Stability analysis of a chemotaxis-convection-diffusion coupling system with the roles of deformed free surface and surface tension
Journal
Journal of Fluid Mechanics
Journal Volume
923
Date Issued
2021
Author(s)
Abstract
We consider a three-dimensional chemotaxis-convection-diffusion coupled system with the effect of surface tension at the deformed free surface. The novelty of this research is to explore the impact of surface tension on bioconvection. Our aim is to determine the nature of the instability at the onset of bioconvection in a chemotaxis-convection-diffusion system involving surface tension by performing a detailed linear stability analysis of steady-state cell and oxygen concentration distributions. The influence of the surface tension on the accumulated chemotaxis cells at the deformed free surface is studied analytically to illustrate its effect on the stability of the system. The Froude number, and capillary number, are two additional parameters introduced here. A detailed parametric study is undertaken to investigate the roles of the critical Rayleigh number, as well as and, in the chemotaxis system. Linear stability results revealed that an increasing value of would stabilize the chemotaxis system. At a higher value of, the motion of the cells is faster towards the free surface, and as the surface tension force increases, less accumulated cells are found at the free surface. A cluster of the cells can be observed mostly at the trough rather than on the crest of the wave profile. While experimental results for the present model are not yet available, the results of the linear stability analysis provide useful information about the system's stability. ? 2021 The Author(s). Published by Cambridge University Press.
Subjects
bioconvection
buoyancy-driven instability
Biochemistry
Cells
Cytology
Diffusion in liquids
Heat convection
Linear stability analysis
Surface tension
Capillary numbers
Convection diffusion
Critical Rayleigh number
Linear Stability
Oxygen concentrations
Stability analysis
Surface tension force
System's stabilities
System stability
buoyancy
chemotaxis
convection
Froude number
Rayleigh number
surface tension
SDGs
Type
journal article