Fluid dynamics simulation on water lubricating performance of micro-/nano-textured surfaces considering roughness structures

Gu Jing-Xuan; Zheng Ting; Guo Ming-Shuai; Xia Dong-Sheng; Zhang Hui-Chen

doi:10.7498/aps.73.20240333

Abstract

With the development of surface precision machining technology and extensive studies on lubrication and friction reduction, the use of surface texture to reduce friction has attracted widespread attention, but few studies have considered the influence of surface roughness on lubrication characteristics. By employing the computational fluid dynamics (CFD) simulation method, the lubrication models with rectangular textures and the introduction of rough asperity structures at the same time are established. The effects of the corresponding structure parameters on the lubrication performance of textured and roughed surfaces are studied under water lubrication conditions. Our results suggest that the adjustment of geometric parameters on the micro-/nano-structured surfaces can influence the load-bearing capacity of the water lubrication film, thus affecting the hydrodynamic lubrication performance on the surface. In addition, the generation of vortex in the micro-textures can bring changes in vorticity, which causes energy dissipation and affects frictional forces. In the lubrication model with rectangular textures, optimal hydrodynamic lubrication performance is obtained under the appropriate depth ratio H = 0.6. Meanwhile, the corresponding lubrication performance can be enhanced by increasing the width ratio (W) of surface texture. After introducing random asperity structures on the micro-textured surface with a standard deviation δ = 0.5, the bearing capacity is increased by 44%, and the friction coefficient is reduced by 30.9%. Moreover, the introduction of half-sine rough asperity structures can only result in relatively minor differences in the lubrication performance, i.e. the changes of bearing capacity and friction coefficient are less than 10%. However, the introduction of compound hierarchical structure consisting of random asperity structures and half-sine rough asperity structures can result in an increase in the corresponding bearing capacity by 42% and a reduction in the friction coefficient by 31.1%, which implies a significant enhancement in the hydrodynamic lubrication performance.

Keywords:

Authors and contacts

Department of Mechanical Engineering, Dalian Maritime University, Dalian 116026, China

Corresponding author: Zheng Ting, whlgzt@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51909023, 51775077), the Natural Science Foundation of Liaoning Province, China (Grant No. 2021-MS-140), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. 3132023122, 3132023516).

