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活性剂对表面声波作用下薄液膜铺展的影响

李春曦 施智贤 庄立宇 叶学民

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活性剂对表面声波作用下薄液膜铺展的影响

李春曦, 施智贤, 庄立宇, 叶学民

Effect of surfactants on thin film spreading under influence of surface acoustic wave

Li Chun-Xi, Shi Zhi-Xian, Zhuang Li-Yu, Ye Xue-Min
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  • 针对表面声波作用下含不溶性活性剂的部分润湿薄液膜的铺展过程, 推导出了液膜厚度和表面活性剂浓度的无量纲演化方程组, 通过数值计算研究了声波引起的漂移流主导的液膜铺展过程及漂移流与毛细力共同控制的铺展过程. 结果表明表面声波驱使液膜铺展及移动, 而活性剂进一步促进了液膜的铺展过程, 且当活性剂存在时受漂移流与毛细力共同控制的铺展过程中出现了铺展半径收缩的现象, 使得液膜达到平衡状态所需的时间更长. 另外, 液膜最大厚度和铺展半径的变化速度随着分离压与活性剂浓度的相关系数α值、Marangoni数M值的增大而加快.
    For the spreading of thin and free film of a partially wetting liquid with insoluble surfactant under the influence of surface acoustic wave, the dimensionless evolution equations governing the spreading dynamics are derived. The evolution equations contain the film thickness and the surface concentration of insoluble surfactant. Assuming that the thickness of the thin film is much smaller than the wavelength of sound in the liquid, the sound leaking off the surface acoustic wave cannot be sustained in the liquid film, and the acoustic radiation pressure and attenuation of the acoustic wave in the solid are both weak. Then the films spreading under different physical mechanisms are observed by numerical simulation. The results show that the surface acoustic wave drives the liquid film to spread and move. When the capillary stress is weak and the liquid film spreading is mainly controlled by the drift induced by surface acoustic wave, the spreading process consists of rapid spreading stage and balancing stage, and the Marangoni effect caused by uneven distribution of surfactant makes the liquid film spread faster in the first stage. When the capillary stress and the drift jointly dominate film spreading, the spreading process contains three stages, i.e. spreading stage, contracting stage and balancing stage. The effect of surfactant accelerates the spreading process, but the existence of contracting stage makes it take longer for the film to reach equilibrium. In addition, the disjoining pressure used in this paper promotes the liquid film spreading, as well as the Marangoni effect. As the correlation coefficient between disjoining pressure and surfactant concentration, α, and the Marangoni number, M, increase, the maximum thickness and the spreading radius of liquid film change faster.
      通信作者: 叶学民, yexuemin@163.com
    • 基金项目: 国家自然科学基金(批准号: 51876065)资助的课题
      Corresponding author: Ye Xue-Min, yexuemin@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51876065)
    [1]

    Bar-Cohen A, Arik M, Ohadi M 2006 Proc. IEEE 94 1549Google Scholar

    [2]

    Lee K S, Ivanova N, Starov V M, Hilal N, Dutschk V 2008 Adv. Colloid Interf. 144 54Google Scholar

    [3]

    Afsar-Siddiqui A B, Luckham P F, Matar O K 2003 Adv. Colloid Interf. 106 183Google Scholar

    [4]

    Brabcova Z, McHale G, Wells G G, Brown C V, Newton M I 2017 Appl. Phys. Lett. 110 121603Google Scholar

    [5]

    Wang Z, Varma V B, Wang Z P, Ramanujan R V 2015 J. Micromech. Microeng. 25 124001Google Scholar

    [6]

    Rezk A, Manor O, Yeo L Y, Friend J R 2014 Proc. R. Soc. A 470 20130765Google Scholar

    [7]

    Rezk A R, Manor O, Friend J R, Yeo L Y 2012 Nat. Commun. 3 1167Google Scholar

    [8]

    Altshuler G, Manor O 2015 Phys. Fluids 27 102103Google Scholar

    [9]

