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针对波纹基底上含不溶性活性剂液滴的铺展历程, 采用润滑理论建立了液滴铺展数理模型, 推导出基态和扰动态下液膜厚度和活性剂浓度的演化方程组, 基于非模态稳定性理论分析了液滴铺展的稳定性及参数的影响规律. 研究表明: 扰动量在液滴中心及铺展前沿处很小, 在液膜最薄处达到最大值且活性剂浓度的负扰动现象比较明显; 扰动波数可增强液滴铺展稳定性, 但随扰动波数增加, 该稳定性逐渐下降甚至转变为不稳定. 增加 Marangoni数将导致液滴铺展不稳定性加剧; 增大基底高度具有增强液滴铺展稳定的作用, Peclet数和基底波数取适中值时有利于液滴铺展的稳定性.For the spreading of an insoluble surfactant-laden droplet over the corrugated topography, the lubrication theory is used to establish the physical and mathematical models of the spreading of droplet and to derive the base state and disturbance evolution equations for thin liquid film thickness and surfactant concentration. The stability of droplet spreading on topography surfaces, as well as the effects of several parameters are investigated based on the non-model stability theory. Results show that disturbance quantities reach minimum at the droplet center and spreading fronts, and achieve the maximum in thinning regions, and the negative disturbance of surfactant concentration is quite obvious. Disturbance wave number can enhance the stability of the droplet spreading, but with increasing wave number, the stability tends to be weak and even transform into instability. The spreading stability is distinctly promoted with decreasing Marangoni number or increasing corrugated topography height. The droplet evolution displays a much stable spreading for moderate values of Peclet number and topography wave number.
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Keywords:
- surfactant-laden droplet /
- topography surface /
- spreading /
- non-modal stability
[1] Ma A X, Wei J J, Yuan M Z, Fang J B 2009 J. Eng. Thermol Physics 30 1324 (in Chinese) [马爱香, 魏进家, 袁敏哲, 方嘉宾 2009 工程热 30 1324]
[2] Matar O K, Sisoev G M, Lawrence C J 2008 Chem. Eng. Sci. 63 2225
[3] Sadiq M R, Tatiana G R, Stephan P 2012 Phys. Fluids 24 014104
[4] Tatiana G R, Alexander A, Peter S 2005 Exp. Therm Fluid Sci. 29 765
[5] Zhang C B, Chen Y P, Shi M H, Fu P P, Wu J F 2009 Acta Phys. Sin. 58 7050 (in Chinese) [张程宾, 陈永平, 施明恒, 付盼盼, 吴嘉峰 2009 58 7050]
[6] Shi Z Y, Hu G H, Zhou Z W 2010 Acta Phys. Sin. 59 2595 (in Chinese) [石自媛, 胡国辉, 周哲玮 2010 59 2595]
[7] Hamraoui A, Cachile M, Poulard C, Cazabat A M 2004 Colloids Surf. A 250 215
[8] Troian S M, Herbolzheimer E, Safran S A 1990 Phys. Rev. Lett. 65 333
[9] Matar O K 2002 Phys. Fluids 14 4216
[10] Warner M R E, Craster R V, Matar O K 2004 Phys. Fluids 16 2933
[11] Edmonstone B D, Matar O K, Craster R V 2005 Physica D 209 62
[12] Hu G H 2005 Phys. Fluids A 17 088105
[13] Li C X, Wang S L, Ye X M 2009 Proc. CSEE. 29 60 (in Chinese) [李春曦, 王松岭, 叶学民 2009 中国电机工程学报 29 60]
[14] Wang H 2012 Spreading and Stability Analysis of a Surfactant-laden drop on Thermally Driven Thin Liquid Film (Baoding: North China Electric Power University) (in Chinese) [王欢 2012 活性剂溶液的受热铺展过程稳定性研究 (保定: 华北电力大学)]
