多孔介质中卡森流体的分形分析

员美娟; 郁伯铭; 郑伟; 袁洁

doi:10.7498/aps.60.024703

摘要

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理.

关键词:

多孔介质 /
卡森流体 /
分形

Abstract

Fractal models for flow rate, velocity, starting pressure gradient and effective permeability for Casson fluid in porous media are proposed based on the fractal properties of porous media and capillary model. The proposed models are expressed as functions of fractal dimension, porosity, maximum pore size and representative length of porous media. All parameters in the proposed expressions have clear physical meaning, and the proposed models relate the properties of Casson fluid to the structural parameters of porous media. The velocity, starting pressure gradient and effective permeability versus different parameters are discussed, and the analytical expressions reveal the physical principles for flow velocity, starting pressure gradient and effective permeability in porous media.

Keywords:

porous media /
Casson fluid /
fractal

作者及机构信息

(1)华中科技大学物理学院,武汉 430074; (2)武汉科技大学理学院应用物理系,冶金工业过程系统科学湖北省重点实验室,武汉 430081; (3)中国科学院测量与地球物理研究所动力大地测量学重点实验室,武汉 430077

基金项目: 湖北省耐火材料与高温陶瓷重点实验室-省部共建国家重点实验室培育基地开放基金(批准号:G201009),湖北省自然科学基金(批准号:2009CDB187), 冶金工业过程系统科学湖北省重点实验室开放基金(批准号:C201019),国家自然科学基金重点项目(批准号:10932010)和中国科学院动力大地测量学重点实验室开放基金(批准号:L09-14)资助的课题.

Authors and contacts

(1)Key Laboratory of Dynamic Geodesy, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China; (2)Key Laboratory of Systems Science in Metallurgical Process of Hubei Province, Department of Applied Physics, School of Science, Wuhan University of Science and Technology, Wuhan 430081, China; (3)School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

参考文献

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[2]	Chhabra R P, Comiti J, Machac I 2001 Chem. Eng. Sci. 56 1
[3]	Guo Y C, Zeng Y S, Lu D T 2005 Acta Phys. Sin. 54 802 (in Chinese) [郭永存、曾亿山、卢德唐 2005 54 802]
[4]	Xu Y S, Wu F M, Chen Y Y, Xu X Z 2003 Chin. Phys. 12 621
[5]	Xu Y S, Xu X Z 2002 Chin. Phys. 11 583
[6]	Wu B Z, Xu Y S, Liu Y, Huang G X 2005 Chin. Phys. 14 2046
[7]	Das B, Batra R L 1995 J. Theor. Biol. 175 1
[8]	Chevalley J 1991 J. Texture Stud. 22 219
[9]	Ochoa F G, Casas J A 1994 Chem. Eng. J. 53 B41
[10]	Kirsanov E A, Remizov S V 1999 Rheol. Acta 38 172
[11]	Casson N 1959 Rheology of Disperse Systems (London: Pergamon Press) p84
[12]	Deng S H, Gao S, Li Y P, Xu X Y, Lin S L 2010 Chin. Phys. B 19 040511
[13]	Xie T, Zou G H, William P, Kuang H L, Chen W 2010 Chin. Phys. B 19 059201
[14]	Han J J, Fu W J 2010 Chin. Phys. B 19 010205
[15]	Guo L X, Ren X C 2008 Chin. Phys. B 17 2956
[16]	Yang J, Lai X M, Peng G, Bian B M, Lu J 2009 Acta Phys. Sin. 58 3008 (in Chinese) [杨娟、赖晓明、彭刚、卞保民、陆建 2009 58 3008]
[17]	Su Y F, Li P X, Chen P, Xu Z F, Zhang X L 2009 Acta Phys. Sin. 58 4531 (in Chinese) [苏亚凤、李普选、陈鹏、徐忠锋、张孝林 2009 58 4531]
[18]	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]
[19]	Jiang Z H, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 7579 (in Chinese) [姜泽辉、赵海发、郑瑞华 2009 58 7579]
[20]	Hua S C, Wang H G, Wang L Y, Zhang W, Liu G 2008 Acta Phys. Sin. 57 1241 (in Chinese) [华邵春、王汉功、汪刘应、张武、刘顾 2008 57 1241]
[21]	Katz A J, Thompson A H 1985 Phys. Rev. Lett. 54 1325
[22]	Shen J, Wang Y, Wu X 1996 Acta Phys. Sin. 45 1501 (in Chinese) [沈军、王钰、吴翔 1996 45 1501]
[23]	Yun M J, Yu B M, Xu P, Cai J C 2008 Chin. Phys. Lett. 25 616
[24]	Yu B M, Cheng P 2002 Int. J. Heat Mass Transfer 45 2983
[25]	Kim S 2002 J. Non-Newton. Fluid Mech. 103 205
[26]	Yu B M 2005 Chin. Phys. Lett. 22 158
[27]	Govier G W, Aziz K 1972 The Flow of Complex Mixtures (New York: Krieger) p73
[28]	Bigyani Das, Batra R 1995 J. Theor. Biol. 175 1
[29]	Yun M J, Yu B M, Cai J C 2008 Int. J. Heat and Mass Transfer 51 1402
[30]	Wu J S, Yu B M 2007 Int. J. Heat and Mass Transfer 50 3925
[31]	Xu P, Yu B M 2008 Advances in Water Resources 31 74
[32]	Tsakiroglou C D 2002 J. Non-Newton. Fluid Mech. 105 79
[33]	Zhang B, Yu B M, Wang H X, Yun M J 2006 Fractals 14 171
[34]	Yu B M, Lee L J, Cao H Q 2002 Polym. Compos. 22 201
[35]	Yu B M, Li J H 2004 Chin. Phys. Lett. 21 1569