    Altshuler G, Manor O 2016 Phys. Fluids 28 72102Google Scholar

    [10]

    Manor O, Dentry M, Friend J R, Yeo L Y 2011 Soft Matter 7 7976Google Scholar

    [11]

    Manor O, Rezk A R, Friend J R, Yeo L Y 2015 Phys. Rev. E 91 53015Google Scholar

    [12]

    Collins D J, Manor O, Winkler A, Schmidt H, Friend J R, Yeo L Y 2012 Phys. Rev. E 86 56312Google Scholar

    [13]

    Qi A, Yeo L Y, Friend J R 2008 Phys. Fluids 20 74103Google Scholar

    [14]

    Warner M R E, Craster R V, Matar O K 2002 Phys. Fluids 14 1642Google Scholar

    [15]

    Schwartz L W, Roy R V 1999 J. Colloid Interface Sci. 218 309Google Scholar

    [16]

    Manev E D, Pugh R J 1991 Langmuir 7 2253Google Scholar

    [17]

    Bhakta A, Ruckenstein E 1997 Adv. Colloid Interf. 70 1Google Scholar

    [18]

    Incropera F P, Lavine A S, Bergman T L, DeWitt D P 2007 Fundamentals of Heat and Mass Transfer (6 ed.) (New York: John Wiley & Sons) p883

    [19]

    Schwartz L W, Roy R V 2003 J. Colloid Interf. Sci. 264 237Google Scholar

    [20]

    Morozov M, Manor O 2017 J. Fluid Mech. 810 307Google Scholar

    [21]

    Riley N 1998 Theoret. Comput. Fluid Dyn. 10 349Google Scholar

    [22]

    Tiberg F, Cazabat A 1994 Langmuir 10 2301Google Scholar

    [23]

    Birch W R, Knewtson M A, Garoff S, Suter R M 1995 Langmuir 11 48Google Scholar

    [24]

    Dean D S, Sentenac D 1997 Europhys. Lett. 38 645Google Scholar

    [25]

    Hayduk W, Laudie H 1974 AIChE J. 20 611Google Scholar

    [26]

    Hu G, Xu A, Xu Z, Zhou Z 2008 Phys. Fluids 20 102101Google Scholar

    [27]

    刘邱祖, 寇子明, 韩振南, 高贵军 2013 物理学报 62 234701Google Scholar

    Liu Q Z, Kou Z M, Han Z N, Gao G J 2013 Acta Phys. Sin. 62 234701Google Scholar

  • 图 1  放置在SAW器件上的含活性剂薄水膜示意图 (a)俯视图; (b)正视图

    Fig. 1.  Schematic diagram of thin water film with surfactant on a SAW device: (a) Top view; (b) front view.

    图 2  漂移流起主导作用, 考虑活性剂影响时水膜的铺展过程 (a)液膜厚度; (b)活性剂浓度; (c)液膜前缘xf与后缘xr; (d)最大厚度与铺展半径

    Fig. 2.  Spreading process when the drift of mass governs the film dynamics: (a) Film thickness; (b) surfactant concentration; (c) the position of the front xf and the rear xr of the liquid film; (d) maximal thickness and spreading radius of the liquid film.

    图 3  不同时刻下液膜内部的流线与水平方向分速度 (a) t = 10; (b) t = 100

    Fig. 3.  Horizontal velocity contour within the film along with streamlines at different time: (a) t = 10; (b) t = 100.

    图 4  漂移流主导时, 考虑活性剂影响和不考虑活性剂影响的液膜演化过程对比

    Fig. 4.  Film profiles at different times during the drift governed spreading process with (blue line) and without (orange line) considering the effect of surfactant.

    图 5  漂移流主导时, 幂指数n随时间t*的变化与Rezk等[6]的实验结果的对比(液膜前缘位置与时间满足规律xf*t*n)

    Fig. 5.  Comparison between simulated and experimental[6] results for the variation of exponent n with dimensional time during the drift governed spreading process (the variation of the position of the front of the film with time accords to the power laws xf*t*n).

