1.School of Energy and Environment, Southeast University, Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, Nanjing 210096, China 2.School of Hydraulic, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China
Fund Project:Project supported by the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (Grant No. U1530260), the National Natural Science Foundation of China (Grant No. 51706193), and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 17KJB470014).
Received Date:05 July 2018
Accepted Date:19 January 2019
Available Online:23 March 2019
Published Online:05 April 2019
Abstract: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. Keywords:liquid-liquid mass transfer/ shadowgraph method/ Rayleigh-Bénard-Marangoni convective structure/ interface morphology
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2.实验系统与实验方法本文利用阴影法观测竖直玻璃狭缝内液-液两相液层间传质过程中的RBM对流, 实验系统如图1(a)所示, 主要包括点光源、玻璃狭缝、投影屏幕以及高速显微成像系统四部分. 传质过程的不均匀将引起狭缝内工质浓度分布的差异, 进而造成非均匀折射率分布. 因此, 光透过玻璃狭缝内的流体介质后, 会发生不同角度的偏转, 从而在屏幕上形成明暗不均的投影图像. 实验使用显微镜(型号: AT-X M100 PRO)观测投影图像的演变过程, 并采用与显微镜配套安装的高速CCD(型号: FASTCAM SA1.1)实时记录及保存. 本文实验采用激光点光源发出的发散光成像, 在屏幕上得到的是实验观测区域的放大图像, 能够清晰地观察和记录实验出现的微小流动结构. 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 Figure1. 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.
表1实验试剂的物性参数(T = 20 ℃, P = 0.1 MPa) Table1.The physical parameters of experimental reagents (T = 20 ℃, P = 0.1 MPa).
图 2T = 20 ℃时不同水相丙酮浓度下水-甲苯两相间的界面张力系数 Figure2. Interfacial tension coefficient between water and toluene phases under different acetone concentrations of aqueous phase with T = 20 ℃.
图 3T = 20 ℃时不同丙酮浓度的水相溶液的密度 Figure3. Density of aqueous solution with different acetone concentrations with T = 20 ℃.
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3.1.RBM对流结构分析
考虑到实验中注液带来的扰动以及液层厚度的不断变化将不利于上部液层RBM对流结构的实验观测与定量化分析. 因此, 本文集中对丙酮组分跨界面传质时下层水相溶液中的RBM对流特性进行研究. 如图4所示, 随着丙酮向上层甲苯液层扩散传质, 靠近界面处的水相丙酮浓度减小, 并且, 由于扩散过程缓慢, 该处近界面处水相中因扩散传质而损失的丙酮组分得不到来自于下部水相的及时补充. 因此, 传质过程初期水相溶液上部出现了浓度分层的现象, 并且由于丙酮浓度不同造成的折射率差异使得投影图像上近界面处水相上下两层之间产生了一条水相内部“界面”. 而由图3可知, 水相中丙酮浓度的分层必然使其内部产生低密度流体支撑高密度流体的(密度)重力分层现象. 此外, 界面处丙酮传质存在着不可避免的非均匀性, 导致水相内部“界面”处产生不规则的扰动, 如图4(b)所示. 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 Figure4. Schematic diagram and experimental result of density stratification caused by mass transfer: (a) Schematic diagram of density stratification; (b) experimental image.
在这样的条件下, 水溶液内部“界面”上便诱发产生了Rayleigh-Taylor不稳定性[35], “界面”上的扰动单元会造成界面上的密度(重力)梯度与静压梯度失调(界面弯曲造成密度梯度和压力梯度不作用在同一水平线上), 导致上层液体克服流体黏性阻力不均匀地侵入下层液体, 并在界面各处产生斜压转矩而产生涡流[36], 如图5所示. 涡流会使扰动“界面”的凹凸程度不断扩大, 从而使扰动“界面”在下降的过程中呈现出向下凸出的非均匀波浪形丘状“界面”, 如图6所示. 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 s Figure6. 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 Figure5. 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.
