20(5): 053302
[43] Galbiati L, Andreini P, Flow pattern transition for vertical downward two-phase flow in capillary tubes, Inlet mixing effects, International Communications in Heat and Mass Transfer, 1992, 19(6): 791~799
[44] Peng S J, Williams R A, Controlled production of emulsions using a crossflow membrane,partⅰ: droplet formation from a single pore. Transaction of IChemE, 1998, 76(8): 894~901
[45] van der Graaf S, Nisisako T, Schro?n C G P H, et al., Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel, Langmuir, 2006, 22(9): 4144~4152
[46] Steegmans M L J, Schro?n C G P H, Boom R M, Generalised insights in droplet formation at T-junctions through statistical analysis, Chemical Engineering Science, 2009, 64(13): 3042~3050
[47] Steegmans M L J, Schro?n K G P H, Boom R M, Characterization of Emulsification at Flat Microchannel Y Junctions, Langmuir, 2009, 25(6): 3396~3401
[48] Shui L, Mugele F, Berg A, et al., Geometry-controlled droplet generation in head-on microfluidic devices, Applied Physics Letters, 2008, 93(15): 153113
[49] Thorsen T, Roberts R W, Arnold F H, et al., Dynamic pattern formation in a vesicle-generating microfluidic device, Physical Review Letters, 2001, 86(18): 4163~4166
[50] De Menech M, Garstecki P, Jousse F, et al., Transition from squeezing to dripping in a microfluidic T-shaped junction, Journal of Fluid Mechanics, 2008, 595: 141~161
[51] Xu J H, Li S W, Tan J, et al., Preparation of Highly Monodisperse Droplet in a T-Junction Microfluidic Device, American Institute of Chemical Engineers Journal, 2006, 52(9): 3005~3010
[52] Xu J H, Li S W, Tan J, et al., Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping, Microfluidics and Nanofluidics, 2008, 5(6): 711~717
[53] Husny J, Cooper-White J J, The effect of elasticity on drop creation in T-shaped microchannels, Journal of Non-Newtonian Fluid Mechanics, 2006, 137(1-3): 121~136
[54]方肇伦,微流控分析芯片的制作及应用,北京:化学工业出版社,2005. 9~61
[55]林炳承,秦建华,微流控芯片实验室,北京:科学出版社,2006. 16~46
[56] BENJAMIN T B. Wave formation in laminar flow down an inclined plane, Journal of Fluid Mechanics, 1957, 2(6): 554~574
[57] Steinbrenner J E, Hidrovo C H, Wang F-M, et al., Measurement and modeling of liquid film thickness evolution in stratified two-phase microchannel flows, Applied Thermal Engineering, 2007, 27(10): 1722~1727
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