Onset of thermosolutal reactive-convection in an Ellis fluid saturated porous layer

This study examines the onset of thermosolutal reactive-convection in a porous layer saturated with an Ellis fluid under a horizontal pressure gradient, generating steady flow. Temperature and concentration gradients induce thermosolutal convection, further complicated by reaction terms. Through linear stability analysis using the normal mode technique, an analytical expression for the Darcy-Rayleigh number is derived, with results validated against limiting cases. Findings show that increasing the solute Darcy-Rayleigh number, Ellis power-law index, and Damkohler number delays convection onset, while higher Darcy-Ellis and Lewis numbers promote it. Results reveal the critical conditions under which buoyancy-driven instabilities arise, with particular emphasis on the role of the Ellis fluid rheology in moderating these instabilities. These insights advance the understanding of reactive-convection control in porous media, relevant to applications in enhanced oil recovery, carbon sequestration, and non-Newtonian fluid reactors.