随着丘状“界面”结构的不断下移, “界面”处密度梯度与压力梯度失调进一步加剧, “界面”各处涡流强度不断提升, 进而使扰动界面不稳定性进一步加剧, 部分丘状 “界面”下端的前凸幅度进一步增大. 随着时间的推移, 当丘状 “界面”下端前凸处从山丘状演变成柱状时, 羽状流形成(如图7所示). 图 7 羽状流的演变过程 (${\varphi _0} = 15\% $, ${\varphi _1} = 0\% $) (a) t = 0 s; (b) t = 18 s; (c) t = 20 s; (d) t = 22 s Figure7. The evolution of the plume flow (${\varphi _0} = 15\% $, ${\varphi _1} = 0\% $): (a) t = 0 s; (b) t = 18 s; (c) t = 20 s; (d) t = 22 s.
实验中, 在不同初始丙酮浓度下, 由于密度梯度不同引起的Rayleigh-Taylor不稳定性强度不同, 使得羽状流呈现出弱羽状流和强羽状流两种典型形态. 弱羽状流出现在水相溶液中丙酮浓度比较低的情况(如图8(a), t = 348 s时). 由于此时水相与甲苯相内的丙酮浓度梯度较小, 传质较弱, 其产生的水相液层内竖直密度差较小, 造成Rayleigh-Taylor不稳定性强度较弱, 羽状流向下延伸较慢. 另外, 起初羽状流内外流体的丙酮浓度差异也较小. 因此, 在羽状流缓慢的下降行程中, 羽流区下端流体可与其四周的大空间流体实现充分的传质, 使羽状流下端流体浓度逐渐增大, 直至与其周围主流区流体的丙酮浓度一致. 由于浓度差异消失, 这样由浓度差异导致的液体折射率差异也消失, 这部分羽状流结构会从屏幕上逐渐变浅并最终消失, 从而呈现出颜色由根部向下端逐渐变浅的羽毛状结构, 即弱羽状流, 如图8(d)所示. 图 8 弱羽状流的演变过程(${\varphi _0} = 15\% $, ${\varphi _1} = 0\% $) (a) t = 348 s; (b) t = 356 s; (c) t = 363 s; (d) t = 370 s Figure8. The evolution of the weak plume flow (${\varphi _0} = 15\% $, ${\varphi _1} = 0\% $): (a) t = 348 s; (b) t = 356 s; (c) t = 363 s; (d) t = 370 s.
为进一步认识羽状流的产生机理, 采用粒子示踪法获取羽状流区域的详细流场信息, 如图9所示. 羽状流区域的流场可划分为羽流区和涡流区两部分. 其中, 涡流区分布在羽流区两侧, 羽流区内流体自上而下运动, 两个涡流区内的流体做涡旋运动且方向相反, 漩涡区内涡量绝对值高于其他区域. 与羽状流的下降速度相比, 涡流区流体流速明显较小, 导致涡流区产生高静压, 羽流区产生低静压, 两者间的压差产生挤压力, 将羽状流颈部压细, 并将流体压向末端. 受到下层相对静止流体的阻碍作用, 快速流向下端的流体流速明显减缓. 这样, 在颈部两侧压差、下层流体阻碍的耦合作用下, 羽状流末端出现体积增大和扁平化的趋势. 特别是(如图10所示), 当水相中丙酮浓度较高时, 羽状流下降快, 导致上述两种效应的耦合作用增强, 使羽状流末端发展成宽扁的弧形帽状, 从而使羽流区整体投影图像呈现出倒蘑菇状(如图10(c), t = 26 s时), 此时, 强羽状流形成. 图 10 强羽状流的演变过程(${\varphi _0} = 15\% $, ${\varphi _1} = 0\% $) (a) t = 22 s; (b) t = 23 s; (c) t = 26 s Figure10. The evolution of the strong plume flow (${\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\% $) Figure9. The velocity vector and vorticity contours of the plume flow (${\varphi _0} = 15\% $, ${\varphi _1} = 0\% $).
