<p>This study investigates the nonlinear dynamics of binary fluid mixtures under the combined effect of viscous dissipation, thermodiffusion, magnetic forces, and porous media resistance. The magnetic field and porous medium add stabilizing mechanisms that reshape convection patterns and alter bifurcation thresholds. Through weakly nonlinear stability analysis, critical conditions for supercritical and subcritical bifurcations are derived and analyzed. The findings indicate that magnetic fields suppress convective motions via Lorentz forces, while porous media dampen flow through drag resistance. These effects increase the system stability by shifting bifurcation thresholds and modifying the behavior of concentration eigenfunctions, temperature, and velocity. Higher <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\textrm{Ha}$</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ha</mtext> </math></EquationSource> </InlineEquation> and lower <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\textrm{Da}$</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Da</mtext> </math></EquationSource> </InlineEquation> values mitigate the destabilizing influences of viscous dissipation and thermodiffusion, promoting supercritical bifurcations. Furthermore, the interplay of Gebhart number (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\textrm{Ge}$</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ge</mtext> </math></EquationSource> </InlineEquation>), separation ratio (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\psi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>), and Lewis number (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\textrm{Le}$</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Le</mtext> </math></EquationSource> </InlineEquation>) is significantly impacted by these external influences, facilitating enhanced vertical mixing and improved stability. This analysis highlights the critical role of magnetic fields and porous media in controlling convection and bifurcation regimes, offering practical insights for applications in energy systems, geophysics, and material processing. The results emphasize strategies for stabilizing fluid mixtures and tailoring convective behavior in complex systems. The numerical solution of the resulting amplitude equations with Runge–Kutta method. The magnetic field is incorporated through a modified Hartmann formulation, while porous media effects are modeled via the Brinkman–Darcy extension.</p>

Stability and bifurcation analysis of binary fluid mixtures under viscous dissipation and magnetic influences

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发表日期：

2025年8月23日

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M. Pushparajan,
M. Muthtamilselvan

摘要

This study investigates the nonlinear dynamics of binary fluid mixtures under the combined effect of viscous dissipation, thermodiffusion, magnetic forces, and porous media resistance. The magnetic field and porous medium add stabilizing mechanisms that reshape convection patterns and alter bifurcation thresholds. Through weakly nonlinear stability analysis, critical conditions for supercritical and subcritical bifurcations are derived and analyzed. The findings indicate that magnetic fields suppress convective motions via Lorentz forces, while porous media dampen flow through drag resistance. These effects increase the system stability by shifting bifurcation thresholds and modifying the behavior of concentration eigenfunctions, temperature, and velocity. Higher $\textrm{Ha}$ $Ha$ and lower $\textrm{Da}$ $Da$ values mitigate the destabilizing influences of viscous dissipation and thermodiffusion, promoting supercritical bifurcations. Furthermore, the interplay of Gebhart number ( $\textrm{Ge}$ $Ge$ ), separation ratio ( $\psi $ $ψ$ ), and Lewis number ( $\textrm{Le}$ $Le$ ) is significantly impacted by these external influences, facilitating enhanced vertical mixing and improved stability. This analysis highlights the critical role of magnetic fields and porous media in controlling convection and bifurcation regimes, offering practical insights for applications in energy systems, geophysics, and material processing. The results emphasize strategies for stabilizing fluid mixtures and tailoring convective behavior in complex systems. The numerical solution of the resulting amplitude equations with Runge–Kutta method. The magnetic field is incorporated through a modified Hartmann formulation, while porous media effects are modeled via the Brinkman–Darcy extension.