Gravitationally modulated bio-convection in complex porous media: a multiscale approach to heat and mass transfer with reactive flow conditions

Convection in porous media plays a vital role in engineering and natural processes such as geothermal energy recovery, environmental remediation, and microbial transport in bioreactors. This study investigates how gravitational modulation influences bio-convective heat and mass transfer in porous materials saturated with motile microorganisms under reactive flow conditions. The main aim is to develop a comprehensive multiscale model that couples thermal, solutal, microbial, and gravitational processes with chemical reactions. The governing equations are formulated using Darcy–Brinkman and energy transport relations, incorporating activation energy, cross-diffusion effects, and microbial motility. Linear stability analysis is used to determine the critical Rayleigh–Darcy number marking the onset of convection, while weakly nonlinear analysis based on the Ginzburg–Landau equation is employed to capture amplitude evolution and post-onset transport dynamics. The results show that gravitational modulation lowers the critical threshold for instability, thereby promoting earlier onset of convection, while parameters, such as Darcy number, Lewis number, and activation energy, exert a stabilizing influence. Nonlinear analysis reveals that heat and mass transfer rates, represented by the Nusselt and Sherwood numbers, are significantly affected by modulation frequency, amplitude, and microbial activity, leading to either enhancement or suppression of convective transport. Overall, the findings highlight the dual role of gravitational modulation as both a destabilizing factor and a control mechanism, showing that higher modulation frequencies stabilize the system, while larger amplitudes promote earlier convection onset.

This study investigates how gravitational modulation influences bio-convective heat and mass transfer in porous media with motile microorganisms. Using Darcy–Brinkman modeling and linear/nonlinear stability analysis, the critical Rayleigh–Darcy threshold is determined. Linear analysis yields marginal stability curves, while nonlinear theory derives a Ginzburg–Landau amplitude equation. The impacts of microbial activity, chemical reactions, Soret and Dufour effects are revealed through variations in Nusselt and Sherwood numbers.