FullText HTML

References

[1]	Hamilton D B, Walowit J A, Allen C M 1966 J. Fluids Eng. 88 177
[2]	Zhong Y H, Zheng L, Gao Y H, Liu Z N 2019 Tribol. Int. 129 151 Google Scholar
[3]	Mourier L, Mazuyer D, Ninove F P, Lubrecht A A 2010 Proc. Inst. Mech. Eng. , Part J: J. Eng. Tribol. 224 697.Google Scholar
[4]	Zhang J Y, Meng Y G 2012 Tribol. Lett. 46 147 Google Scholar
[5]	Gropper D, Wang L, Harvey T J 2016 Tribol. Int. 94 509 Google Scholar
[6]	Braun D, Greiner C, Schneider J, Gumbsch P 2014 Tribol. Int. 77 142 Google Scholar
[7]	Hsu S M, Jing Y, Hua D, Zhang H 2014 J. Phys. D: Appl. Phys. 47 335307 Google Scholar
[8]	安书董, 王晓燕, 陈仙, 王炎武, 王晓波, 赵玉清 2015 64 036801 Google Scholar An S D, Wang X Y, Chen X, Wang Y W, Wang X B, Zhao Y Q 2015 Acta Phys. Sin. 64 036801 Google Scholar
[9]	Rosenkranz A, Szurdak A, Gachot C, Hirt G, Mücklich F 2016 Tribol. Int. 95 290.Google Scholar
[10]	纪敬虎, 管采薇, 符昊, 华希俊, 符永宏 2018 润滑与密封 43 20 Google Scholar Ji J H, Guan C W, Fu H, Hua X J, Fu Y H 2018 Lubr. Eng. 43 20 Google Scholar
[11]	Qiu Y, Khonsari M M 2011 J. Tribol. 133 021704 Google Scholar
[12]	Lahayne O, Pichler B, Reihsner R, Eberhardsteiner J, Suh J, Kim D, Nam S, Paek H, Lorenz B, Persson B N J 2016 Tribol. Lett. 62 17 Google Scholar
[13]	Feng D, Shen M X, Peng X D, Meng X K 2017 Tribol. Lett. 65 1 Google Scholar
[14]	Sedlaček M, Podgornik B, Vižintin J 2009 Wear 266 482 Google Scholar
[15]	Menezes P L, Kishore, Kailas S V, Lovell M R 2011 Tribol. Lett. 41 1 Google Scholar
[16]	Rasp W, Wichern C M 2002 J. Mater. Process. Technol. 125 379
[17]	王悦昶, 刘莹, 黄伟峰, 郭飞, 王玉明 2016 摩擦学学报 36 520 Wang Y C, Liu Y, Huang W F, Guo F, Wang Y M 2016 Tribology 36 520
[18]	Rosenkranz A, Costa H L, Profito F, Gachot C, Medina S, Dini D 2019 Tribol. Int. 134 190 Google Scholar
[19]	Brajdic-Mitidieri P, Gosman A D, Ioannides E, Spikes H A 2005 J. Tribol. 127 803 Google Scholar
[20]	Sahlin F, Glavatskih S B, Almqvist T, Larsson R 2005 J. Tribol. 127 96 Google Scholar
[21]	Vilhena L, Sedlaček M, Podgornik B, Rek Z, Žun I 2018 Lubricants 6 15 Google Scholar
[22]	Zhang L, Luo J, Yuan R B, He M 2012 Procedia Eng. 31 220 Google Scholar
[23]	禄晓敏, 王权岱, 肖继明, 杨振朝 2016 润滑与密封 41 70 Google Scholar Lu X M, Wang Q D, Xiao J M, Yang Z C 2016 Lubr. Eng. 41 70 Google Scholar
[24]	Mao Y, Zeng L C, Lu Y 2016 Tribol. Int. 104 212 Google Scholar
[25]	Ma X 2023 Lubricants 11 270 Google Scholar
[26]	Li Q, Zhang S, Wang Y J, Xu W W, Wang Z B 2019 Ind. Lubr. Tribol. 71 109 Google Scholar
[27]	He T, Li J M, Deng H S, Wang C L, Shi R, Chen G Y, Li Z P 2021 AIP Adv. 11 015222 Google Scholar
[28]	Singhal A K, Athavale M M, Li H, Jiang Y 2002 ASME J. Fluids Eng. 124 617 Google Scholar
[29]	Pellone C, Franc J P, Perrin M 2004 C. R. Math. 332 827
[30]	Buscaglia G C, El Alaoui Talibi M, Jai M 2015 Math. Comput. Simul 118 130 Google Scholar
[31]	Wei Y, Tomkowski R, Archenti A 2020 Metals 10 361 Google Scholar
[32]	Wang W, He Y Y, Li Y, Wei B, Hu Y T, Luo J B 2018 Ind. Lubr. Tribol. 70 754 Google Scholar
[33]	Gao G Y, Yin Z W, Jiang D, Zhang X L 2014 Tribol. Int. 75 31 Google Scholar
[34]	Podgornik B, Vilhena L M, Sedlaček M, Rek Z, Žun I 2012 Meccanica 47 1613 Google Scholar
[35]	Shankar P N, Deshpande M D 2000 Annu. Rev. Fluid Mech. 32 93 Google Scholar
[36]	Sahlin F, Almqvist A, Larsson R, Glavatskih S 2007 Tribol. Int. 40 1294 Google Scholar
[37]	Ausas R, Ragot P, Leiva J, Jai M, Bayada G, Buscaglia G C 2007 J. Tribol. 129 868 Google Scholar
[38]	Wahl R, Schneider J, Gumbsch P 2012 Tribol. Int. 55 81.Google Scholar
[39]	刘天霞, 李靖, 卢星, 江志波 2023 润滑与密封 48 74 Google Scholar Liu T X, Li J, Lu X, Jiang Z B 2023 Lubr. Eng. 48 74 Google Scholar
[40]	Babu P V, Ismail S, Ben B S 2021 Proc. Inst. Mech. Eng. , Part J: J. Eng. Tribol. 235 360 Google Scholar
[41]	Wos S, Koszela W, Pawlus P 2020 Tribol. Int. 146 106205.Google Scholar
[42]	Wang J H, Yan Z J, Fang X, Shen Z Y, Pan X X 2020 Lubr. Sci. 32 404 Google Scholar
[43]	Venkateswara Babu P, Syed I, Benbeera S 2020 Mater. Today Proc. 24 1112 Google Scholar
[44]	樊智敏, 马瑞磷, 江峰 2021 润滑与密封 46 44 Google Scholar Fan Z M, Ma R L, Jiang F 2021 Lubr. Eng. 46 44 Google Scholar
[45]	纪敬虎, 周加鹏, 王沫阳, 王伟, 符永宏 2019 表面技术 48 139 Ji J H, Zhou J P, Wang M Y, Wang W, Fu Y H 2019 Surf. Technol. 48 139
[46]	Jiang Y Y, Yan Z J, Zhang S W, Shen Z Y, Sun H C 2022 Sci. Rep. 12 13455 Google Scholar
[47]	Wang Y, Jacobs G, König F, Zhang S, von Goeldel S 2023 Lubricants 11 20 Google Scholar
[48]	Huang J Y, Guan Y C, Ramakrishna S 2021 Tribol. Int. 162 107115 Google Scholar

