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For the flow of an insoluble surfactant-laden thin film and droplet on inclined random topography, the lubrication theory is used to derive the evolution equations of thin liquid film thickness and interfacial surfactant concentration. Characteristics of thin film flow and droplet spreading, as well as the influence of topography structure are numerically simulated with PDECOL code. Results show that under the action of gravitational component and Marangoni effects, the thin film flow and droplet spreading is accelerated; the capillary ridge emerges at the thin film edge and the droplet center; and at the bottom of the thin film and droplet, the depression is generated. While the deformation of liquid film free surface is more significant due to the effect of random topography. The increasing θ has a role of enhancing gravitational component and Marangoni effects, leading to the enhancement of the capillary ridge and depression. The increase of D promotes the thin film flow and droplet spreading, but causes the deformation amplified; and the increased k0 can induce the evolutions of thin film flow and droplet spreading to slow down and inhibit the formation of capillary ridge and depression. In addition, compared with the thin film flow, the impact of D and k0 on the speed of droplet spreading is relatively weak.
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Keywords:
- random topography /
- thin films /
- Marangoni effects /
- inclined flow
[1] Wen S Z, Huang P 2011 Interface Science and Technology (Beijing: Tsinghua Press) (in Chinese) [温诗铸, 黄平 2011 界面科学与技术 (北京: 清华大学出版社)]
[2] Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131
[3] Ye X M, Shen L, Li C X 2012 CIESC J. 63 2507 (in Chinese) [叶学民, 沈雷, 李春曦 2012 化工学报 63 2507]
[4] Kalliadasis S, Bielarz C, Homsy G M 2000 Phys. Fluids 12 1889
[5] Savva N, Pavliotis G A, Kalliadasis S 2011 J. Fluid Mech. 672 358
[6] Nonomura Y, Morita Y, Hikima T, Seino E, Chida S, Mayama H 2010 Langmuir 26 16150
[7] Chandra D, Yang S 2011 Langmuir 27 13401
[8] Argyriadi K, Vlachogiannis M, Bontozoglou V 2006 Phys. Fluids 18 012102
[9] Lee Y C, Thompson H M, Gaskell P H 2011 Comput Fluids 46 306
[10] Liao Q, Wang H, Zhu X, Li M W 2007 Scientia Sinica Technologica 37 402 (in Chinese) [廖强, 王宏, 朱恂, 李明伟 2007 中国科学: 技术科学 37 402]
[11] Zhang M K, Chen S, Shang Z 2012 Acta Phys. Sin. 61 034701 (in Chinese) [张明焜, 陈硕, 尚智 2012 物理学报 61 034701]
[12] Bi F F, Guo Y L, Shen S Q, Chen J X, Li Y Q 2012 Acta Phys. Sin. 61 184702 (in Chinese) [毕菲菲, 郭亚丽, 沈胜强, 陈觉先, 李熠桥 2012 物理学报 61 184702]
[13] Craster R V, Matar O K 2007 Langmuir 23 2588
[14] Edmonstone B D, Matar O K, Craster R V 2005 Phsica D 209 62
[15] Matar O K 2002 Phys. Fluids 14 4216
[16] Warner M R E, Craster R V, Matar O K 2004 Phys. Fluids 16 2933
[17] Blanchette F, Shapiro A M 2012 Phys. Fluids 24 042104
[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] Liu P Y, Chu Y, Wu Z S, Yan Z, Kang W L 1995 Acta Phys. Chim. Sin. 11 320 (in Chinese) [刘沛妍, 褚莹, 吴子生, 严忠, 康万利 1995 物理化学学报 11 320]
[21] Zhang X G, Liu J X, Wang H Y, Wang M Y, Fan Z J 2010 Acta Phys. Chim. Sin. 26 617 (in Chinese) [张晓光, 刘洁翔, 王海英, 王满意, 范志金 2010 物理化学学报 26 617]
[22] 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页–第186页]
[23] Yuan Q Z, Zhao Y P 2013 Sci. Rep. 3 1944
[24] Yuan Q Z, Zhao Y P 2013 J. Fluid. Mech. 716 17
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[1] Wen S Z, Huang P 2011 Interface Science and Technology (Beijing: Tsinghua Press) (in Chinese) [温诗铸, 黄平 2011 界面科学与技术 (北京: 清华大学出版社)]
[2] Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131
[3] Ye X M, Shen L, Li C X 2012 CIESC J. 63 2507 (in Chinese) [叶学民, 沈雷, 李春曦 2012 化工学报 63 2507]
[4] Kalliadasis S, Bielarz C, Homsy G M 2000 Phys. Fluids 12 1889
[5] Savva N, Pavliotis G A, Kalliadasis S 2011 J. Fluid Mech. 672 358
[6] Nonomura Y, Morita Y, Hikima T, Seino E, Chida S, Mayama H 2010 Langmuir 26 16150
[7] Chandra D, Yang S 2011 Langmuir 27 13401
[8] Argyriadi K, Vlachogiannis M, Bontozoglou V 2006 Phys. Fluids 18 012102
[9] Lee Y C, Thompson H M, Gaskell P H 2011 Comput Fluids 46 306
[10] Liao Q, Wang H, Zhu X, Li M W 2007 Scientia Sinica Technologica 37 402 (in Chinese) [廖强, 王宏, 朱恂, 李明伟 2007 中国科学: 技术科学 37 402]
[11] Zhang M K, Chen S, Shang Z 2012 Acta Phys. Sin. 61 034701 (in Chinese) [张明焜, 陈硕, 尚智 2012 物理学报 61 034701]
[12] Bi F F, Guo Y L, Shen S Q, Chen J X, Li Y Q 2012 Acta Phys. Sin. 61 184702 (in Chinese) [毕菲菲, 郭亚丽, 沈胜强, 陈觉先, 李熠桥 2012 物理学报 61 184702]
[13] Craster R V, Matar O K 2007 Langmuir 23 2588
[14] Edmonstone B D, Matar O K, Craster R V 2005 Phsica D 209 62
[15] Matar O K 2002 Phys. Fluids 14 4216
[16] Warner M R E, Craster R V, Matar O K 2004 Phys. Fluids 16 2933
[17] Blanchette F, Shapiro A M 2012 Phys. Fluids 24 042104
[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] Liu P Y, Chu Y, Wu Z S, Yan Z, Kang W L 1995 Acta Phys. Chim. Sin. 11 320 (in Chinese) [刘沛妍, 褚莹, 吴子生, 严忠, 康万利 1995 物理化学学报 11 320]
[21] Zhang X G, Liu J X, Wang H Y, Wang M Y, Fan Z J 2010 Acta Phys. Chim. Sin. 26 617 (in Chinese) [张晓光, 刘洁翔, 王海英, 王满意, 范志金 2010 物理化学学报 26 617]
[22] 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页–第186页]
[23] Yuan Q Z, Zhao Y P 2013 Sci. Rep. 3 1944
[24] Yuan Q Z, Zhao Y P 2013 J. Fluid. Mech. 716 17
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