EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

双自由面溶质−热毛细液层的不稳定性

赵诚卓 胡开鑫

赵诚卓, 胡开鑫. 双自由面溶质−热毛细液层的不稳定性. 力学学报, 2022, 54(2): 291-300 doi: 10.6052/0459-1879-21-148
引用本文: 赵诚卓, 胡开鑫. 双自由面溶质−热毛细液层的不稳定性. 力学学报, 2022, 54(2): 291-300 doi: 10.6052/0459-1879-21-148
Zhao Chengzhuo, Hu Kaixin. Instability in the solutal-thermocapillary liquid layer with two free surface. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 291-300 doi: 10.6052/0459-1879-21-148
Citation: Zhao Chengzhuo, Hu Kaixin. Instability in the solutal-thermocapillary liquid layer with two free surface. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 291-300 doi: 10.6052/0459-1879-21-148

双自由面溶质−热毛细液层的不稳定性

doi: 10.6052/0459-1879-21-148
基金项目: 国家自然科学基金(11872032)和浙江省自然科学基金(LY21A020006)资助项目
详细信息
    作者简介:

    胡开鑫, 副教授, 主要研究方向: 非牛顿流体, 流动稳定性, 微重力流体. Email: hukaixin@nbu.edu.cn

  • 中图分类号: O357.1

INSTABILITY IN THE SOLUTAL-THERMOCAPILLARY LIQUID LAYER WITH TWO FREE SURFACE

  • 摘要: 溶质−热毛细对流是流体界面的浓度和温度分布不均导致的表面张力梯度驱动的流动, 它主要存在于空间微重力环境、小尺度流动等表面张力占主导的情况中, 例如晶体生长、微流控、合金浇筑凝固、有机薄液膜生长等. 对其流动进行稳定性分析具有重要意义. 本文采用线性稳定性理论研究了双自由面溶质−热毛细液层对流的不稳定性, 得到了两种负毛细力比(η)下的临界Marangoni数与Prandtl数(Pr)的函数关系, 并分析了临界模态的流场和能量机制. 研究发现: 溶质−热毛细对流和纯热毛细对流的临界模态有较大的差别, 前者是同向流向波、逆向流向波、展向稳态模态和逆向斜波, 后者是逆向斜波和逆向流向波. 在Pr较大时, Pr增加会降低流动稳定性; 在其他参数下, Pr增加会增强流动稳定性. 在中低Pr, 溶质毛细力使流动更加不稳定; 在大Pr时, 溶质毛细力的出现可能使流动更加稳定; 在其他参数下, 溶质毛细力会减弱流动稳定性. 流动稳定性不随η单调变化. 在多数情况下, 扰动浓度场与扰动温度场都是相似的. 能量分析表明: 扰动动能的主要能量来源是表面张力做功, 但其中溶质毛细力和热毛细力做功的正负性与参数有关.

     

  • 图  1  双自由面溶质−热毛细液层对流的示意图

    Figure  1.  Schematic of the solutal-thermocapillary liquid layer with two free surfaces

    图  2  临界参数随$ Pr $的变化曲线: (a)$M{a_{\rm{c}}}$; (b)波传播角$ \theta $; (c)波数$ k $; (d)角频率$ \omega $. 曲线对应: UOW ($ {a_1} $, $ {e_3} $), SSM ($ {a_2} $, $ {b_2} $, $ {d_3} $), DSW ($ {b_3} $, $ {b_1} $, $ {c_2} $, $ {c_3} $), USW ($ {a_3} $, $ {c_3} $, $ {d_2} $, $ {c_1} $, $ {f_3} $)

    Figure  2.  The variation of critical parameter with $ Pr $. (a) $M{a_{\rm{c}}}$, (b) wave propagation angle $ \theta $, (c) wave number $ k $ and (d) angular frequency $ \omega $. The curves correspond to: UOW ($ {a_1} $, $ {e_3} $), SSM ($ {a_2} $, $ {b_2} $, $ {d_3} $), DSW ($ {b_3} $, $ {b_1} $, $ {c_2} $, $ {c_3} $), USW ($ {a_3} $, $ {c_3} $, $ {d_2} $, $ {c_1} $, $ {f_3} $)

    图  3  $ \eta = - 0.5 $时临界模态的扰动流场. (a) SSM ($ Pr = 0.01 $), (b) SSM ($ Pr = 50 $), (c) DSW ($ Pr = 70 $), (d) USW ($ Pr = 100 $)

    Figure  3.  The perturbation flow field of the different preferred modes at $ \eta = - 0.5 $. (a) SSM ($ Pr = 30 $), (b) SSM ($ Pr = 0.01 $), (c) DSW ($ Pr = $ 70), (d) USW ($ Pr = 100 $)