强羽状流在向下发展过程中, 周边水相内的丙酮组分不断向羽流区进行传质, 导致其内部丙酮组分浓度升高. 因此, 在强羽状流产生的后期, 由于靠近帽状头部的下半部分沉降时间较长, 上述传质过程进行得比较充分, 头部丙酮浓度率先与周边水相内的丙酮浓度趋于一致(折射率趋于一致), 在投影上逐渐消失. 此时, 对流结构从蘑菇云状 变成了羽毛状, 即强羽状流演变为弱羽状流, 如图11 所示. 图 11 强羽状流向弱羽状流的演变过程(${\varphi _0} = 15\% $, ${\varphi _1} = 0\% $) (a) t = 228 s; (b) t = 234 s; (c) t = 238 s; (d) t = 245 s Figure11. The evolution of the strong plume flow to the weak plume flow (${\varphi _0} = 15\% $, ${\varphi _1} = 0\% $): (a) t = 228 s; (b) t = 234 s; (c) t = 238 s; (d) t = 245 s.
当丙酮初始浓度梯度较大(如${\varphi _0} = 30\% $, ${\varphi _1} = $0%)时, 丙酮向甲苯传质得很剧烈, 传质导致的密度差以及初始扰动的频率很大, 其产生的Rayleigh-Taylor不稳定性很强, 造成液-液界面处产生大量微小的细胞状对流结构. 由于这些对流结构数量大、彼此间距很小, 且其两侧的夹带流相互作用强, 导致这些对流结构在向下延伸时, 快速聚并成大对流团(如图12红色方框所示), 而不能充分发展成独立的羽状流形态. 图 12 传质初期对流结构的聚并过程(${\varphi _0} \!=\! 30\% $, ${\varphi _1} \!=\! 0\% $) (a) t = 15 s; (b) t = 20 s; (c) t = 24 s; (d) t = 30 s Figure12. Convergence process of convective structure at the beginning of the mass transfer (${\varphi _0} = 30\% $, ${\varphi _1} = 0\% $): (a) t = 15 s; (b) t = 20 s; (c) t = 24 s; (d) t = 30 s.
随着传质过程的进行, 水相与甲苯相丙酮浓度梯度逐渐降低, 传质过程减弱, Rayleigh-Taylor不稳定性减弱, 导致界面处产生的对流结构数量减少、间距增大、相互叠加现象逐渐减弱. 这时, 如图13所示, 卷吸对流团的混乱程度降低, 且其体积逐渐变小直到消失, 最终形成独立的羽状流结构(如图13(d), t = 350 s时), 即强羽状流. 图 13 对流团的消失以及强羽状流的出现(${\varphi _0} = 30\% $, ${\varphi _1} = 0\% $) (a) t = 101 s; (b) t = 196 s; (c) t = 259 s; (d) t = 350 s Figure13. The disappearance of convective cloud and the appearance of the strong plume (${\varphi _0} = 30\% $, ${\varphi _1} = 0\% $): (a) t = 101 s; (b) t = 196 s; (c) t = 259 s; (d) t = 350 s.
为了探讨溶质初始浓度对RBM对流强度的影响, 本研究借助图像处理手段, 采用对流结构延伸速度v以及羽状流个数n对RBM对流特征进行定量表征. 其中, v定义为第一个RBM对流结构向下延伸的速度, 表征了其向下层主流区发展的快慢; n定义为羽状流的羽流区“枝杈”个数. 图14给出了水相丙酮初始浓度对对流结构延伸速度的影响. 如图14所示, 随着水相丙酮初始浓度的增大, 水相与甲苯相丙酮浓度梯度增大, 界面处丙酮传质强度增强, 造成如图4所示的水相近界面处的密度分层现象加剧, 且高、低密度层间“界面”处的扰动增强, 从而诱发了更强的Rayleigh-Taylor不稳定性, 导致水相近界面处上层高密度液体更快地侵入下层低密度液体, 因此, 对流结构向下延伸的速度加快. 图 14 水相丙酮初始浓度对第一个RBM对流结构向下延伸速度的影响 Figure14. The influence of initial concentration of acetone in aqueous phase on the elongation velocity of the first RBM convective structure.
