Linear Stability Analysis on Thermo-Bioconvection of Gyrotactic Microorganisms in a Horizontal Porous Layer Saturated by a Power-Law Fluid

DAI Dexuan; WANG Shaowei

doi:10.21656/1000-0887.390298

Volume 40 Issue 8

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DAI Dexuan, WANG Shaowei. Linear Stability Analysis on Thermo-Bioconvection of Gyrotactic Microorganisms in a Horizontal Porous Layer Saturated by a Power-Law Fluid[J]. Applied Mathematics and Mechanics, 2019, 40(8): 856-865. doi: 10.21656/1000-0887.390298

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Linear Stability Analysis on Thermo-Bioconvection of Gyrotactic Microorganisms in a Horizontal Porous Layer Saturated by a Power-Law Fluid

doi: 10.21656/1000-0887.390298

School of Civil Engineering, Shandong University, Jinan 250061, P.R.China

Funds: The National Natural Science Foundation of China（11672164）

Received Date: 2018-11-21
Rev Recd Date: 2018-12-17
Publish Date: 2019-08-01

Abstract

Abstract

To study the stability of bioconvection in a non-Newtonian fluid-saturated porous medium, the linear stability analysis with the model for gyrotactic microorganisms and power-law fluids was carried out. Based on the Galerkin method, the governing equation was solved to get the numerical solution of the biological Rayleigh number, which represents the stability of bioconvection. The effects of various parameters on the change of power-law indexes were studied in detail. It is concluded that, as the fluid velocity increases, the influence of the power-law index on the stability of the bioconvection will change, and this change will be affected by the thermal Rayleigh number and the biological Lewis number. The results also show that, as the gyrotactic capability of microorganisms increases, the bioconvection stability will decrease, and properly increasing the power-law index is conducive to the stability.
- bioconvection,
- power-law fluid,
- gyrotactic capability,
- porous medium,
- Galerkin method

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References

[1]	WAGER H. On the effect of gravity upon the movements and aggregation of euglena viridis, ehrb, and other microorganisms[J]. Philosophical Transactions of the Royal Society B: Biological Sciences,1911,201(1): 333-390.
[2]	KESSLER J O. Hydrodynamic focusing of motile algal cells[J]. Nature,1985,313(5999): 218-220.
[3]	KUZNETSOV A V, AVRAMENKO A A. Stability analysis of bioconvection of gyrotactic motile microorganisms in a fluid saturated porous medium[J]. Transport in Porous Media,2003,53(1): 95-104.
[4]	NIELD D A, KUZNETSOV A V. The onset of bio-thermal convection in a suspension of gyrotactic microorganisms in a fluid layer: oscillatory convection[J]. International Journal of Thermal Sciences,2006,45(10): 990-997.
[5]	ZHAO M, XIAO Y, WANG S. Linear stability of thermal-bioconvection in a suspension of gyrotactic micro-organisms[J]. International Journal of Heat and Mass Transfer,2018,126: 95-102.
[6]	BARLETTA A, NIELD D A. Linear instability of the horizontal throughflow in a plane porous layer saturated by a power-law fluid[J]. Physics of Fluids,2011,23(1): 013102.
[7]	BARLETTA A, STORESLETTEN L. Linear instability of the vertical throughflow in a horizontal porous layer saturated by a power-law fluid[J]. International Journal of Heat and Mass Transfer,2016,99: 293-302.
[8]	罗艳, 李鸣, 杨大勇. 微通道内电渗压力混合驱动幂律流体流动模拟[J]. 应用数学和力学, 2016,37(4): 373-381.(LUO Yan, LI Ming, YANG Dayong. Simmulation of mixed electroosmotic and pressure-driven flows of power-law fluids in microchannels[J]. Applied Mathematics and Mechanics,2016,37(4): 373-381.(in Chinese))
[9]	田兴旺, 王平, 徐士鸣. 颗粒堆积多孔介质内幂律流体的流动阻力特性[J]. 哈尔滨工业大学学报, 2017,49(1): 126-132.(TIAN Xingwang, WANG Ping, XU Shiming. Flow resistance characteristics of power law fluid flow through granular porous medium[J]. Journal of Harbin Institute of Technology,2017,49(1): 126-132.(in Chinese))
[10]	杨旭, 梁英杰, 孙洪广, 等. 空间分数阶非Newton流体本构及圆管流动规律研究[J]. 应用数学和力学, 2018,39(11): 1213-1226.(YANG Xu, LIANG Yingjie, SUN Hongguang, et al. A study on the constitutive relation and the flow of spatial fractional non-Newtonian fluid in circular pipes[J]. Applied Mathematics and Mechanics,2018,39(11): 1213-1226.(in Chinese))
[11]	CHRISTOPHER R H, MIDDLEMAN S. Power-law flow through a packed tube[J]. Industrial & Engineering Chemistry Fundamentals,1965,4(4): 422-426.
[12]	GRAY D D, GIORGINI A. The validity of the Boussinesq approximation for liquids and gases[J]. International Journal of Heat and Mass Transfer,1976,19(5): 545-551.
[13]	PEDLEY T J, KESSLER J O. The orientation of spheroidal microorganisms swimming in a flow field[J]. Proceedings of the Royal Society of London,1987,231(1262): 47-70.
[14]	NARAYANA M, SIBANDA P, MOTSA S S, et al. Linear and nonlinear stability analysis of binary Maxwell fluid convection in a porous medium[J]. Heat and Mass Transfer,2012,48(5): 863-874.
[15]	WANG S, TAN W. Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below[J]. Physics Letters A,2008,372(17): 3046-3050.