    图  4  $ \eta = - 2 $时不同临界模态所对应的扰动流场. (a) USW ($ Pr = 1 $), (b) DSW ($ Pr = 50 $), (c) USW ($ Pr = 100 $)

    Figure  4.  The perturbation flow field of the different preferred modes at $ \eta = - 2 $. (a) DSW ($ Pr = 1 $), (b) USW ($ Pr = 50 $), (c) DSW ($ Pr = 100 $)

    表  1  298.15 K时甲苯/正己烷混合溶液(C0 = 26.17%)的物性参数

    Table  1.   Physical properties of toluene/n-henxane mixture at T0 = 298.15 K and C0 = 26.17%

    Physical propertiesValue
    Density $\rho /({\rm{kg}} \cdot {\rm{m}}^{ - 3} )$$ 699.35 $
    Thermal diffusivity $ \xi /({{\rm{m}}}^{2}\cdot{{\rm{s}}}^{-1} )$$ 8.70 \times {10^{ - 8}} $
    Solute diffusion coefficient $ D/({{\rm{m}}}^{2}\cdot{{\rm{s}}}^{-1} )$$ 3.37 \times {10^{ - 9}} $
    Soret coefficient $ \zeta /{{\rm{K}}^{ - 1}} $$ 4.02 \times {10^{ - 3}} $
    Dynamic viscosity $ \mu /({\rm{kg}}\cdot{{\rm{m}}}^{-1}\cdot{{\rm{s}}}^{-1} )$$ 3.37 \times {10^{ - 4}} $
    Dynamic viscosity $ Sc $$ 142.99 $
    Temperature coefficient of surface tension $ {\gamma }_{{\rm{T}}}/({\rm{N}}\cdot{{\rm{m}}}^{-1}\cdot{{\rm{K}}}^{-1} )$$ 9.34 \times {10^{ - 5}} $
    Concentration coefficient of surface tension $ {\gamma }_{{\rm{C}}}/({\rm{N}}\cdot{{\rm{m}}}^{-1} )$$ - 8.62 \times {10^{ - 3}} $
    Prandtl number$ Pr $$ 5.54 $
    下载: 导出CSV

    表  2  不同参数下各扰动能量变化项的值

    Table  2.   Values of perturbation energy variation terms at different parameters.

    PrηNMIMTMCθ
    0.01 −0.5 −362.156 0 362.155 6 0.000 2 −0.075 1 362.230 7 90
    30 −0.5 −207.597 3 207.594 3 0.000 4 −386.273 2 593.867 5 90
    50 −0.5 −7.590 7 7.588 7 0.002 0 −11.631 3 19.220 0 90
    70 −0.5 −0.968 0 0.971 9 −0.003 8 2.025 7 −1.053 8 0
    100 −0.5 −3.649 1 3.645 6 0.003 5 6.603 7 −2.958 0 180
    200 −0.5 −10.465 3 10.463 8 0.001 6 7.276 4 3.187 4 180
    0.1 −2 −5.313 0 5.317 9 −0.004 9 −0.004 4 5.322 3 180
    10 −2 −4.706 1 4.709 8 −0.003 7 −1.750 6 6.460 5 180
    40 −2 −9.238 8 9.232 2 0.006 6 2.135 2 7.097 0 0
    70 −2 −7.777 6 7.770 8 0.006 9 −3.676 0 11.446 7 0
    100 −2 −2.349 7 2.356 6 −0.006 9 −2.403 4 4.760 0 180
    150 −2 −20.198 4 20.195 4 0.003 1 75.575 8 −55.380 5 90
    0.01 0 −0.037 3 0.000 0 0.037 2 —— —— 107
    1 0 −0.241 7 0.000 3 0.241 4 —— —— 114.1
    10 0 −0.790 0 −0.011 1 0.801 1 —— —— 0
    100 0 −2.446 4 −0.006 7 2.453 1 —— —— 0
    下载: 导出CSV
  • [1] Ouriemi M, Vasseur P, Bahloul A, et al. Natural convection in a horizontal layer of a binary mixture. International Journal of Thermal Sciences, 2006, 45(8): 752-759 doi: 10.1016/j.ijthermalsci.2005.11.004
    [2] Saravanan S, Sivakumar T. Combined influence of throughflow and Soret effect on the onset of Marangoni convection. Journal of Engineering Mathematics, 2014, 85(1): 55-64 doi: 10.1007/s10665-013-9631-z
    [3] 胡文瑞. 微重力科学概论. 北京: 科学出版社, 2018

