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Rayleigh-Bénard-Marangoni convection (RBM convection) induced by the mass transfer has a great influence on the performance of real chemical engineering process. However, the researches of RBM convection characteristics during mass transfer across the interface in liquid-liquid system and their influence on the interface morphology are still limited. In this research, a visualization experiment via the amplified shadowgraph method is conducted to investigate the mass transfer in water-toluene-acetone system in a vertical slit. The convective structure of RBM and its evolution are visually observed. The effects of the initial acetone concentration of aqueous phase and toluene phase, and the thickness of toluene layer on the RBM characteristics and the morphology of the liquid-liquid interface are investigated. The experimental results show that these structures are induced by the interface tension difference along the interface and the vertical density difference caused by non-uniform mass transfer at the interface. As a result of the mass transfer at the interface, the density stratification occurs at the top of the aqueous phase, where the light liquid layer supports heavy one. In addition, non-uniform mass transfer produces perturbation at the top of the aqueous phase, which induces the Rayleigh-Taylor instability at the " interface” between the heavy and light liquid layer. Consequently, a wave-shaped-mound " interface” in the upper aqueous phase is formed as the heavy liquid comes down into the light one, and it can be further evolved into a plume flow with the enhancement of the imbalance between density and pressure at the " interface”. Due to the difference in mass transfer characteristic caused by different concentration gradients in the plume " interface”, the plumes can also evolve into weak plumes and strong plumes. Under the large acetone concentration gradient, a number of RBM convective structures are generated near the interface in a short time and the convective cloud is formed due to the dramatic interaction and coalescence between these structures. With the weakening of mass transfer, the convective cloud disappears and the strong plume is gradually formed. In addition, the strength of RBM convection is demonstrated to be positively correlated with the acetone concentration gradient across the aqueous solution- toluene interface. In addition, the roughness of the interface and its unsteady fluctuation grow up with the increase of acetone concentration gradient across the interface.
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Keywords:
- liquid-liquid mass transfer /
- shadowgraph method /
- Rayleigh-Bénard-Marangoni convective structure /
- interface morphology
[1] Yao F, Chen Y P, Peterson G P 2013 Int. J. Heat Mass Transfer 64 418
Google Scholar
[2] Liu X D, Chen Y P, Shi M H 2013 Int. J. Therm. Sci. 65 224
Google Scholar
[3] Chen Y P, Cheng P 2005 Int. J. Heat Mass Transfer 32 931
Google Scholar
[4] Bodenschatz E, Pesch W, Ahlers G 2000 Annu. Rev. Fluid Mech. 32 709
Google Scholar
[5] 王飞, 彭岚, 张全壮, 刘佳 2015 64 140202
Google Scholar
Wang F, Peng L, Zhang Q Z, Liu J 2015 Acta Phys. Sin. 64 140202
Google Scholar
[6] 翟薇, 王楠, 魏炳波 2007 56 2353
Google Scholar
Zhai W, Wang N, Wei B B 2007 Acta Phys. Sin. 56 2353
Google Scholar
[7] Schwabe D 1999 Adv. Space Res. 24 1347
Google Scholar
[8] Touazi O, Chénier E, Doumenc F, Guerrier B 2010 Int. J. Heat Mass Transfer 53 656
Google Scholar
[9] Chen J, Yang C, Mao Z S 2015 Eur. Phys. J. Spec. Top. 224 389
Google Scholar
[10] Bo Z, Mao S, Han Z J, Cen K F, Chen J H, Kostya O 2015 Chem. Soc. Rev. 44 2018
[11] 张婷, 施保昌, 柴振华 2015 64 254701
Zhang T, Shi B C, Chai Z H 2015 Acta Phys. Sin. 64 254701
[12] 郑连存, 盛晓艳, 张欣欣 2006 55 5298
Google Scholar
Zheng L C, Sheng X Y, Zhang X X 2006 Acta Phys. Sin. 55 5298
Google Scholar
[13] Kline J L, Hager J D 2016 Matter Radiat. Extremes 2 16
[14] Dong S X, Han W, Liu M F, Zhang Z W, Li B, Ge L Q 2016 Colloids Surf. A 509 32
Google Scholar
