Bioconvection of gravitactic micro-organisms in rectangular enclosures |
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| Affiliation: | 1. Institut Montpelliérain Alexander Grothendieck, University of Montpellier, France;2. INRA, UR0050, Laboratoire de Biotechnologie de l’Environnement, Narbonne 11100, France;3. Dep. Mat., Universidad Tecnica Federico Santa Maria, Avda Espana 1680, Valparaiso, Chile;1. Department of Mathematics, School of Science, Dalian Maritime University, Dalian 116026 Liaoning, PR China;2. College of Transportation Engineering, Dalian Maritime University, Dalian 116026 Liaoning, PR China;3. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024 Liaoning, PR China;4. Key Laboratory of Intelligent Control and Optimization for Industrial Equipment (Dalian University of Technology), Ministry of Education;5. Teaching and Research Office of Mathematics, Department of Basics, PLA Dalian Naval Academy, Dalian 116018, Liaoning, PR China;6. School of Mathematical Sciences, Sunway University, Bandar Sunway, 47500 Selangor Darul Ehsan, Malaysia;7. The Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China |
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| Abstract: | This paper investigates the gravitactic bioconvection in rectangular enclosures. The governing equations are the continuity, the Navier–Stokes equations with the Boussinesq approximation and the diffusion equation for the motile micro-organisms. The control volume method is used to solve numerically the complete set of governing equations. The effects of bioconvection Peclet number from 0.1 to 10 and the aspect ratio from 1 to 5 are investigated on the onset of bioconvection. It was found that the bifurcation was subcritical in all cases. The critical Rayleigh number is decreased with increasing bioconvection Peclet number and with increasing aspect ratio. |
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