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针对含非溶性活性剂液滴在倾斜粗糙壁面上的铺展过程, 应用润滑理论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, 基于非模态理论研究了液滴铺展的稳定性特征, 探讨了相关参数的影响及其内在机理. 研究表明: 液膜厚度和活性剂浓度扰动量均呈现双驼峰型变化, 且峰值位于液滴底部凹陷处; 随扰动波数k增加, 最易失稳区域由液滴底部右侧凹陷处移至左侧凹陷, 壁面结构的影响逐渐减弱, 液滴铺展历程趋于稳定; 增加壁面倾角θ 将导致液滴铺展不稳定性加剧, 增大壁面高度D和壁面波数k0均导致液滴铺展稳定性先增强后减弱; 随毛细数C减小, 液滴铺展稳定性下降, 重力的影响逐渐突显, 扰动量最大值呈现先增大后减小的变化趋势.For the spreading of a droplet covered with insoluble surfactant over an inclined random heterogeneous substrate, the base state and disturbance evolution equations for the film thickness and surfactant concentration are derived using the lubrication theory. Stability of the droplet spreading on the heterogeneous substrates, and effects of dimensionless parameters as well as the internal mechanism are investigated based on the non-modal stability theory. Results show that the disturbances of film thickness and surfactant concentration exihibit a double-hump shape and the crests lie in thinning regions at the bottom of the droplet. With increasing disturbance wave number, the stability of the droplet spreading is enhanced, but the maximal disturbance transfers from the right-side to the left-side of the droplet bottom. Increasing inclined angle leads to severe instability distinctly. Improving topographical height or increasing wave number of the substrate leads the spreading stability to firstly enhance and then to weaken. The droplet evolution displays an unstable spreading under smaller capillary number, with the maximum disturbance to be increasing before decreasing.
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Keywords:
- surfactant-laden droplet /
- topographical surface /
- spreading /
- non-modal stability
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[2] Matar O K 2002 Phys. Fluids 14 4216
[3] Warner M R E, Craster R V, Matar O K 2004 Phys. Fluids 16 2933
[4] Edmonstone B D, Matar O K, Craster R V 2005 Physica D 209 62
[5] Mavromoustaki A, Matar O K, Craster R V 2012 J. Colloid Interface Sci. 371 121
[6] Ye X M, Jiang K, Shen L, Li C X 2013 Journal of Theoretical and Applied Mechanics 45 681 (in Chinese) [叶学民, 姜凯, 沈雷, 李春曦 2013 力学学报 45 681]
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[10] Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131
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[13] Kalliadasis S, Bielarz C, Homsy G M 2000 Phys. Fluids 12 1889
[14] Nonomura Y, Morita Y, Hikima T, Seino E, Chida S, Mayama H 2010 Langmuir 26 16150
[15] Liu M, Wang S L, Wu Z R 2014 Acta Phys. Sin. 63 154702 (in Chinese) [刘梅, 王松岭, 吴正人 2014 63 154702]
[16] Tseluiko D, Blyth M G, Papageorgiou D T 2011 J. Eng. Math. 69 169
[17] Fischer B J, Troian S M 2003 Phys. Rev. B 67 016309
[18] Nouar C, Kabouya N, Duesk J 2007 Journal of Fluid Mechanics 577 211.
[19] Li C X, Pei J J, Ye X M 2013 Acta Phys. Sin. 62 174702 (in Chinese) [李春曦, 裴建军, 叶学民 2013 62 174702]
[20] Li C X, Pei J J, Ye X M 2013 Acta Phys. Sin. 62 214704 (in Chinese) [李春曦, 裴建军, 叶学民 2013 62 214704]
[21] 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]
[22] Edmonstone B D, Matar O K, Craster R V 2004 J. Eng. Math. 50 141
[23] 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]
[24] Warner M R E, Craster R V, Matar O K 2004 J. Fluid Mech. 510 169
[25] Sadiq M R, Tatiana G R, Stephan P 2012 Phys. Fluids 24 014104
[26] Li C X, Pei J J, Ye X M 2013 CIESC J. 64 3308 (in Chinese) [李春曦, 裴建军, 叶学民 2013 化工学报 64 3308]
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[1] Hamraoui A, Cachile M, Poulard C, Cazabat A M 2004 Colloids Surf. A 250 215
[2] Matar O K 2002 Phys. Fluids 14 4216
[3] Warner M R E, Craster R V, Matar O K 2004 Phys. Fluids 16 2933
[4] Edmonstone B D, Matar O K, Craster R V 2005 Physica D 209 62
[5] Mavromoustaki A, Matar O K, Craster R V 2012 J. Colloid Interface Sci. 371 121
[6] Ye X M, Jiang K, Shen L, Li C X 2013 Journal of Theoretical and Applied Mechanics 45 681 (in Chinese) [叶学民, 姜凯, 沈雷, 李春曦 2013 力学学报 45 681]
[7] Hu G H 2005 Phys. Fluids A 17 088105
[8] Wang W, Li Z X, Guo Z Y 2003 J. Eng. Thermophys. 24 85 (in Chinese) [王玮, 李志信, 过增元 2003 工程热 24 85]
[9] Gerbig Y B, Phani A R, Haefke H 2005 Appl. Surf. Sci. 242 251
[10] Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131
[11] Pang H Y, Zhang X F, Zhang H Y, Du F P 2006 Chin. J. Pestic. Sci. 8 157 (in Chinese) [庞红宇, 张现峰, 张红艳, 杜凤沛 2006 农药学学报 8 157]
[12] Lee K S, Ivanova N, Starov V M Hilal N, Dutschk V 2008 Adv. Colloid Interfac. 244 54
[13] Kalliadasis S, Bielarz C, Homsy G M 2000 Phys. Fluids 12 1889
[14] Nonomura Y, Morita Y, Hikima T, Seino E, Chida S, Mayama H 2010 Langmuir 26 16150
[15] Liu M, Wang S L, Wu Z R 2014 Acta Phys. Sin. 63 154702 (in Chinese) [刘梅, 王松岭, 吴正人 2014 63 154702]
[16] Tseluiko D, Blyth M G, Papageorgiou D T 2011 J. Eng. Math. 69 169
[17] Fischer B J, Troian S M 2003 Phys. Rev. B 67 016309
[18] Nouar C, Kabouya N, Duesk J 2007 Journal of Fluid Mechanics 577 211.
[19] Li C X, Pei J J, Ye X M 2013 Acta Phys. Sin. 62 174702 (in Chinese) [李春曦, 裴建军, 叶学民 2013 62 174702]
[20] Li C X, Pei J J, Ye X M 2013 Acta Phys. Sin. 62 214704 (in Chinese) [李春曦, 裴建军, 叶学民 2013 62 214704]
[21] 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]
[22] Edmonstone B D, Matar O K, Craster R V 2004 J. Eng. Math. 50 141
[23] 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]
[24] Warner M R E, Craster R V, Matar O K 2004 J. Fluid Mech. 510 169
[25] Sadiq M R, Tatiana G R, Stephan P 2012 Phys. Fluids 24 014104
[26] Li C X, Pei J J, Ye X M 2013 CIESC J. 64 3308 (in Chinese) [李春曦, 裴建军, 叶学民 2013 化工学报 64 3308]
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