[15] Bai L, Zhao S F, Fu Y H, Cheng Y 2016 Biochem. Eng. J. 298 281
[16] Sun Z F 2012 Chem. Eng. Sci. 68 579
Google Scholar
[17] Liu C, Zeng A, Yuan X, Yu G 2008 Chem. Eng. Res. Des. 86 201
Google Scholar
[18] Alvarez-Herrera C, Moreno-Hernández D, Barrientos-García B, Guerrero-Viramontes J A 2005 Opt. Laser Technol. 41 233
[19] Piekarska W, Kubiak M 2013 Appl. Math. Modell. 37 2051
Google Scholar
[20] Szymczyk J A 1991 Can. J. Chem. Eng. 69 1233
[21] Okhotsimskii A, Hozawa M 1998 Chem. Eng. Sci. 53 2547
Google Scholar
[22] 王勇, 张泽廷 2002 北京化工大学学报 29 11
Google Scholar
Wang Y, Zhang Z T 2002 J. Beijing Univ. Chem. Technol. 29 11
Google Scholar
[23] Sun Z F, Yu K T, S Y W, Miao Y Z 2002 Ind. Eng. Chem. Res. 41 1905
Google Scholar
[24] 沙勇, 李樟云, 林芬芬, 吐芬, 肖宗源, 叶李艺 2010 化工学报 61 844
Sha Y, Li Z Y, Lin F F, Tu F, Xiao Z Y, Ye L Y 2010 J. Chem. Ind. Eng. 61 844
[25] Orell A, Westwater J W 1961 AlChE J. 8 350
[26] Zhang S H, Wang Z M, Su Y F 1990 Chem. Eng. Res. Des. 68 84
[27] Guzun-Stoica A, Kurzeluk M, Floarea O 2000 Chem. Eng. Sci. 55 3813
Google Scholar
[28] Kostarev K G, Shmyrov A V, Zuev A L, Viviani A 2011 Exp. Fluids 51 457
Google Scholar
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Google Scholar
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Google Scholar
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[37] 胡楠, 张会书, 傅强, 李陆星, 袁希钢 2016 化工学报 68 584
Hu L, Zhang H S, Fu Q, Li L X, Yuan X G 2016 J. Chem. Ind. Eng. 68 584
[38] Puthenveettil B A, Arakeri J H 2005 J. Fluid Mech. 542 217
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图 1 RBM对流的实验系统图 (a) 阴影法实验系统图; (b) 示踪粒子法实验系统图; (c) 玻璃狭缝尺寸图
Figure 1. Schematic diagram of the experimental system for RBM convection: (a) Schematic diagram of the experimental system based on shadowgraph method; (b) schematic diagram of the experimental system based on particle tracer method; (c) size of the glass slit.
图 2 T = 20 ℃时不同水相丙酮浓度下水-甲苯两相间的界面张力系数
Figure 2. Interfacial tension coefficient between water and toluene phases under different acetone concentrations of aqueous phase with T = 20 ℃.
图 3 T = 20 ℃时不同丙酮浓度的水相溶液的密度
Figure 3. Density of aqueous solution with different acetone concentrations with T = 20 ℃.
图 4 传质过程引起的密度分层示意图与实验结果 (a) 密度分层示意图; (b) 实验图像
Figure 4. Schematic diagram and experimental result of density stratification caused by mass transfer: (a) Schematic diagram of density stratification; (b) experimental image.
图 6 丘状“界面”的形成过程(水相丙酮初始体积浓度
${\varphi _0} = 5\% $ , 甲苯相丙酮初始体积浓度${\varphi _1} = 0\% $ ) (a) t = 13 s; (b) t = 30 s; (c) t = 36 s; (d) t = 42 sFigure 6. The forming process of the mound “interface” (the initial volume concentration of acetone in aqueous phase
${\varphi _0} = 5\% $ , the initial volume concentration of acetone in the toluene phase${\varphi _1} = 0\% $ ): (a) t = 13 s; (b) t = 30 s; (c) t = 36 s; (d) t = 42 s.
图 5 密度分层引起的Rayleigh-Taylor不稳定性示意图
$\omega $ 是涡流, P是压力,$\rho $ 是密度, u是速度, g是重力加速度; 粗的环形箭头表示涡旋产生的速度场Figure 5. Schematic diagram of Rayleigh-Taylor instability caused by density stratification.
$\omega $ is vorticity, P is pressure,$\rho $ is density, u is velocity and g is acceleration of gravity; the thick circular arrows represent the velocity field created by the vortex.
图 7 羽状流的演变过程 (
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ) (a) t = 0 s; (b) t = 18 s; (c) t = 20 s; (d) t = 22 sFigure 7. The evolution of the plume flow (
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ): (a) t = 0 s; (b) t = 18 s; (c) t = 20 s; (d) t = 22 s.
图 8 弱羽状流的演变过程(
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ) (a) t = 348 s; (b) t = 356 s; (c) t = 363 s; (d) t = 370 sFigure 8. The evolution of the weak plume flow (
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ): (a) t = 348 s; (b) t = 356 s; (c) t = 363 s; (d) t = 370 s.
图 10 强羽状流的演变过程(
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ) (a) t = 22 s; (b) t = 23 s; (c) t = 26 sFigure 10. The evolution of the strong plume flow (
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ): (a) t = 22 s; (b) t = 23 s; (c) t = 26 s.