[15] Zhao Y P 2012 Physical Mechanics of Surface and Interface (Beijing: Science Press) pp185-186m (in Chinese) [赵亚溥 2012 表面与界面物理力学 (北京: 科学出版社) 第185-186页]
[16] Warner M R E, Craster R V, Matar O K 2004 J. Fluid Mech. 510 169
[17] Edmonstone B D, Matar O K, Craster R V 2006 J. Colloid Interface Sci. 293 222
[18] Wang S L, Li C X, Ye X M 2011 Proc. CSEE 31 60 (in Chinese) [王松岭, 李春曦, 叶学民 2011 中国电机工程学报 31 60]
[19] Wang S L, Li C X, Ye X M 2011 CIESC J 62 2512 (in Chinese) [王松岭, 李春曦, 叶学民 2011 化工学报 62 2512]
[20] Fischer B J, Troian S M 2003 Phys. Rev. 67 016309
[21] Zhou H, Zhao G F 2003 Hydrodynamic Stability (Beijing: National Defense Press) pp2-4m (in Chinese) [周恒, 赵耕夫 2003 流动稳定性 (北京: 国防工业出版社) 第2-4页]
[22] Yuan Q Z, Zhao Y P 2013 J. Fluid Mech. 716 171
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[1] Ma A X, Wei J J, Yuan M Z, Fang J B 2009 J. Eng. Thermol Physics 30 1324 (in Chinese) [马爱香, 魏进家, 袁敏哲, 方嘉宾 2009 工程热 30 1324]
[2] Matar O K, Sisoev G M, Lawrence C J 2008 Chem. Eng. Sci. 63 2225
[3] Sadiq M R, Tatiana G R, Stephan P 2012 Phys. Fluids 24 014104
[4] Tatiana G R, Alexander A, Peter S 2005 Exp. Therm Fluid Sci. 29 765
[5] Zhang C B, Chen Y P, Shi M H, Fu P P, Wu J F 2009 Acta Phys. Sin. 58 7050 (in Chinese) [张程宾, 陈永平, 施明恒, 付盼盼, 吴嘉峰 2009 58 7050]
[6] Shi Z Y, Hu G H, Zhou Z W 2010 Acta Phys. Sin. 59 2595 (in Chinese) [石自媛, 胡国辉, 周哲玮 2010 59 2595]
[7] Hamraoui A, Cachile M, Poulard C, Cazabat A M 2004 Colloids Surf. A 250 215
[8] Troian S M, Herbolzheimer E, Safran S A 1990 Phys. Rev. Lett. 65 333
[9] Matar O K 2002 Phys. Fluids 14 4216
[10] Warner M R E, Craster R V, Matar O K 2004 Phys. Fluids 16 2933
[11] Edmonstone B D, Matar O K, Craster R V 2005 Physica D 209 62
[12] Hu G H 2005 Phys. Fluids A 17 088105
[13] Li C X, Wang S L, Ye X M 2009 Proc. CSEE. 29 60 (in Chinese) [李春曦, 王松岭, 叶学民 2009 中国电机工程学报 29 60]
[14] Wang H 2012 Spreading and Stability Analysis of a Surfactant-laden drop on Thermally Driven Thin Liquid Film (Baoding: North China Electric Power University) (in Chinese) [王欢 2012 活性剂溶液的受热铺展过程稳定性研究 (保定: 华北电力大学)]
[15] Zhao Y P 2012 Physical Mechanics of Surface and Interface (Beijing: Science Press) pp185-186m (in Chinese) [赵亚溥 2012 表面与界面物理力学 (北京: 科学出版社) 第185-186页]
[16] Warner M R E, Craster R V, Matar O K 2004 J. Fluid Mech. 510 169
[17] Edmonstone B D, Matar O K, Craster R V 2006 J. Colloid Interface Sci. 293 222
[18] Wang S L, Li C X, Ye X M 2011 Proc. CSEE 31 60 (in Chinese) [王松岭, 李春曦, 叶学民 2011 中国电机工程学报 31 60]
[19] Wang S L, Li C X, Ye X M 2011 CIESC J 62 2512 (in Chinese) [王松岭, 李春曦, 叶学民 2011 化工学报 62 2512]
[20] Fischer B J, Troian S M 2003 Phys. Rev. 67 016309
[21] Zhou H, Zhao G F 2003 Hydrodynamic Stability (Beijing: National Defense Press) pp2-4m (in Chinese) [周恒, 赵耕夫 2003 流动稳定性 (北京: 国防工业出版社) 第2-4页]
[22] Yuan Q Z, Zhao Y P 2013 J. Fluid Mech. 716 171
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