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Targeting the flowing of insoluble surfactant-laden film over topography substrate, the lubrication theory is adopted to derive the evolution equations of thin liquid film thickness and interfacial surfactant concentration. The flowing characteristics of the film on topography surfaces, and the influence of topography structure are examined based on the numerical simulation with PDECOL code. The results show that when the thin film of insoluble surfactant flows over periodic grooving topography, the depression appears at the negative step, while the ridge is shaped at the positive step, both of which increase gradually with time going by. Compared with the case of the flat base, the surfactant-laden film spreading speed is enhanced. Increasing the groove depth or reducing the groove steepness leads to the increase of the rupture possibility of the film. Improving the groove width promotes the film flowing. The decrease of the steepness can cause the film to form a ridge feature before entering into the first groove. Gravity has the opposite effects on the up-hilling and down-hilling processes of liquid film flow, which causes the flow stability to deteriorate. Conjoining pressure induced by intermolecular forces can accelerate the film, giving rise to a notable dewetting phenomenon, while disjoining pressure has an adverse effect.
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Keywords:
- surfactant-laden film /
- topography surface /
- spreading /
- intermolecular forces
[1] 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]
[2] Lee K S, Ivanova N, Starov V M Hilal N, Dutschk V 2008 Adv. Colloid Interfac. 244 54
[3] Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131
[4] Matar O K 2002 Phys. Fluids 14 4216
[5] Warner M R E, Craster R V, Matar O K 2004 Phys. Fluids 16 2933
[6] Edmonstone B D, Matar O K, Craster R V 2005 Physica D 209 62
[7] 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]
[8] 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]
[9] Mavromoustaki A, Matar O K, Craster R V 2012 J. Colloid Interface Sci. 371 107
[10] 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 工程热物理学报 24 85]
[11] Gerbig Y B, Phani A R, Haefke H 2005 Appl. Surf. Sci. 242 251
[12] Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131
[13] Kalliadasis S, Bielarz C, Homsy G M 2000 Phys. Fluids 12 1889
[14] 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 物理学报 63 154702]
[15] Argyriadi K, Vlachogiannis M, Bontozoglou V 2006 Phys. Fluids 18 012102
[16] Tseluiko D, Blyth M G, Papageorgiou D T 2011 J. Eng. Math. 69 169
[17] Piao M R, Hu G H 2011 Chin. J. Comput. Phys. 28 843 (in Chinese) [朴明日, 胡国辉 2011 计算物理 28 843]
[18] Li C X, Pei J J, Ye X M 2013 J. Xi'an Jiaotong Univ. 47 40 (in Chinese) [李春曦, 裴建军, 叶学民 2013 西安交通大学学报 47 40]
[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 物理学报 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 物理学报 62 214704]
[21] Warner M R E, Craster R V, Matar O K 2002 Phys. Fluids 14 4040
[22] Ye X M, Shen L, Li C X 2013 J. Xi'an Jiaotong Univ. 47 96 (in Chinese) [叶学民, 沈雷, 李春曦 2013 西安交通大学学报 47 96]
[23] Zhao Y P 2012 Physical Mechanics of Surface and Interface (Beijing: Science Press pp185-186 (in Chinese) [赵亚溥 2012 表面与界面物理力学 (北京: 科学出版社) 第185–第186页]
[24] Oron A, Davis S H, Bankoff S G 1997 Rev. Mod. Phys. 69 931
[25] Edmonstone B D, Matar O K, Craster R V 2004 J. Eng. Math. 50 141
[26] Afsar-Siddiqui A B, Luckham P F, Matar O K 2003 Langmuir 19 696
[27] Edmonstone B D, Matar O K 2004 J. Colloid Interf. Sci. 274 183
[28] Li C X 2011 Ph. D. Dissertation (Baoding: North China Electric Power University) (in Chinese) [李春曦 2011 博士学位论文 (保定: 华北电力大学)]
[29] Bhakta A, Ruchkenstein E 1997 Adv. Colloid Interf. 70 1
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[1] 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]
[2] Lee K S, Ivanova N, Starov V M Hilal N, Dutschk V 2008 Adv. Colloid Interfac. 244 54
[3] Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131
[4] Matar O K 2002 Phys. Fluids 14 4216
[5] Warner M R E, Craster R V, Matar O K 2004 Phys. Fluids 16 2933
[6] Edmonstone B D, Matar O K, Craster R V 2005 Physica D 209 62
[7] 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]
[8] 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]
[9] Mavromoustaki A, Matar O K, Craster R V 2012 J. Colloid Interface Sci. 371 107
[10] 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 工程热物理学报 24 85]
[11] Gerbig Y B, Phani A R, Haefke H 2005 Appl. Surf. Sci. 242 251
[12] Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131
[13] Kalliadasis S, Bielarz C, Homsy G M 2000 Phys. Fluids 12 1889
[14] 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 物理学报 63 154702]
[15] Argyriadi K, Vlachogiannis M, Bontozoglou V 2006 Phys. Fluids 18 012102
[16] Tseluiko D, Blyth M G, Papageorgiou D T 2011 J. Eng. Math. 69 169
[17] Piao M R, Hu G H 2011 Chin. J. Comput. Phys. 28 843 (in Chinese) [朴明日, 胡国辉 2011 计算物理 28 843]
[18] Li C X, Pei J J, Ye X M 2013 J. Xi'an Jiaotong Univ. 47 40 (in Chinese) [李春曦, 裴建军, 叶学民 2013 西安交通大学学报 47 40]
[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 物理学报 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 物理学报 62 214704]
[21] Warner M R E, Craster R V, Matar O K 2002 Phys. Fluids 14 4040
[22] Ye X M, Shen L, Li C X 2013 J. Xi'an Jiaotong Univ. 47 96 (in Chinese) [叶学民, 沈雷, 李春曦 2013 西安交通大学学报 47 96]
[23] Zhao Y P 2012 Physical Mechanics of Surface and Interface (Beijing: Science Press pp185-186 (in Chinese) [赵亚溥 2012 表面与界面物理力学 (北京: 科学出版社) 第185–第186页]
[24] Oron A, Davis S H, Bankoff S G 1997 Rev. Mod. Phys. 69 931
[25] Edmonstone B D, Matar O K, Craster R V 2004 J. Eng. Math. 50 141
[26] Afsar-Siddiqui A B, Luckham P F, Matar O K 2003 Langmuir 19 696
[27] Edmonstone B D, Matar O K 2004 J. Colloid Interf. Sci. 274 183
[28] Li C X 2011 Ph. D. Dissertation (Baoding: North China Electric Power University) (in Chinese) [李春曦 2011 博士学位论文 (保定: 华北电力大学)]
[29] Bhakta A, Ruchkenstein E 1997 Adv. Colloid Interf. 70 1
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