图 9 羽状流的速度矢量及涡量云图(
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ )Figure 9. The velocity vector and vorticity contours of the plume flow (
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ).
图 11 强羽状流向弱羽状流的演变过程(
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ) (a) t = 228 s; (b) t = 234 s; (c) t = 238 s; (d) t = 245 sFigure 11. The evolution of the strong plume flow to the weak plume flow (
${\varphi _0} = 15\% $ ,${\varphi _1} = 0\% $ ): (a) t = 228 s; (b) t = 234 s; (c) t = 238 s; (d) t = 245 s.
图 12 传质初期对流结构的聚并过程(
${\varphi _0} \!=\! 30\% $ ,${\varphi _1} \!=\! 0\% $ ) (a) t = 15 s; (b) t = 20 s; (c) t = 24 s; (d) t = 30 sFigure 12. Convergence process of convective structure at the beginning of the mass transfer (
${\varphi _0} = 30\% $ ,${\varphi _1} = 0\% $ ): (a) t = 15 s; (b) t = 20 s; (c) t = 24 s; (d) t = 30 s.
图 13 对流团的消失以及强羽状流的出现(
${\varphi _0} = 30\% $ ,${\varphi _1} = 0\% $ ) (a) t = 101 s; (b) t = 196 s; (c) t = 259 s; (d) t = 350 sFigure 13. The disappearance of convective cloud and the appearance of the strong plume (
${\varphi _0} = 30\% $ ,${\varphi _1} = 0\% $ ): (a) t = 101 s; (b) t = 196 s; (c) t = 259 s; (d) t = 350 s.
图 14 水相丙酮初始浓度对第一个RBM对流结构向下延伸速度的影响
Figure 14. The influence of initial concentration of acetone in aqueous phase on the elongation velocity of the first RBM convective structure.
图 15 水相丙酮初始浓度对羽状流数量的影响
Figure 15. The influence of initial concentration of acetone in aqueous phase on the number of the plumes.
图 16 水相丙酮初始浓度对水-甲苯界面形貌的影响 (a)界面粗糙度; (b)界面波动程度
Figure 16. The influence of initial concentration of acetone in aqueous phase on water-toluene interface morphology: (a) Interfacial roughness; (b) the degree of interface fluctuation.
图 17 不同甲苯相丙酮初始浓度下的投影图像(t = 35 s,
${\varphi _0} = 20\% $ ) (a)${\varphi _1} = 5\% $ ; (b)${\varphi _1} = 7.5\% $ ; (c)${\varphi _1} = 10\% $ ; (d)${\varphi _1} = 15\% $ Figure 17. Schlieren images under different initial concentrations of acetone in the toluene phase (t = 35 s,
${\varphi _0} = 20\% $ ): (a)${\varphi _1} = 5\% $ (b)${\varphi _1} = 7.5\% $ ; (c)${\varphi _1} = 10\% $ ; (d)${\varphi _1} = 15\% $ .
图 18 甲苯相丙酮初始浓度对第一个RBM对流结构向下延伸速度的影响
Figure 18. The influence of initial concentration of acetone in the toluene phase on the elongation velocity of the first RBM convective structure.
图 19 甲苯相丙酮初始浓度对羽状流数量的影响
Figure 19. The influence of initial concentration of acetone in the toluene phase on the number of the plumes.
图 20 甲苯相丙酮初始浓度对水-甲苯界面形貌的影响 (a)界面粗糙度; (b)界面波动程度
Figure 20. The influence of initial concentration of acetone in the toluene phase on water-toluene interface morphology: (a) Interfacial roughness; (b) the degree of interface fluctuation.
图 21 甲苯层厚度对羽状流数量的影响
Figure 21. The influence of thickness of toluene layer on the number of the plumes.
图 22 甲苯层厚度对水-甲苯界面形貌的影响
Figure 22. The influence of thickness of toluene layer on water - toluene interface morphology.
表 1 实验试剂的物性参数(T = 20 ℃, P = 0.1 MPa)
Table 1. The physical parameters of experimental reagents (T = 20 ℃, P = 0.1 MPa).
