<p>This study presents advanced numerical simulation of thermotaxis behavior in thermotactic microorganisms suspended within a fluid-saturated porous medium. Based on our previously established linear stability analysis framework, we extend the investigation to supercritical regimes, where thermotactic bioconvection patterns emerge due to the dynamic coupling between microorganism motility, thermal diffusion, and induced fluid flow. The mathematical formulation employs volume-averaged governing equations incorporating Darcy’s law and the Boussinesq approximation, with a focus on key dimensionless parameters including the Peclet number (Pe), Lewis number (Le), thermal Rayleigh number (Ra<sub><i>T</i></sub>), and bioconvection Rayleigh number (Ra<sub><i>N</i></sub>).The simulation explores various heating configurations—namely heated-from-below and heated-from-above—demonstrating how Pe modulates the onset of pattern formation, while Le exerts a stabilizing influence. This research provides the first numerical evidence of thermotactic bioconvection beyond critical thresholds in porous media. The findings elucidate fundamental mechanisms governing microorganism gradient-based motion and have potential applications in biosystems modeling, including thermally guided sperm migration, and explanations for Harmful Algal Bloom formation on water surfaces. The interplay between parameters offers a comprehensive insight into the regulation of bioconvection regimes, contributing to broader understanding in biological transport phenomena, microfluidics, and environmental modeling.</p>

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Navigating Gradient-Based Motion Patterns: Modeling and Advanced Simulation of Microorganism Thermotaxis in Porous Media

  • My Thi Nguyen,
  • Tri Nguyen-Quang

摘要

This study presents advanced numerical simulation of thermotaxis behavior in thermotactic microorganisms suspended within a fluid-saturated porous medium. Based on our previously established linear stability analysis framework, we extend the investigation to supercritical regimes, where thermotactic bioconvection patterns emerge due to the dynamic coupling between microorganism motility, thermal diffusion, and induced fluid flow. The mathematical formulation employs volume-averaged governing equations incorporating Darcy’s law and the Boussinesq approximation, with a focus on key dimensionless parameters including the Peclet number (Pe), Lewis number (Le), thermal Rayleigh number (RaT), and bioconvection Rayleigh number (RaN).The simulation explores various heating configurations—namely heated-from-below and heated-from-above—demonstrating how Pe modulates the onset of pattern formation, while Le exerts a stabilizing influence. This research provides the first numerical evidence of thermotactic bioconvection beyond critical thresholds in porous media. The findings elucidate fundamental mechanisms governing microorganism gradient-based motion and have potential applications in biosystems modeling, including thermally guided sperm migration, and explanations for Harmful Algal Bloom formation on water surfaces. The interplay between parameters offers a comprehensive insight into the regulation of bioconvection regimes, contributing to broader understanding in biological transport phenomena, microfluidics, and environmental modeling.