    (Hu Wenrui. Introduction to Microgravity Science. Beijing: Science Press, 2018 (in Chinese))
    [4] Venerus DC, Simavilla DN. Tears of wine: New insights on an old phenomenon. Scientific Reports, 2015, 5(1): 1-10 doi: 10.9734/JSRR/2015/14076
    [5] Bormashenko E, Pogreb R, Stanevsky O, et al. Mesoscopic patterning in evaporated polymer solutions: New experimental data and physical mechanisms. Langmui, 2005, 21: 9604-9609 doi: 10.1021/la0518492
    [6] Cröll A, Mitric A, Aniol O, et al. Solutocapillary convection in germanium‐silicon melts. Crystal Research and Technology: Journal of Experimental and Industrial Crystallography, 2009, 44(10): 1101-1108 doi: 10.1002/crat.200900435
    [7] Abbasoglu S, Sezai I. Three-dimensional modelling of melt flow and segregation during Czochralski growth of Ge xSi1− x single crystals. International Journal of Thermal Sciences, 2007, 46(6): 561-572 doi: 10.1016/j.ijthermalsci.2006.07.010
    [8] Matsui A, Yonenaga I, Sumino K. Czochralski growth of bulk crystals of Ge1− xSix alloys. Journal of Crystal Growth, 1998, 183(1-2): 109-116 doi: 10.1016/S0022-0248(97)00405-3
    [9] Schena M, Shalon D, Davis RW, et al. Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science, 1995, 270(5235): 467-470 doi: 10.1126/science.270.5235.467
    [10] Dugas V, Broutin J, Souteyrand E. Droplet evaporation study applied to DNA chip manufacturing. Langmuir, 2005, 21(20): 9130-9136 doi: 10.1021/la050764y
    [11] Yasuhiro S, Sato T, Imaishi N, et al. Numerical simulation of solutal Marangoni convection during liquid mixing under microgravity. Microgravity Science and Technology, 1996, 9(4): 237-244
    [12] Arafune K, Hirata A. Thermal and solutal Marangoni convection in In–Ga–Sb system. Journal of Crystal Growth, 1999, 197(4): 811-817 doi: 10.1016/S0022-0248(98)01071-9
    [13] Craster RV, Matar OK. Dynamics and stability of thin liquid films. Reviews of Modern Physics, 2009, 81(3): 1131-1198 doi: 10.1103/RevModPhys.81.1131
    [14] Serpetsi SK, Yiantsios SG. Stability characteristics of solutocapillary Marangoni motion in evaporating thin films. Physics of Fluids, 2012, 24(12): 122104 doi: 10.1063/1.4771903
    [15] Subramanian P, Zebib A, McQuillan B. Solutocapillary convection in spherical shells. Physics of Fluids, 2005, 17(1): 017103 doi: 10.1063/1.1818611
    [16] Kanouff M, Greif R. The unsteady development of a GTA weld pool. International Journal of Heat and Mass Transfer, 1992, 35(4): 967-979 doi: 10.1016/0017-9310(92)90261-P
    [17] 游仁然, 胡文瑞. 浮区中热和溶质的毛细对流. 半导体学报, 1992, 13(4): 209-216 (You Renran, Hu Wenrui. Capillary convection of heat and solute in the floating zone. Chinese Journal of Semiconductors, 1992, 13(4): 209-216 (in Chinese) doi: 10.3321/j.issn:0253-4177.1992.04.002
    [18] McTaggart CL. Convection driven by concentration-and temperature-dependent surface tension. Journal of Fluid Mechanics, 1983, 134: 301-310 doi: 10.1017/S0022112083003377
    [19] Chen CF, Su TF. Effect of surface tension on the onset of convection in a double-diffusive layer. Physics of Fluids A: Fluid Dynamics, 1992, 4(11): 2360-2367 doi: 10.1063/1.858477
    [20] 王铁晗, 富庆飞, 杨立军. 横向交流电场下液膜参数不稳定性分析. 力学学报, 2021, 53(02): 352-361 (Wang Tiehan, Fu Qingfei, Yang Lijun. Analysis of the instability of liquid film parameters under a transverse AC electric field. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(02): 352-361 (in Chinese)
    [21] 王佳, 吴笛, 段俐等. 大尺寸液桥热毛细对流失稳性地面实验研究. 力学学报, 2015, 47(4): 580-586) (Wang Jia, Wu Di, Duan Li, et al. Experimental study on the stability of large-size liquid bridge thermocapillary on the ground. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4): 580-586) (in Chinese)
    [22] 邹勇, 朱桂平, 李来等. 液桥内热质耦合对流不稳定性及旋转磁场法控制. 力学学报, 2017, 49(6): 1280-1289 (Zou Yong, Zhu Guiping, Li Lai, et al. Heat-mass coupled convection instability and rotating magnetic field control in a liquid bridge. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1280-1289 (in Chinese)
    [23] 罗佳倩, 吴春梅, 张利等. 表面散热对双组分溶液热-溶质毛细对流的影响. 工程热物理, 2018, 39(5): 1097-1103 (Luo Jiaqian, Wu Chunmei, Zhang Li, et al. The effect of surface heat dissipation on the heat-solute capillary convection of two-component solutions. Journal of Engineering Thermophysics, 2018, 39(5): 1097-1103
    [24] 陈捷超, 李友荣, 于佳佳. 毛细力比对环形液池内耦合热-溶质对流的影响. 工程热物理学报, 2014, 35(12): 2496-2499 (Chen Jiechao, Li Yourong, Yu Jiajia. Influence of capillary force ratio on coupled heat-solute convection in annular liquid pool. Journal of Engineering Thermophysics, 2014, 35(12): 2496-2499 (in Chinese)
    [25] 陈捷超. 环形液池内溶质毛细对流及其与热毛细对流的耦合效应. [博士论文]. 重庆: 重庆大学, 2016

