趋旋性微生物在幂律流体饱和水平多孔层中的热-生物对流稳定性分析

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

基于趋旋性微生物和幂律流体模型,研究了在含有非 Newton 流体饱和多孔介质中生物对流的线性稳定性问题.利用 Galerkin 数值方法求解了该系统的控制方程,得到生物Rayleigh 数的数值解,讨论了非 Newton 流体的幂律指数对生物对流稳定性在假塑性流体和膨胀性流体间的变化规律.研究结果表明,随着幂律流体的速度增大,幂律指数对生物对流稳定性的影响会发生变化,并且这种变化会受到热Rayleigh 数和生物 Lewis 数的影响.另外,微生物趋旋性特征越明显,生物对流系统就越不稳定,而适当增大非 Newton 流体的幂律指数则有利于系统的稳定性.

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.