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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.
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Keywords:
- porous media /
- Casson fluid /
- fractal
[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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