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<p>This study explores chemical reactions in bidisperse porous medium convection under generalised solute boundary conditions, highlighting the effects of these reactions on fluid dynamics. It accounts for solute distribution by integrating both concentration and its gradient (salt flux). The research introduces innovative mathematical and numerical techniques to determine the critical values for linear and nonlinear stability analyses, including two novel algorithms for accurately identifying critical values under oscillatory loading. In the framework of linear instability and for any nonzero boundary salt flux coefficient, the traditional approach to finding analytical solutions utilising the series of the form <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10665_2025_10438_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\( \sin (n \pi z) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>sin</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mi>π</mi> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is unsuitable for this situation since it requires all boundary conditions to be zero. This motivates us to utilise the Jordan form to derive a novel analytical method to find the critical salt Rayleigh number. This method enhances the Chebyshev collocation technique, enabling precise identification of instability and stability regions. Results reveal critical Rayleigh number thresholds that induce instability in convection, highlighting the significance of the bidisperse properties of the medium and the kinetics of the reactions involved. The methodologies presented are poised to significantly advance future research in this field.</p>

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New mathematical methods for convection stability in bidisperse porous media with solute variations

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • Sanaa L. Khalaf,
  • Akil J. Harfash

摘要

This study explores chemical reactions in bidisperse porous medium convection under generalised solute boundary conditions, highlighting the effects of these reactions on fluid dynamics. It accounts for solute distribution by integrating both concentration and its gradient (salt flux). The research introduces innovative mathematical and numerical techniques to determine the critical values for linear and nonlinear stability analyses, including two novel algorithms for accurately identifying critical values under oscillatory loading. In the framework of linear instability and for any nonzero boundary salt flux coefficient, the traditional approach to finding analytical solutions utilising the series of the form \( \sin (n \pi z) \) sin ( n π z ) is unsuitable for this situation since it requires all boundary conditions to be zero. This motivates us to utilise the Jordan form to derive a novel analytical method to find the critical salt Rayleigh number. This method enhances the Chebyshev collocation technique, enabling precise identification of instability and stability regions. Results reveal critical Rayleigh number thresholds that induce instability in convection, highlighting the significance of the bidisperse properties of the medium and the kinetics of the reactions involved. The methodologies presented are poised to significantly advance future research in this field.