Cited By

图 1 计入粗糙峰的矩形微观复合织构的润滑模型

Figure 1. The lubrication model of textured surfaces consisting of rectangular grooves and rough peaks.

DownLoad: Full-Size Img PowerPoint

图 2 润滑模型Ⅰ和Ⅱ的润滑特性　(a) 模型Ⅰ的承载力与摩擦力; (b) 模型Ⅰ的摩擦系数; (c) 模型Ⅱ的承载力与摩擦力; (d) 模型Ⅱ的摩擦系数

Figure 2. The lubrication performance in models I and II: (a) Bearing capacity and friction force in model I; (b) frictional coefficient in model I; (c) bearing capacity and friction force in model II; (d) frictional coefficient in model II.

DownLoad: Full-Size Img PowerPoint

图 3 润滑模型Ⅰ和Ⅱ中流场流线分布图　(a) 模型Ⅰ; (b) 模型Ⅱ

Figure 3. Distribution of streamlines in models I and II: (a) Model I; (b) Model II.

DownLoad: Full-Size Img PowerPoint

图 4 润滑模型Ⅰ和Ⅱ中的上表面涡量云图　(a) 模型Ⅰ; (b) 模型Ⅱ

Figure 4. Distribution of vorticity in models I and II: (a) Model I; (b) Model II.

DownLoad: Full-Size Img PowerPoint

图 5 润滑模型Ⅰ和Ⅱ中的上表面压力和空化气相分布图　(a) 模型Ⅰ; (b) 模型Ⅱ

Figure 5. Distribution of pressure and gas volume fraction on the upper surfaces of models I and II: (a) Model I; (b) Model II.

DownLoad: Full-Size Img PowerPoint

图 6 计入不同粗糙峰结构的润滑模型的润滑特性　(a) Gauss模型中承载力、摩擦力与摩擦系数; (b) Sin模型中承载力、摩擦力与摩擦系数; (c) Sin+Gauss模型中承载力、摩擦力与摩擦系数

Figure 6. The lubrication performance on the textured models with rough peaks: (a) The bearing capacity, frictional force and frictional coefficient in the Gauss model; (b) the bearing capacity, frictional force and frictional coefficient in the Sin model; (c) the bearing capacity, frictional force and frictional coefficient in the Sin+Gauss model.