    图 6  漂移流主导时, 液膜前缘移动速度dxf*/dt*U *2的变化与Rezk等[7]实验结果的对比

    Fig. 6.  Comparison between simulated and experimental[7] results for the variation of dimensional velocity dxf*/dt* with U *2 during the drift governed spreading process

    图 7  毛细力和漂移流作用相当, 考虑活性剂影响时水膜的铺展过程 (a)液膜厚度; (b)活性剂浓度; (c)液膜前缘xf与后缘xr; (d)液膜最大厚度hmax与铺展半径r

    Fig. 7.  Spreading process when the equal effect of drift and the capillary stress is considered: (a) Film thickness; (b) surfactant concentration; (c) the position of the front xf and the rear xr of the liquid film; (d) maximal thickness and spreading radius of the liquid film.

    图 8  考虑活性剂影响和不考虑活性剂影响的液膜演化过程对比 (a)液膜最大厚度; (b)液膜铺展半径

    Fig. 8.  Film spreading when both the capillary stress and the drift govern the dynamics of the film with (blue line) and without (orange line) considering the effect of surfactant: (a) Maximal thickness of the liquid film; (b) spreading radius of the liquid film.

    图 9  漂移流和毛细力作用相当时, 液膜前缘移动速度的模拟结果和文献[8]的实验结果对比

    Fig. 9.  Comparison between simulated and experimental[8] results for the variation of velocity dxf/dt with θ3/We when both the capillary stress and the drift govern the dynamics of the film.

    图 10  不同α下部分润湿薄液膜的铺展过程对比 (a)最大厚度; (b)铺展半径

    Fig. 10.  Evolution of partially wetting film with different values of α: (a) Maximal thickness of the liquid film; (b) spreading radius of the liquid film.

    图 11  不同M下部分润湿薄液膜的铺展过程对比 (a)最大厚度; (b)铺展半径

    Fig. 11.  Evolution of partially wetting film with different values of M: (a) Maximal thickness of the liquid film; (b) spreading radius of the liquid film.

    表 1  有量纲参数取值范围

    Table 1.  Order of magnitude estimates for dimensional parameters.

    有量纲参数符号单位取值范围
    表面张力系数${\varSigma ^ * }$N·m2/mol5 × 10–3
    液膜无活性剂时表面张力γ0*N/m0.072
    液体黏度μ*Pa·s0.001
    液体密度ρ*kg/m31000
    SAW速度振幅U *m/s0.1—0.26
    液膜最大厚度H *m10–7—9 × 10–6
    液膜特征长度L*m10–5—9 × 10–4
    临界胶束浓度Gm*mol/L0.0086
    初始时刻最大活性剂浓度G0*mol/L0.002—0.0086
    有量纲三相接触角θ*(º)3—28
    表面扩散系数Ds*m2/s10–8—10–6
    黏性渗透长度${\delta ^ * }$m10–7
    下载: 导出CSV

    表 2  无量纲参数取值范围

    Table 2.  Order of magnitude estimates for nondimensional parameters.

    无量纲参数定义取值范围
    无量纲预置液膜厚度hf0.1
    分离压稳定常数C0.5
    初始活性剂浓度的
    最大值
    G00.2—1
    厚度小量ε = (δ */H *)1/30.22—1
    分离压与活性剂
    浓度的相关系数
    α–100—100
    无量纲三相接触角θ = θ */120°0.025—0.233
    Marangoni数$ M = \theta \varepsilon \varSigma ^ * G_m^ */{\rho ^ * }{\delta ^ * }{U^{ * 2} }$0.1—100
    Weber数We = ρ*U*2H*/γ0*10–5—5 × 10-3
    Reynolds数Re = ρ*U*δ*/μ*0.01—0.03
    Peclet数Pe = U*L*/Ds*1—1000
    下载: 导出CSV
  • [1]

