Stability Analysis Of Bioconvection Of Gyrotatic Microorganisms In A Horizontal Porous Layer Saturated By Non-Newtonian Fluid

Bioconvection is a natural phenomenon that occurs frequently in fluids with microorganisms and is of great significance to human beings.Moreover,bioconvection is a developing interdisciplinary branch of learning,the study of which can involve microbiology,fluid dynamics,stability theory,and seepage mechanics.In this paper,the bioconvection stability of gyrotatic microorganisms in non-Newtonian fluid-saturated porous media was studied.Characteristics of microorganisms and properties of non-Newtonian fluids were used to examine the effects on bioconvection stability.The non-Newtonian fluids used in the study included viscoelastic fluids and power-law fluids.For viscoelastic fluids,the Maxwell linear viscoelastic model is adopted;for power-law fluids,the Ostwald-de Waele model is applied.Considering the properties of porous and non-Newtonian fluids,the classical Darcy law needs to be extended.In addition,heating or cooling at the bottom of the porous layer is used to affect the bioconvection stability.In this paper,the stability analysis and numerical solution of the governing equations of the system are carried out by linear stability theory and Galerkin method,respectively.Linear stability analysis includes the onset of steady convection and the instability of oscillatory convection.The expression of the bio-Rayleigh number is numerically calculated to represent the stability of the bioconvection,and the expression contains all the influence parameters that need to be studied.The greater the bio-Rayleigh number,the stronger the stability of bioconvection.For viscoelastic fluids,the parameters that affect the bio-Rayleigh number mainly include temperature gradient,relaxation time of viscoelastic fluid and microbial gyrotaxis,average swimming velocity and diffusion coefficient.The results show that the stronger the gyrotaxis and the higher the diffusion coefficient,the more instable of bioconvection.The effect of microbial average swimming velocity on the stability of bioconvection is divided into two cases.When the velocity is small,it has a destructive effect on stability;when its velocity is large,it will enhance the stability of the system.In the oscillatory convection,the average swimming velocity of the microorganisms only has a destructive effect on the stability of the bioconvection.The stronger the elasticity of the viscoelastic fluid,the weaker the stability of bioconvection.As the fluid elasticity increases,the oscillatory convection phenomenon is more likely to occur.For power-law fluids,the parameters that affect the bio-Rayleigh number mainly include temperature gradient,power-law index,steady velocity of vertical flow and microbial gyrotaxis,average swimming velocity and diffusion coefficient.The results show that the velocity of vertical flow affects the stability of bioconvection in power-law fluids as follows:when the fluid is a pseudoplastic,the smaller the flow velocity is,the more stable the system is.When the fluid is a dilatant fluid,the greater the flow velocity,the more stable the system.The power of gyrotaxis of microorganisms will accelerate the generation of bioconvection and weaken the stability of the system.At the same time,the microorganisms of stronger gyrotaxis are more sensitive to the power-law index.In the case of oscillatory convection,the study found that pseudoplastic fluids are more prone to oscillatory motion than dilatant fluids.This study extends the application of bioconvection in non-Newtonian fluids and provides theoretical support for bioconvection experiments in non-Newtonian fluids like viscoelastic fluids and power-law fluids.