<p>This study investigates the influence of self-generated fluid motion, primarily driven by buoyancy, on bio-convection within a Newtonian fluid populated by gyrotactic microorganisms. We have analyzed the weakly nonlinear instability of bio-convection induced by self-induced flows an infinite horizontal plate system, separated by a constant distance in buoyant fluid. To achieve this, we haveve driven the Ginzburg-Landau equation (GLE). The Sherwood number is calculated to quantify the mass transfer. The solvability condition is utilized to determine the third-order perturbation of the variable, which is subsequently used to calculate the GLE. The findings are visually presented to elucidate the impact of various system parameters on mass transfer. The current study shows that an increment in Schmidt number (<i>Sc</i>) will enhance the rate of mass transport. The primary objective of this study is to demonstrate that convection commences later with conduction when the cell shape (eccentricity <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_825_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha _0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>) is circular (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_825_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha _0\rightarrow 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>α</mi> <mn>0</mn> </msub> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>) in comparison to when it becomes more parabolic. Consequently, the convection rate will be elevated for a parabolic cell shape (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_825_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha _0 \rightarrow 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>α</mi> <mn>0</mn> </msub> <mo stretchy="false">→</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>). Conversely, the bio-convection Lewis number (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_825_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$L_b$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>b</mi> </msub> </math></EquationSource> </InlineEquation>) exhibits a reverse effect on the rate of mass transport. This work has potential application in environmental, industrial, and biomedical fields.</p>

Investigating the nonlinear behavior of microorganisms in buoyant fluids

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发表日期：

2025年3月19日

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Anurag,
Anupama Singh,
Anand Kumar,
Atul Jakhar

摘要

This study investigates the influence of self-generated fluid motion, primarily driven by buoyancy, on bio-convection within a Newtonian fluid populated by gyrotactic microorganisms. We have analyzed the weakly nonlinear instability of bio-convection induced by self-induced flows an infinite horizontal plate system, separated by a constant distance in buoyant fluid. To achieve this, we haveve driven the Ginzburg-Landau equation (GLE). The Sherwood number is calculated to quantify the mass transfer. The solvability condition is utilized to determine the third-order perturbation of the variable, which is subsequently used to calculate the GLE. The findings are visually presented to elucidate the impact of various system parameters on mass transfer. The current study shows that an increment in Schmidt number (Sc) will enhance the rate of mass transport. The primary objective of this study is to demonstrate that convection commences later with conduction when the cell shape (eccentricity $\alpha _0$ $α_{0}$ ) is circular ( $\alpha _0\rightarrow 0$ $α_{0} \to 0$ ) in comparison to when it becomes more parabolic. Consequently, the convection rate will be elevated for a parabolic cell shape ( $\alpha _0 \rightarrow 1$ $α_{0} \to 1$ ). Conversely, the bio-convection Lewis number ( $L_b$ $L_{b}$ ) exhibits a reverse effect on the rate of mass transport. This work has potential application in environmental, industrial, and biomedical fields.