The collective movement or flow of microorganisms, such as bacteria or algae, brought on by their biological activity is called bioconvection. This study investigates a hybrid nanofluid’s unstable boundary layer stagnation point flow through a permeable sheet containing nanoparticles and gyrotactic bacteria. The potential applications of this finding in bioconvection, which is critical to ecological and biotechnological processes, make it significant. The study takes a mathematical modeling approach, using group-theoretical methods to convert a system of partial differential equations (PDEs) into a system of ordinary differential equations (ODEs). This allows for a thorough examination of the hybrid nanofluid’s flow characteristics. The latest investigation was spurred by the need to examine several parameters, such as the Prandtl number Pr, Peclet number Pe, Brownian motion coefficient <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2025_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>B</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$D_{B}$</EquationSource> </InlineEquation>, microorganism diffusion coefficient <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2025_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>N</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$D_{N}$</EquationSource> </InlineEquation>, thermophoresis diffusion coefficient <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2025_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>T</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$D_{T}$</EquationSource> </InlineEquation>, temperature ratio δT, concentration difference ΔC, and Schmidt number SC. As the value of ΔC increases, the velocity also rises. On the other hand, when Pr and δT increase, the velocity decreases. The temperature rises in proportion to the levels of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2025_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>B</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$D_{B}$</EquationSource> </InlineEquation>. The values of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2025_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>T</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$D_{T}$</EquationSource> </InlineEquation>, δT, and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2025_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>B</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$D_{B}$</EquationSource> </InlineEquation> increase along with the nanoparticles. However, it decreases when ΔC and SC increase. Elevations in <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2025_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>N</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$D_{N} $</EquationSource> </InlineEquation> are associated with increased densities of microorganisms. However, it drops when Pr, <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2025_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>T</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$D_{T}$</EquationSource> </InlineEquation>, and Pe increase. This study adds to the body of knowledge on bioconvection by addressing the interactions between nanoparticles and gyrotactic microorganisms in hybrid nanofluids and their previously unstudied consequences in a stagnation point flow setting, which make it novel and not discussed before.

Hybrid nanofluids and bioconvection: insights into bacterial behavior and particle interaction

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2025年2月27日

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E. M. Mohamed,
E. H. Nasr,
Karim K. Ahmed,
Homan Emadifar,
Hamdy M. Ahmed,
Soliman Alkhatib

摘要

The collective movement or flow of microorganisms, such as bacteria or algae, brought on by their biological activity is called bioconvection. This study investigates a hybrid nanofluid’s unstable boundary layer stagnation point flow through a permeable sheet containing nanoparticles and gyrotactic bacteria. The potential applications of this finding in bioconvection, which is critical to ecological and biotechnological processes, make it significant. The study takes a mathematical modeling approach, using group-theoretical methods to convert a system of partial differential equations (PDEs) into a system of ordinary differential equations (ODEs). This allows for a thorough examination of the hybrid nanofluid’s flow characteristics. The latest investigation was spurred by the need to examine several parameters, such as the Prandtl number Pr, Peclet number Pe, Brownian motion coefficient $D_{B}$ $D_{B}$ , microorganism diffusion coefficient $D_{N}$ $D_{N}$ , thermophoresis diffusion coefficient $D_{T}$ $D_{T}$ , temperature ratio δT, concentration difference ΔC, and Schmidt number SC. As the value of ΔC increases, the velocity also rises. On the other hand, when Pr and δT increase, the velocity decreases. The temperature rises in proportion to the levels of $D_{B}$ $D_{B}$ . The values of $D_{T}$ $D_{T}$ , δT, and $D_{B}$ $D_{B}$ increase along with the nanoparticles. However, it decreases when ΔC and SC increase. Elevations in $D_{N}$ $D_{N} $ are associated with increased densities of microorganisms. However, it drops when Pr, $D_{T}$ $D_{T}$ , and Pe increase. This study adds to the body of knowledge on bioconvection by addressing the interactions between nanoparticles and gyrotactic microorganisms in hybrid nanofluids and their previously unstudied consequences in a stagnation point flow setting, which make it novel and not discussed before.