The onset of Marangoni bio-thermal convection in a layer of fluid containing gyrotactic microorganisms

AIMS Mathematics

Latifa I. Khayyat¹  Abdullah A. Abdullah² 

[1] 1. Department of Biology, College of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia;2. Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia;

关键词: linear stability;    bio-thermal convection;    marangoni;    gyrotactic microorganisms;    chebyshev tau method;   

DOI  :  10.3934/math.2021787

来源: DOAJ

【 摘 要 】

The problem of the onset of Marangoni bio-thermal convection is investigated for a horizontal layer of fluid containing motile gyrotactic microorganisms. The fluid layer is assumed to rest on a rigid surface with fixed temperature and the top boundary of the layer is assumed to be a free non deformable surface. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau numerical method. The critical values of the thermal Marangoni number are calculated for several values of the bioconvection Péclet number, bioconvection Marangoni number, bioconvection Lewis number and gyrotaxis number. The results of this study showed that the existence of gyrotactic microorganisms increases the critical thermal Marangoni numbers. Moreover, the critical eigenvalues obtained were real-valued indicating that the mode of instability is via a stationary mode, however oscillatory mode is possible for some ranges of the parameters values.

【 授权许可】

Unknown