DownLoad: Full-Size Img PowerPoint

图 7 不同粗糙峰结构模型组流场流线分布图

Figure 7. Distribution of streamlines in the lubrication models with rough peaks.

DownLoad: Full-Size Img PowerPoint

图 8 不同粗糙峰结构模型组上、下壁面涡量云图　(a)下壁面涡量云图; (b)上表面涡量云图

Figure 8. Distribution of vorticity on the surfaces of lubrication models with rough peaks: (a) Distribution of vorticity on the lower wall surfaces; (b) distribution of vorticity on the upper wall surfaces.

DownLoad: Full-Size Img PowerPoint

图 9 不同粗糙峰结构模型组上表面压力和气相体积分数图

Figure 9. Distribution of pressure and gas volume fraction on the upper wall surface of lubrication models with rough peaks.

DownLoad: Full-Size Img PowerPoint

表 1 水润滑微织构模型参数变化

Table 1. The geometrical parameters for textured models.

模型	T₀	W	H
模型Ⅰ (恒定宽度比W )	500/600	0.60	0.2/ 0.4/ 0.6/ 0.8 /1.0/ 1.2
模型Ⅱ (恒定深度比H )	400/500/600	0.50/ 0.55/ 0.60 /0.65/ 0.70	1.0

DownLoad: CSV

表 2 润滑模型中的下壁面微观形貌示意图

Table 2. Sketch maps of textures on the lower wall surfaces of the lubrication models.

模型名称	微织构表面粗糙峰轮廓	函数变化参数
光滑表面 (Smooth)		δ = 0 h_s = 0
Gauss		δ = 0.25/0.5/0.75/1 h_s = 0
Sin		δ = 0 h_s = 1/2/3/4/5 l = 3 i = 1
Sin+Gauss		δ = 0.25/0.5/0.75/1 h_s = 1/2/3/4/5 l = 3 i = 3

