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A fractal model for Herschel-Bulkley fluid in a capillary is proposed based on the fractal theory. The proposed model relates flow rate, velocity, starting pressure gradient and effective permeability to the rheological characteristics of fluid and the structural parameters of capillary, and all parameters in the proposed expressions have clear physical meanings. The analytical expressions reveal the physical principle for Herschel-Bulkley fluid flow in a capillary.
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Keywords:
- fractal /
- capillary /
- Herschel-Bulkley fluid
[1] Herschel W H, Bulkley R 1926 Colloid. Polym. Sci. 39 291
[2] Govier G W, Aziz K 1972 The Flow of Complex Mixtures in Pipes (New York: Litton) p143
[3] Balhoff M T, Thompson K E 2004 AICHE J. 50 3034
[4] Balhoff M T, Thompson K E 2006 Chem. Eng. Sci. 61 698
[5] Xu Y S, Wu F M, Chen Y Y, Xu X Z 2003 Chin. Phys. 12 621
[6] Yuan Y, Shi S H, Luo M K 2011 Chin. Phys. B 20 040509
[7] Xu Y S, Xu X Z 2002 Chin. Phys. 11 583
[8] Wu B Z, Xu Y S, Liu Y, Huang G X 2005 Chin. Phys. 14 2046
[9] Cai J C, Yu B M, Zou M Q, Mei M F 2010 Chem. Eng. Sci. 65 5178
[10] 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]
[11] Cai J C, Yu B M, Zou M Q, Luo L 2010 Energy Fuels 24 1860
[12] 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]
[13] 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]
[14] Cai J C, Yu B M 2010 Fractals 18 417
[15] Katz A J, Thompson A H 1985 Phys. Rev. Lett. 54 1325
[16] Shen J, Wang Y, Wu X 1996 Acta Phys. Sin. 45 1501 (in Chinese) [沈军, 王钰, 吴翔1996 451501]
[17] Yu B M, Cheng P 2002 Int. J. Heat Mass Transfer 45 2983
[18] Yun M J, Yu B M, Zheng W, Yuan J 2011 Acta Phys. Sin. 60 024703 (in Chinese) [员美娟, 郁伯铭, 郑伟, 袁洁 2011 60 024703]
[19] Wheatcraft S W, Tyler S W 1988 Water Res. Researches 24 566
[20] Yu B M 2005 Chin. Phys. Lett. 22 158
[21] Cai J C, Yu B M, Mei M F, Luo L 2010 Chin. Phys. Lett. 27 054701
[22] Yun M J, Yu B M, Xu P, Cai J C 2008 Chin. Phys. Lett. 25 616
[23] Cai J C, Yu B M 2011 Transp. Porous Media 89 251
[24] Borghesani A F 1988 Encyclopedia of Fluid Mechanics (Houston: Gulf) p89
[25] Deshpande N S, Barigou M 2001 Chem. Eng. Sci. 56 3845
[26] Cavatorta O N, Tonini R D 1987 Int. Commun. Heat Mass 14 359
[27] Yu B M, Li J H 2004 Chin. Phys. Lett. 21 1569
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[1] Herschel W H, Bulkley R 1926 Colloid. Polym. Sci. 39 291
[2] Govier G W, Aziz K 1972 The Flow of Complex Mixtures in Pipes (New York: Litton) p143
[3] Balhoff M T, Thompson K E 2004 AICHE J. 50 3034
[4] Balhoff M T, Thompson K E 2006 Chem. Eng. Sci. 61 698
[5] Xu Y S, Wu F M, Chen Y Y, Xu X Z 2003 Chin. Phys. 12 621
[6] Yuan Y, Shi S H, Luo M K 2011 Chin. Phys. B 20 040509
[7] Xu Y S, Xu X Z 2002 Chin. Phys. 11 583
[8] Wu B Z, Xu Y S, Liu Y, Huang G X 2005 Chin. Phys. 14 2046
[9] Cai J C, Yu B M, Zou M Q, Mei M F 2010 Chem. Eng. Sci. 65 5178
[10] 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]
[11] Cai J C, Yu B M, Zou M Q, Luo L 2010 Energy Fuels 24 1860
[12] 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]
[13] 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]
[14] Cai J C, Yu B M 2010 Fractals 18 417
[15] Katz A J, Thompson A H 1985 Phys. Rev. Lett. 54 1325
[16] Shen J, Wang Y, Wu X 1996 Acta Phys. Sin. 45 1501 (in Chinese) [沈军, 王钰, 吴翔1996 451501]
[17] Yu B M, Cheng P 2002 Int. J. Heat Mass Transfer 45 2983
[18] Yun M J, Yu B M, Zheng W, Yuan J 2011 Acta Phys. Sin. 60 024703 (in Chinese) [员美娟, 郁伯铭, 郑伟, 袁洁 2011 60 024703]
[19] Wheatcraft S W, Tyler S W 1988 Water Res. Researches 24 566
[20] Yu B M 2005 Chin. Phys. Lett. 22 158
[21] Cai J C, Yu B M, Mei M F, Luo L 2010 Chin. Phys. Lett. 27 054701
[22] Yun M J, Yu B M, Xu P, Cai J C 2008 Chin. Phys. Lett. 25 616
[23] Cai J C, Yu B M 2011 Transp. Porous Media 89 251
[24] Borghesani A F 1988 Encyclopedia of Fluid Mechanics (Houston: Gulf) p89
[25] Deshpande N S, Barigou M 2001 Chem. Eng. Sci. 56 3845
[26] Cavatorta O N, Tonini R D 1987 Int. Commun. Heat Mass 14 359
[27] Yu B M, Li J H 2004 Chin. Phys. Lett. 21 1569
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