In this study, natural bioconvection flow in the presence of magnetotactic bacteria is numerically investigated in a square cavity involving water and two concentrations. The concentrations are considered as oxygen and iron (Fe) concentrations. This is the first study to simultaneously incorporate dual concentration equations into the governing bioconvection model, thereby extending the existing single-concentration frameworks. The time-independent governing dimensionless equations in stream function-vorticity form are numerically solved using the radial basis function collocation method. The numerical results are observed in different Rayleigh (Ra), bioconvection Rayleigh (Rb), Peclet (Pe), Lewis (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">${\text{Le}}_1, {\text{Le}}_2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>Le</mtext> <mn>1</mn> </msub> <mo>,</mo> <msub> <mtext>Le</mtext> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>) numbers and the buoyancy ratio parameters (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$Nr_1, Nr_2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>N</mi> <msub> <mi>r</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>). The average Nusselt and Sherwood numbers along the heated wall, and the average density of bacteria are calculated as well as plotted contours. In the case of two concentrations, the diffusivity of bacteria is assumed to be equal to one of the concentration diffusivity. Firstly, the diffusivity of bacteria is assumed to be equal to the diffusivity of oxygen concentration. The average Nusselt number as a measurement of convective heat transfer increases 216.8%, 43.3%, 104% and 29.7% with the rise in Ra, Rb, Pe and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">${\text{Le}}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Le</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, respectively. The elevation in buoyancy ratio parameters affects average Nusselt number, the average Sherwood number for Fe concentration and the average density of bacteria inversely. The average Sherwood number for Fe concentration as an indicator for the convective mass transfer of Fe remarkably decreases 55.1% as <InlineEquation ID="IEq4"> <EquationSource Format="TEX">${\text{Le}}_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Le</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> increases in this first assumption. On the other side, the second assumption for equality of diffusivity of bacteria to the diffusivity of Fe reduces the convective heat transfer significantly as <InlineEquation ID="IEq5"> <EquationSource Format="TEX">${\text{Le}}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Le</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> rises. These findings establish new benchmarks for understanding multi-concentration bioconvective transport in magnetotactic systems, offering insights for future bioengineering and environmental applications.

Numerical investigation on bioconvection flow in the presence of two concentrations

期刊论文
发表日期：

2025年12月1日

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Bengisen Pekmen,
Merve Gurbuz-Caldag

摘要

In this study, natural bioconvection flow in the presence of magnetotactic bacteria is numerically investigated in a square cavity involving water and two concentrations. The concentrations are considered as oxygen and iron (Fe) concentrations. This is the first study to simultaneously incorporate dual concentration equations into the governing bioconvection model, thereby extending the existing single-concentration frameworks. The time-independent governing dimensionless equations in stream function-vorticity form are numerically solved using the radial basis function collocation method. The numerical results are observed in different Rayleigh (Ra), bioconvection Rayleigh (Rb), Peclet (Pe), Lewis ( ${\text{Le}}_1, {\text{Le}}_2$ ${Le}_{1}, {Le}_{2}$ ) numbers and the buoyancy ratio parameters ( $Nr_1, Nr_2$ $N r_{1}, N r_{2}$ ). The average Nusselt and Sherwood numbers along the heated wall, and the average density of bacteria are calculated as well as plotted contours. In the case of two concentrations, the diffusivity of bacteria is assumed to be equal to one of the concentration diffusivity. Firstly, the diffusivity of bacteria is assumed to be equal to the diffusivity of oxygen concentration. The average Nusselt number as a measurement of convective heat transfer increases 216.8%, 43.3%, 104% and 29.7% with the rise in Ra, Rb, Pe and ${\text{Le}}_2$ ${Le}_{2}$ , respectively. The elevation in buoyancy ratio parameters affects average Nusselt number, the average Sherwood number for Fe concentration and the average density of bacteria inversely. The average Sherwood number for Fe concentration as an indicator for the convective mass transfer of Fe remarkably decreases 55.1% as ${\text{Le}}_1$ ${Le}_{1}$ increases in this first assumption. On the other side, the second assumption for equality of diffusivity of bacteria to the diffusivity of Fe reduces the convective heat transfer significantly as ${\text{Le}}_2$ ${Le}_{2}$ rises. These findings establish new benchmarks for understanding multi-concentration bioconvective transport in magnetotactic systems, offering insights for future bioengineering and environmental applications.