施引文献

[1]	Myers T G 2002 Phys. Rev. E 72 1
[2]	Chhabra R P, Comiti J, Machac I 2001 Chem. Eng. Sci. 56 1
[3]	Guo Y C, Zeng Y S, Lu D T 2005 Acta Phys. Sin. 54 802 (in Chinese) [郭永存、曾亿山、卢德唐 2005 54 802]
[4]	Xu Y S, Wu F M, Chen Y Y, Xu X Z 2003 Chin. Phys. 12 621
[5]	Xu Y S, Xu X Z 2002 Chin. Phys. 11 583
[6]	Wu B Z, Xu Y S, Liu Y, Huang G X 2005 Chin. Phys. 14 2046
[7]	Das B, Batra R L 1995 J. Theor. Biol. 175 1
[8]	Chevalley J 1991 J. Texture Stud. 22 219
[9]	Ochoa F G, Casas J A 1994 Chem. Eng. J. 53 B41
[10]	Kirsanov E A, Remizov S V 1999 Rheol. Acta 38 172
[11]	Casson N 1959 Rheology of Disperse Systems (London: Pergamon Press) p84
[12]	Deng S H, Gao S, Li Y P, Xu X Y, Lin S L 2010 Chin. Phys. B 19 040511
[13]	Xie T, Zou G H, William P, Kuang H L, Chen W 2010 Chin. Phys. B 19 059201
[14]	Han J J, Fu W J 2010 Chin. Phys. B 19 010205
[15]	Guo L X, Ren X C 2008 Chin. Phys. B 17 2956
[16]	Yang J, Lai X M, Peng G, Bian B M, Lu J 2009 Acta Phys. Sin. 58 3008 (in Chinese) [杨娟、赖晓明、彭刚、卞保民、陆建 2009 58 3008]
[17]	Su Y F, Li P X, Chen P, Xu Z F, Zhang X L 2009 Acta Phys. Sin. 58 4531 (in Chinese) [苏亚凤、李普选、陈鹏、徐忠锋、张孝林 2009 58 4531]
[18]	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]
[19]	Jiang Z H, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 7579 (in Chinese) [姜泽辉、赵海发、郑瑞华 2009 58 7579]
[20]	Hua S C, Wang H G, Wang L Y, Zhang W, Liu G 2008 Acta Phys. Sin. 57 1241 (in Chinese) [华邵春、王汉功、汪刘应、张武、刘顾 2008 57 1241]
[21]	Katz A J, Thompson A H 1985 Phys. Rev. Lett. 54 1325
[22]	Shen J, Wang Y, Wu X 1996 Acta Phys. Sin. 45 1501 (in Chinese) [沈军、王钰、吴翔 1996 45 1501]
[23]	Yun M J, Yu B M, Xu P, Cai J C 2008 Chin. Phys. Lett. 25 616
[24]	Yu B M, Cheng P 2002 Int. J. Heat Mass Transfer 45 2983
[25]	Kim S 2002 J. Non-Newton. Fluid Mech. 103 205
[26]	Yu B M 2005 Chin. Phys. Lett. 22 158
[27]	Govier G W, Aziz K 1972 The Flow of Complex Mixtures (New York: Krieger) p73
[28]	Bigyani Das, Batra R 1995 J. Theor. Biol. 175 1
[29]	Yun M J, Yu B M, Cai J C 2008 Int. J. Heat and Mass Transfer 51 1402
[30]	Wu J S, Yu B M 2007 Int. J. Heat and Mass Transfer 50 3925
[31]	Xu P, Yu B M 2008 Advances in Water Resources 31 74
[32]	Tsakiroglou C D 2002 J. Non-Newton. Fluid Mech. 105 79
[33]	Zhang B, Yu B M, Wang H X, Yun M J 2006 Fractals 14 171
[34]	Yu B M, Lee L J, Cao H Q 2002 Polym. Compos. 22 201
[35]	Yu B M, Li J H 2004 Chin. Phys. Lett. 21 1569

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