Purpose

This paper aims to present a study on stability analysis of Jeffrey fluids in the presence of emergent chemical gradients within microbial systems of anisotropic porous media.

Design/methodology/approach

This study uses an effective method that combines non-dimensionalization, normal mode analysis and linear stability analysis to examine the stability of Jeffrey fluids in the presence of emergent chemical gradients inside microbial systems in anisotropic porous media. The study focuses on determining critical values and understanding how temperature gradients, concentration gradients and chemical reactions influence the onset of bioconvection patterns. Mathematical transformations and analytical approaches are used to investigate the system’s complicated dynamics and the interaction of numerous characteristics that influence stability.

Findings

The analysis is performed using the Jeffrey-Darcy type and Boussinesq estimation. The process involves using non-dimensionalization, using the normal mode approach and conducting linear stability analysis to convert the field equations into ordinary differential equations. The conventional thermal Rayleigh Darcy number RDa,c is derived as a comprehensive function of various parameters, and it remains unaffected by the bio convection Lewis number Łe. Indeed, elevating the values of ζ and γ′ in the interval of 0 to 1 has been noted to expedite the formation of bioconvection patterns while concurrently expanding the dimensions of convective cells. The purpose of this investigation is to learn how the temperature gradient affects the concentration gradient and, in turn, the stability and initiation of bioconvection by taking the Soret effect into the equation. The results provide insightful understandings of the intricate dynamics of fluid systems affected by chemical and biological elements, providing possibilities for possible industrial and biological process applications. The findings illustrate that augmenting both microbe concentration and the bioconvection Péclet number results in an unstable system. In this study, the experimental Rayleigh number RDa,c was determined to be 4π2at the critical wave number ( δcˇ) of π.

Originality/value

The study’s novelty originated from its investigation of a novel and complicated system incorporating Jeffrey fluids, emergent chemical gradients and anisotropic porous media, as well as the use of mathematical and analytical approaches to explore the system’s stability and dynamics.

中文翻译：

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探索杰弗里流体在各向异性多孔介质中的稳定性：结合索雷特效应和微生物系统

 目的

本文旨在研究各向异性多孔介质微生物系统中存在紧急化学梯度时 Jeffrey 流体的稳定性分析。

设计/方法论/途径

本研究采用一种结合无量纲、简正模态分析和线性稳定性分析的有效方法来检查杰弗里流体在各向异性多孔介质中微生物系统内存在新兴化学梯度的情况下的稳定性。该研究的重点是确定临界值并了解温度梯度、浓度梯度和化学反应如何影响生物对流模式的发生。数学变换和分析方法用于研究系统的复杂动力学以及影响稳定性的众多特征的相互作用。

 发现

使用 Jeffrey-Darcy 类型和 Boussinesq 估计进行分析。该过程涉及使用无量纲化、使用简正模态方法并进行线性稳定性分析，将场方程转换为常微分方程。常规热瑞利达西数右D一个, c是作为各种参数的综合函数导出的，并且不受生物对流路易斯数的影响Ł e 。事实上，提高ze和γ ′在 0 到 1 的区间内，人们注意到可以加速生物对流模式的形成，同时扩大对流单元的尺寸。本研究的目的是通过将索雷效应纳入方程，了解温度梯度如何影响浓度梯度，进而了解生物对流的稳定性和启动。研究结果提供了对受化学和生物元素影响的流体系统的复杂动力学的深刻理解，为可能的工业和生物过程应用提供了可能性。研究结果表明，增加微生物浓度和生物对流佩克莱特数会导致系统不稳定。 本研究中，实验瑞利数右D一个, c被确定为4 π 2在临界波数（ δ c ˇ ) 的π 。

 原创性/价值

该研究的新颖性源于其对包含杰弗里流体、涌现化学梯度和各向异性多孔介质的新颖而复杂的系统的研究，以及使用数学和分析方法来探索系统的稳定性和动力学。