    (Chen Jiechao, Solute capillary convection in an annular liquid pool and its coupling effect with thermocapillary convection. [PhD Thesis]. Chongqing: Chongqing University, 2016 (in Chinese))
    [26] Pettit D. Saturday morning science videos. URL http://mix.msfc.nasa.gov/IMAGES/QTVR/0601211.mov. 2003
    [27] Sarma R, Mondal PK. Thermosolutal Marangoni instability in a viscoelastic liquid film: effect of heating from the free surface. Journal of Fluid Mechanics, 2021, 909: 1-26
    [28] Yamamoto T, Takagi Y, Okano Y, et al. Numerical investigation of oscillatory thermocapillary flows under zero gravity in a circular liquid film with concave free surfaces. Physics of Fluids, 2016, 28(3): 032106 doi: 10.1063/1.4943246
    [29] Hu KX, Zhao CZ, Zhang SN, et al. Instabilities of thermocapillary liquid layers with two free surfaces. International Journal of Heat and Mass Transfer, 2021, 173: 121217 doi: 10.1016/j.ijheatmasstransfer.2021.121217
    [30] 于佳佳. 环形液池内双组分溶液毛细—浮力对流研究. [博士论文]. 重庆: 重庆大学, 2017

    (Yu Jiajia. Study on the capillary-buoyancy convection of the two-component solution in the annular liquid tank. [PhD Thesis]. Chongqing: Chongqing University, 2017 (in Chinese))
    [31] Lücke M. Influence of the Dufour effect on convection in binary gas mixtures. Physical Review E, 1995, 52(1): 642-657 doi: 10.1103/PhysRevE.52.642
    [32] Smith MK, Davis SH. Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities. Journal of Fluid Mechanics, 1983, 132: 119-144 doi: 10.1017/S0022112083001512
    [33] Riley RJ, Neitzel GP. Instability of thermocapillary–buoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities. Journal of Fluid Mechanics, 1998, 359: 143-164 doi: 10.1017/S0022112097008343
    [34] Patne R, Yehuda A, Alexander O. Thermocapillary instabilities in a liquid layer subjected to an oblique temperature gradient. Journal of Fluid Mechanics, 2021, 906: A12
    [35] Ueno I, Takamitsu T. Thermocapillary-driven flow in a thin liquid film sustained in a rectangular hole with temperature gradient. Acta Astronautica, 2010, 66(7-8): 1017-1021 doi: 10.1016/j.actaastro.2009.09.027
    [36] Platten JK, Costesèque P, Soret C. A short biography A. The European Physical Journal E, 2004, 15(3): 235-239
    [37] Platten JK. The Soret effect: A review of recent experimental results. Journal of Applied Mechanics, 2006, 73(1): 5-15 doi: 10.1115/1.1992517
    [38] Zhan JM, Chen ZW, Li YS, et al. Three-dimensional double-diffusive Marangoni convection in a cubic cavity with horizontal temperature and concentration gradients. Physical Review E, 2010, 82: 066305
    [39] Hu KX, Peng J, Zhu KQ. The linear stability of plane Poiseuille flow of Burgers fluid at very low Reynolds numbers. Journal of Non-Newtonian Fluid Mechanics, 2012, 167: 87-94
  • 加载中
图(4) / 表(2)
计量
  • 文章访问数:  443
  • HTML全文浏览量:  116
  • PDF下载量:  91
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-04-11
  • 录用日期:  2021-08-26
  • 网络出版日期:  2021-08-27
  • 刊出日期:  2022-02-17

目录

    /

    返回文章
    返回