实验试剂 ρ/kg·m–3 µ/10–4Pa·s 水 998 10.04 甲苯 867 5.86 丙酮 790 3.26 
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[1] Yao F, Chen Y P, Peterson G P 2013 Int. J. Heat Mass Transfer 64 418
Google Scholar
[2] Liu X D, Chen Y P, Shi M H 2013 Int. J. Therm. Sci. 65 224
Google Scholar
[3] Chen Y P, Cheng P 2005 Int. J. Heat Mass Transfer 32 931
Google Scholar
[4] Bodenschatz E, Pesch W, Ahlers G 2000 Annu. Rev. Fluid Mech. 32 709
Google Scholar
[5] 王飞, 彭岚, 张全壮, 刘佳 2015 64 140202
Google Scholar
Wang F, Peng L, Zhang Q Z, Liu J 2015 Acta Phys. Sin. 64 140202
Google Scholar
[6] 翟薇, 王楠, 魏炳波 2007 56 2353
Google Scholar
Zhai W, Wang N, Wei B B 2007 Acta Phys. Sin. 56 2353
Google Scholar
[7] Schwabe D 1999 Adv. Space Res. 24 1347
Google Scholar
[8] Touazi O, Chénier E, Doumenc F, Guerrier B 2010 Int. J. Heat Mass Transfer 53 656
Google Scholar
[9] Chen J, Yang C, Mao Z S 2015 Eur. Phys. J. Spec. Top. 224 389
Google Scholar
[10] Bo Z, Mao S, Han Z J, Cen K F, Chen J H, Kostya O 2015 Chem. Soc. Rev. 44 2018
[11] 张婷, 施保昌, 柴振华 2015 64 254701
Zhang T, Shi B C, Chai Z H 2015 Acta Phys. Sin. 64 254701
[12] 郑连存, 盛晓艳, 张欣欣 2006 55 5298
Google Scholar
Zheng L C, Sheng X Y, Zhang X X 2006 Acta Phys. Sin. 55 5298
Google Scholar
[13] Kline J L, Hager J D 2016 Matter Radiat. Extremes 2 16
[14] Dong S X, Han W, Liu M F, Zhang Z W, Li B, Ge L Q 2016 Colloids Surf. A 509 32
Google Scholar
[15] Bai L, Zhao S F, Fu Y H, Cheng Y 2016 Biochem. Eng. J. 298 281
[16] Sun Z F 2012 Chem. Eng. Sci. 68 579
Google Scholar
[17] Liu C, Zeng A, Yuan X, Yu G 2008 Chem. Eng. Res. Des. 86 201
Google Scholar
[18] Alvarez-Herrera C, Moreno-Hernández D, Barrientos-García B, Guerrero-Viramontes J A 2005 Opt. Laser Technol. 41 233
[19] Piekarska W, Kubiak M 2013 Appl. Math. Modell. 37 2051
Google Scholar
[20] Szymczyk J A 1991 Can. J. Chem. Eng. 69 1233
[21] Okhotsimskii A, Hozawa M 1998 Chem. Eng. Sci. 53 2547
Google Scholar
[22] 王勇, 张泽廷 2002 北京化工大学学报 29 11
Google Scholar
Wang Y, Zhang Z T 2002 J. Beijing Univ. Chem. Technol. 29 11
Google Scholar
[23] Sun Z F, Yu K T, S Y W, Miao Y Z 2002 Ind. Eng. Chem. Res. 41 1905
Google Scholar
[24] 沙勇, 李樟云, 林芬芬, 吐芬, 肖宗源, 叶李艺 2010 化工学报 61 844
Sha Y, Li Z Y, Lin F F, Tu F, Xiao Z Y, Ye L Y 2010 J. Chem. Ind. Eng. 61 844
[25] Orell A, Westwater J W 1961 AlChE J. 8 350
[26] Zhang S H, Wang Z M, Su Y F 1990 Chem. Eng. Res. Des. 68 84
[27] Guzun-Stoica A, Kurzeluk M, Floarea O 2000 Chem. Eng. Sci. 55 3813
Google Scholar
[28] Kostarev K G, Shmyrov A V, Zuev A L, Viviani A 2011 Exp. Fluids 51 457
Google Scholar
[29] Chen Y, Cheng P 2005 Int. Commun. Heat Mass Transfer 32 175
Google Scholar
[30] Agble D, Mendes-Tatsis M A 2000 Int. J. Heat Mass Transfer 43 1025
Google Scholar
[31] Shi Y, Kerstin E 2007 Chin. J. Chem. Eng. 15 748
Google Scholar
[32] Chen Y P, Liu X D, Shi M H 2013 Appl. Phys. Lett. 102 051609
Google Scholar
[33] Chen Y P, Liu X D, Zhao Y J 2015 Appl. Phys. Lett. 106 141601
Google Scholar
[34] Chen Y P, Wu L Y, Zhang L 2015 Int. J. Heat Mass Transfer 82 42
Google Scholar
[35] Sharp D H 1984 Physica D 12 3
Google Scholar
[36] Roberts M S, Jacobs J W 2015 J. Fluid Mech. 787 50
[37] 胡楠, 张会书, 傅强, 李陆星, 袁希钢 2016 化工学报 68 584
Hu L, Zhang H S, Fu Q, Li L X, Yuan X G 2016 J. Chem. Ind. Eng. 68 584
[38] Puthenveettil B A, Arakeri J H 2005 J. Fluid Mech. 542 217
Google Scholar
[39] Yang C, Tartaglino U, Persson B N 2006 J. Phys. Rev. Lett. 97 11
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