Blood flow in capillaries by using porous media model

Springer Science and Business Media LLC - Tập 14 - Trang 46-49 - 2007
Fu-quan Song1, You-sheng Xu1, Hua-mei Li1
1Department of Physics, Zhejiang Normal University, Jinhua, China

Tóm tắt

The blood and tissue liquid flow are studied by microcirculation method or porous flow model. The blood flow in capillaries is studied by used the porous media flow model in this paper. The advantage of the model is to research the whole flow characteristics, and it can be used to study the blood flow in animal viscera. By used the Casson constitutive model, the differential equation of blood flow in capillaries is derived, and the characteristics of steady flow and transient flow are solved by numerical method. The result shows that the more threshold stress is, the bigger flow resistance is, and the flow is different from the newtonian fluid flow. This method is a new useful approach to study the biological fluid mechanics.

Tài liệu tham khảo

TAO Zu-lai. Biological Fluid Mechanics[M]. Beijing: Science Press, 1984. (in Chinese) GUO Shang-ping, YU Da-shen, WU Wan-ti. The physical characteristics of the porous media concerning flow in viscera[J]. Acta Mechanica Sinica, 1982, 15(1): 26–33. (in Chinese) WU Wang-yi, SHI Chang-chun, WANG Lu. The double porosity media model for the mass transfer between capillary and tissue [J]. Acta Mechanica Sinica, 1989, 21(6): 649–656. (in Chinese) LI Zhao-qiang, LI Li. A mathematical model of blood flow in lung microcirculation[J]. Journal of Biomath Ematics, 1994, 9(1): 85–90. (in Chinese) LIU Qing-jie, GUO Shang-ping. A double porosity model and flow pattern for the liver lobule[J]. Journal of Chongqing University: Natural Science Edition, 2000, 23(S1): 177–180.(in Chinese) XU Shi-xiong, LIU Yu-feng, ZHOU Zu-wei. Effect of dynamical variation of tissue pressure on exchange between capillary and tissue[J]. Journal of Medical Biomechanics, 2001, 16(3): 129–134. (in Chinese) JIA Xiao-bo, PAN Yi-shan, ZHANG Fang. The analysis of double porosity model[J]. Journal of Medical Biomechanics, 2003, 18(1): 42–45. (in Chinese) KHALED A R A, VAFAI K. The role of porous media in modeling flow and heat transfer in biological tissues[J]. International Journal of Heat and Mass Transfer, 2003, 46(26): 4989–5003. PREZIOSI L, FARINA A. On Darcy’s law for growing porous media[J]. International Journal of Non-Linear Mechanics, 2002, 37: 485–491. BRINKMAN H C. On the permeability of media consisting of closely packed porous particles[J]. Appl Sci Res A, 1947(1): 81–86. KONG Xiang-yan. Advanced Mechanics of Fluid in Porous Media[M]. Hefei: Press of University of Science and Technology of China, 1984. (in Chinese) SONG Fu-quan, LIU Ci-qun. Transient pressure of percolation during one production and one shutting in one dimension porous media with threshold pressure gradient[J]. Applied Mathematics and Mechanics, 1999, 20(1): 25–29. (in Chinese)