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

The article explores the phenomenon of convection in bidisperse porous media, which is characterised by two distinct pore scales: macropores and micropores. This dual porosity is crucial for accurately modelling real-world challenges in various fields, such as contaminant transport in groundwater and geothermal reservoir utilisation. The study introduces new mathematical methods to analyse convective flows under generalised solute boundary conditions, which offer a more adaptable and accurate representation of solute transport at the boundaries. The research investigates the criteria for linear instability and nonlinear stability in chemical reactions within bidisperse porous materials, specifically concerning an incompressible fluid situated between two horizontal planes. The article presents a detailed theoretical framework and employs advanced numerical techniques, such as the Chebyshev collocation method, to delineate regions of instability and stability. The findings provide essential insights into the behaviour of porous media under various conditions, enhancing our understanding of convective patterns and their applications in diverse scientific and engineering contexts. The study also highlights the significance of the boundary salt flux coefficient and other non-dimensional parameters in influencing the stability of the system, offering valuable implications for optimising industrial processes and environmental management.