图15给出了水相丙酮初始浓度对羽状流数量的影响. 由图可知, 随着水相丙酮初始浓度的增加, 初始阶段界面处的传质更为剧烈, 造成水相内近界面处的扰动频率升高[37], 使得羽状流产生的“种子”数量增加, 羽状流数目随之升高; 随着时间的推移, 不同强度的羽状流先后消失-再生-消失, 如此循环便造成羽流区“枝杈”个数出现波动, 并且, 随着丙酮初始浓度的增加, 羽状流消失-再生-消失的演变周期缩短, 使其羽流区“枝杈”数量波动不断增大. 另一方面, 随着羽流区“枝杈”数量的增多, 其相对间距减小, 造成彼此间聚并增强[38]. 因此, 羽流区“枝杈”数量的增幅会随着初始浓度的增大而减小(${\varphi _0} > 10\% $). 特别是, 当羽状流聚并速度大于其生成速度时, 羽流区“枝杈”总数甚至会变少(如${\varphi _0} = 20\% $和${\varphi _0} = 15\% $相比). 图 15 水相丙酮初始浓度对羽状流数量的影响 Figure15. The influence of initial concentration of acetone in aqueous phase on the number of the plumes.
为进一步展示甲苯相丙酮初始浓度对RBM对流特性的影响, 图18— 图20分别给出了${\varphi _0} = 20\% $时不同甲苯相丙酮初始浓度下RBM对流结构延伸速度、羽状流数量和水-甲苯界面形貌的变化. 如上所述, 甲苯相丙酮初始浓度提高引发界面处丙酮传质强度降低, 造成水相近界面处的密度分层现象减弱, 高、低密度层间“界面”处的扰动频率减小. 因此, RBM对流结构延伸速度降低(见图18), 羽状流数目减少(见图19). 再者, 界面处丙酮传质强度的降低造成RBM对流紊乱程度变小, 近界面处流场扰动减弱, 从而使得液-液界面粗糙度降低且粗糙度数值的波动减小, 如图20所示. 图 18 甲苯相丙酮初始浓度对第一个RBM对流结构向下延伸速度的影响 Figure18. The influence of initial concentration of acetone in the toluene phase on the elongation velocity of the first RBM convective structure.
图 19 甲苯相丙酮初始浓度对羽状流数量的影响 Figure19. The influence of initial concentration of acetone in the toluene phase on the number of the plumes.
图 20 甲苯相丙酮初始浓度对水-甲苯界面形貌的影响 (a)界面粗糙度; (b)界面波动程度 Figure20. The influence of initial concentration of acetone in the toluene phase on water-toluene interface morphology: (a) Interfacial roughness; (b) the degree of interface fluctuation.
23.4.甲苯相液层厚度对RBM对流特性影响 -->
3.4.甲苯相液层厚度对RBM对流特性影响
值得注意的是, 由于本实验中上部甲苯液层的体积有限, 因此丙酮向甲苯相的扩散传质将使得甲苯相中的丙酮浓度(分压力)升高, 从而降低水相与甲苯相间的丙酮浓度梯度, 进而影响到RBM对流特性. 为此, 图21和图22分别给出了${\varphi _0} = 20\% $时甲苯液层厚度d对RBM对流特性的影响. 图 21 甲苯层厚度对羽状流数量的影响 Figure21. 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 Figure22. The influence of thickness of toluene layer on water - toluene interface morphology.