    Bar-Cohen A, Arik M, Ohadi M 2006 Proc. IEEE 94 1549Google Scholar

    [2]

    Lee K S, Ivanova N, Starov V M, Hilal N, Dutschk V 2008 Adv. Colloid Interf. 144 54Google Scholar

    [3]

    Afsar-Siddiqui A B, Luckham P F, Matar O K 2003 Adv. Colloid Interf. 106 183Google Scholar

    [4]

    Brabcova Z, McHale G, Wells G G, Brown C V, Newton M I 2017 Appl. Phys. Lett. 110 121603Google Scholar

    [5]

    Wang Z, Varma V B, Wang Z P, Ramanujan R V 2015 J. Micromech. Microeng. 25 124001Google Scholar

    [6]

    Rezk A, Manor O, Yeo L Y, Friend J R 2014 Proc. R. Soc. A 470 20130765Google Scholar

    [7]

    Rezk A R, Manor O, Friend J R, Yeo L Y 2012 Nat. Commun. 3 1167Google Scholar

    [8]

    Altshuler G, Manor O 2015 Phys. Fluids 27 102103Google Scholar

    [9]

    Altshuler G, Manor O 2016 Phys. Fluids 28 72102Google Scholar

    [10]

    Manor O, Dentry M, Friend J R, Yeo L Y 2011 Soft Matter 7 7976Google Scholar

    [11]

    Manor O, Rezk A R, Friend J R, Yeo L Y 2015 Phys. Rev. E 91 53015Google Scholar

    [12]

    Collins D J, Manor O, Winkler A, Schmidt H, Friend J R, Yeo L Y 2012 Phys. Rev. E 86 56312Google Scholar

    [13]

    Qi A, Yeo L Y, Friend J R 2008 Phys. Fluids 20 74103Google Scholar

    [14]

    Warner M R E, Craster R V, Matar O K 2002 Phys. Fluids 14 1642Google Scholar

    [15]

    Schwartz L W, Roy R V 1999 J. Colloid Interface Sci. 218 309Google Scholar

    [16]

    Manev E D, Pugh R J 1991 Langmuir 7 2253Google Scholar

    [17]

    Bhakta A, Ruckenstein E 1997 Adv. Colloid Interf. 70 1Google Scholar

    [18]

    Incropera F P, Lavine A S, Bergman T L, DeWitt D P 2007 Fundamentals of Heat and Mass Transfer (6 ed.) (New York: John Wiley & Sons) p883

    [19]

    Schwartz L W, Roy R V 2003 J. Colloid Interf. Sci. 264 237Google Scholar

    [20]

    Morozov M, Manor O 2017 J. Fluid Mech. 810 307Google Scholar

    [21]

    Riley N 1998 Theoret. Comput. Fluid Dyn. 10 349Google Scholar

    [22]

    Tiberg F, Cazabat A 1994 Langmuir 10 2301Google Scholar

    [23]

    Birch W R, Knewtson M A, Garoff S, Suter R M 1995 Langmuir 11 48Google Scholar

    [24]

    Dean D S, Sentenac D 1997 Europhys. Lett. 38 645Google Scholar

    [25]

    Hayduk W, Laudie H 1974 AIChE J. 20 611Google Scholar

    [26]

    Hu G, Xu A, Xu Z, Zhou Z 2008 Phys. Fluids 20 102101Google Scholar

    [27]

    刘邱祖, 寇子明, 韩振南, 高贵军 2013 物理学报 62 234701Google Scholar

    Liu Q Z, Kou Z M, Han Z N, Gao G J 2013 Acta Phys. Sin. 62 234701Google Scholar

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出版历程
  • 收稿日期:  2019-05-23
  • 修回日期:  2019-07-19
  • 上网日期:  2019-11-01
  • 刊出日期:  2019-11-05

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