DownLoad: CSV

map

[1]	Hamilton D B, Walowit J A, Allen C M 1966 J. Fluids Eng. 88 177
[2]	Zhong Y H, Zheng L, Gao Y H, Liu Z N 2019 Tribol. Int. 129 151 Google Scholar
[3]	Mourier L, Mazuyer D, Ninove F P, Lubrecht A A 2010 Proc. Inst. Mech. Eng. , Part J: J. Eng. Tribol. 224 697.Google Scholar
[4]	Zhang J Y, Meng Y G 2012 Tribol. Lett. 46 147 Google Scholar
[5]	Gropper D, Wang L, Harvey T J 2016 Tribol. Int. 94 509 Google Scholar
[6]	Braun D, Greiner C, Schneider J, Gumbsch P 2014 Tribol. Int. 77 142 Google Scholar
[7]	Hsu S M, Jing Y, Hua D, Zhang H 2014 J. Phys. D: Appl. Phys. 47 335307 Google Scholar
[8]	安书董, 王晓燕, 陈仙, 王炎武, 王晓波, 赵玉清 2015 64 036801 Google Scholar An S D, Wang X Y, Chen X, Wang Y W, Wang X B, Zhao Y Q 2015 Acta Phys. Sin. 64 036801 Google Scholar
[9]	Rosenkranz A, Szurdak A, Gachot C, Hirt G, Mücklich F 2016 Tribol. Int. 95 290.Google Scholar
[10]	纪敬虎, 管采薇, 符昊, 华希俊, 符永宏 2018 润滑与密封 43 20 Google Scholar Ji J H, Guan C W, Fu H, Hua X J, Fu Y H 2018 Lubr. Eng. 43 20 Google Scholar
[11]	Qiu Y, Khonsari M M 2011 J. Tribol. 133 021704 Google Scholar
[12]	Lahayne O, Pichler B, Reihsner R, Eberhardsteiner J, Suh J, Kim D, Nam S, Paek H, Lorenz B, Persson B N J 2016 Tribol. Lett. 62 17 Google Scholar
[13]	Feng D, Shen M X, Peng X D, Meng X K 2017 Tribol. Lett. 65 1 Google Scholar
[14]	Sedlaček M, Podgornik B, Vižintin J 2009 Wear 266 482 Google Scholar
[15]	Menezes P L, Kishore, Kailas S V, Lovell M R 2011 Tribol. Lett. 41 1 Google Scholar
[16]	Rasp W, Wichern C M 2002 J. Mater. Process. Technol. 125 379
[17]	王悦昶, 刘莹, 黄伟峰, 郭飞, 王玉明 2016 摩擦学学报 36 520 Wang Y C, Liu Y, Huang W F, Guo F, Wang Y M 2016 Tribology 36 520
[18]	Rosenkranz A, Costa H L, Profito F, Gachot C, Medina S, Dini D 2019 Tribol. Int. 134 190 Google Scholar
[19]	Brajdic-Mitidieri P, Gosman A D, Ioannides E, Spikes H A 2005 J. Tribol. 127 803 Google Scholar
[20]	Sahlin F, Glavatskih S B, Almqvist T, Larsson R 2005 J. Tribol. 127 96 Google Scholar
[21]	Vilhena L, Sedlaček M, Podgornik B, Rek Z, Žun I 2018 Lubricants 6 15 Google Scholar
[22]	Zhang L, Luo J, Yuan R B, He M 2012 Procedia Eng. 31 220 Google Scholar
[23]	禄晓敏, 王权岱, 肖继明, 杨振朝 2016 润滑与密封 41 70 Google Scholar Lu X M, Wang Q D, Xiao J M, Yang Z C 2016 Lubr. Eng. 41 70 Google Scholar
