Exploring stability of Jeffrey fluids in anisotropic porous media: incorporating Soret effects and microbial systems

Abstract

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.