[24]	Mao Y, Zeng L C, Lu Y 2016 Tribol. Int. 104 212 Google Scholar
[25]	Ma X 2023 Lubricants 11 270 Google Scholar
[26]	Li Q, Zhang S, Wang Y J, Xu W W, Wang Z B 2019 Ind. Lubr. Tribol. 71 109 Google Scholar
[27]	He T, Li J M, Deng H S, Wang C L, Shi R, Chen G Y, Li Z P 2021 AIP Adv. 11 015222 Google Scholar
[28]	Singhal A K, Athavale M M, Li H, Jiang Y 2002 ASME J. Fluids Eng. 124 617 Google Scholar
[29]	Pellone C, Franc J P, Perrin M 2004 C. R. Math. 332 827
[30]	Buscaglia G C, El Alaoui Talibi M, Jai M 2015 Math. Comput. Simul 118 130 Google Scholar
[31]	Wei Y, Tomkowski R, Archenti A 2020 Metals 10 361 Google Scholar
[32]	Wang W, He Y Y, Li Y, Wei B, Hu Y T, Luo J B 2018 Ind. Lubr. Tribol. 70 754 Google Scholar
[33]	Gao G Y, Yin Z W, Jiang D, Zhang X L 2014 Tribol. Int. 75 31 Google Scholar
[34]	Podgornik B, Vilhena L M, Sedlaček M, Rek Z, Žun I 2012 Meccanica 47 1613 Google Scholar
[35]	Shankar P N, Deshpande M D 2000 Annu. Rev. Fluid Mech. 32 93 Google Scholar
[36]	Sahlin F, Almqvist A, Larsson R, Glavatskih S 2007 Tribol. Int. 40 1294 Google Scholar
[37]	Ausas R, Ragot P, Leiva J, Jai M, Bayada G, Buscaglia G C 2007 J. Tribol. 129 868 Google Scholar
[38]	Wahl R, Schneider J, Gumbsch P 2012 Tribol. Int. 55 81.Google Scholar
[39]	刘天霞, 李靖, 卢星, 江志波 2023 润滑与密封 48 74 Google Scholar Liu T X, Li J, Lu X, Jiang Z B 2023 Lubr. Eng. 48 74 Google Scholar
[40]	Babu P V, Ismail S, Ben B S 2021 Proc. Inst. Mech. Eng. , Part J: J. Eng. Tribol. 235 360 Google Scholar
[41]	Wos S, Koszela W, Pawlus P 2020 Tribol. Int. 146 106205.Google Scholar
[42]	Wang J H, Yan Z J, Fang X, Shen Z Y, Pan X X 2020 Lubr. Sci. 32 404 Google Scholar
[43]	Venkateswara Babu P, Syed I, Benbeera S 2020 Mater. Today Proc. 24 1112 Google Scholar
[44]	樊智敏, 马瑞磷, 江峰 2021 润滑与密封 46 44 Google Scholar Fan Z M, Ma R L, Jiang F 2021 Lubr. Eng. 46 44 Google Scholar
[45]	纪敬虎, 周加鹏, 王沫阳, 王伟, 符永宏 2019 表面技术 48 139 Ji J H, Zhou J P, Wang M Y, Wang W, Fu Y H 2019 Surf. Technol. 48 139
[46]	Jiang Y Y, Yan Z J, Zhang S W, Shen Z Y, Sun H C 2022 Sci. Rep. 12 13455 Google Scholar
[47]	Wang Y, Jacobs G, König F, Zhang S, von Goeldel S 2023 Lubricants 11 20 Google Scholar
[48]	Huang J Y, Guan Y C, Ramakrishna S 2021 Tribol. Int. 162 107115 Google Scholar

[1]	Tang Peng-Bo, Wang Guan-Qing, Wang Lu, Shi Zhong-Yu, Li Yuan, Xu Jiang-Rong. Experimental investigation on dynamic behavior of single droplet impcating normally on dry sphere. Acta Physica Sinica, 2020, 69(2): 024702. doi: 10.7498/aps.69.20191141
[2]	Liu Chen-Hao, Liu Tian-Yu, Huang Ren-Zhong, Gao Tian-Fu, Shu Yao-Gen. Transport performance of coupled Brownian particles in rough ratchet. Acta Physica Sinica, 2019, 68(24): 240501. doi: 10.7498/aps.68.20191203
[3]	Li Rui-Tao, Tang Gang, Xia Hui, Xun Zhi-Peng, Li Jia-Xiang, Zhu Lei. Numerical simulation of melting dynamic process and surface scale properties of two-dimensional honeycomb lattice. Acta Physica Sinica, 2019, 68(5): 050301. doi: 10.7498/aps.68.20181774
[4]	Mei Tao, Chen Zhan-Xiu, Yang Li, Wang Kun, Miao Rui-Can. Effect of rough inner wall of nanochannel on fluid flow behavior. Acta Physica Sinica, 2019, 68(9): 094701. doi: 10.7498/aps.68.20181956
[5]	Zhang Yong-Jian, Ye Fang-Xia, Dai Jun, He Bin-Feng, Zang Du-Yang. Influence of nano-scaled roughness on evaporation patterns of colloidal droplets. Acta Physica Sinica, 2017, 66(6): 066101. doi: 10.7498/aps.66.066101
[6]	Chen Lei-Ming. Hydrodynamic theory of dry active matter. Acta Physica Sinica, 2016, 65(18): 186401. doi: 10.7498/aps.65.186401
[7]	Jiang Yue-Song, Nie Meng-Yao, Zhang Chong-Hui, Xin Can-Wei, Hua Hou-Qiang. Terahertz scattering property for the coated object of rough surface. Acta Physica Sinica, 2015, 64(2): 024101. doi: 10.7498/aps.64.024101
[8]	Mao Xiao-Li, Xiao Shao-Rong, Liu Qing-Quan, Li Min, Zhang Jia-Hong. Fluid dynamic analysis on solar heating error of radiosonde humidity measurement. Acta Physica Sinica, 2014, 63(14): 144701. doi: 10.7498/aps.63.144701
[9]	Zhang Cheng-Bin, Xu Zhao-Lin, Chen Yong-Ping. Molecular dynamics simulation on fluid flow and heat transfer in rough nanochannels. Acta Physica Sinica, 2014, 63(21): 214706. doi: 10.7498/aps.63.214706
[10]	Song Bao-Wei, Guo Yun-He, Luo Zhuang-Zhu, Xu Xiang-Hui, Wang Ying. Investigation about drag reduction annulus experiment of hydrophobic surface. Acta Physica Sinica, 2013, 62(15): 154701. doi: 10.7498/aps.62.154701
[11]	Jiang Yi-Min, Liu Mario. Hydrodynamic theory of grains, water and air. Acta Physica Sinica, 2013, 62(20): 204501. doi: 10.7498/aps.62.204501
[12]	Du Meng, Jin Ning-De, Gao Zhong-Ke, Zhu Lei, Wang Zhen-Ya. Multiscale permutation entropy analysis of oil-in-water type two-phase flow pattern. Acta Physica Sinica, 2012, 61(23): 230507. doi: 10.7498/aps.61.230507
[13]	Gao Zhong-Ke, Jin Ning-De, Yang Dan, Zhai Lu-Sheng, Du Meng. Complex networks from multivariate time series for characterizing nonlinear dynamics of two-phase flow patterns. Acta Physica Sinica, 2012, 61(12): 120510. doi: 10.7498/aps.61.120510
[14]	Xue Wei, Xie Guo-Xin, Wang Quan, Zhang Miao, Zheng Bei-Rong. The surface energy and nano-adhesion behavior of some micro-component material in MEMS. Acta Physica Sinica, 2009, 58(4): 2518-2522. doi: 10.7498/aps.58.2518
[15]	Zhang Bao-Ling, He Zhi-Bing, Wu Wei-Dong, Liu Xing-Hua, Yang Xiang-Dong. Influence of duty ratio on the fabrication of a-C:H film on microshell. Acta Physica Sinica, 2009, 58(9): 6436-6440. doi: 10.7498/aps.58.6436
[16]	Zhang Cheng-Bin, Chen Yong-Ping, Shi Ming-Heng, Fu Pan-Pan, Wu Jia-Feng. Fractal characteristics of surface roughness and its effect on laminar flow in microchannels. Acta Physica Sinica, 2009, 58(10): 7050-7056. doi: 10.7498/aps.58.7050
[17]	Wang Wei, Zhang Jie, Zhao Gang. Effect of a Planckian radiation field on population of bound-electrons. Acta Physica Sinica, 2008, 57(3): 1759-1764. doi: 10.7498/aps.57.1759
[18]	Hao Peng-Fei, Yao Zhao-Hui, He Feng. Experimental study of flow characteristics in rough microchannels. Acta Physica Sinica, 2007, 56(8): 4728-4732. doi: 10.7498/aps.56.4728
[19]	Zhang Cui-Ling, Zheng Rui-Lun, Teng Jiao. Influence of NiFeNb seed layer on hysteresis loops of permalloy films. Acta Physica Sinica, 2005, 54(11): 5389-5394. doi: 10.7498/aps.54.5389
[20]	XIA JIANG-FAN, ZHANG JUN, ZHANG JIE. MODELING THE ASTROPHYSICAL DYNAMICAL PROCESS WITH LASER-PLASMAS. Acta Physica Sinica, 2001, 50(5): 994-1000. doi: 10.7498/aps.50.994

Catalog

Vol. 73, Issue 11 - 2024-06-05

Metrics

Abstract views: 2030
PDF Downloads: 64
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板