Triple-diffusive instabilities in Ellis fluid-saturated porous layers: Dynamics of oscillatory convection

Abstract

Triple-diffusive convection in Ellis fluid-saturated porous layers has a wide array of real-world applications, including enhanced oil recovery, optimized geothermal energy extraction, and improved food processing and drug delivery systems. It also plays a crucial role in environmental management, particularly in controlling groundwater contamination and maintaining soil health by modeling pollutant transport and nutrient dynamics. This study explores the onset of convection in an Ellis fluid-saturated porous layer, influenced by three stratifying agents with differing diffusivities. A modified Darcy porous medium, salted from below, is subjected to horizontal throughflow driven by a prescribed pressure gradient. Through normal mode analysis, a linear stability analysis is conducted, resulting in explicit threshold conditions for the onset of convection. The findings reveal that convection begins with oscillatory motion, driven by the combined effects of the pressure gradient and solute concentration gradients. Notably, the study uncovers the emergence of disconnected, closed, heart-shaped oscillatory neutral curves, indicating the presence of three critical values of the solutal Darcy-Rayleigh number required to establish linear instability criteria and novel discovery for an Ellis fluid-saturated porous medium. Moreover, the results show that increasing the solutal Darcy-Rayleigh number and the Ellis power-law index stabilizes the system, while a higher Darcy-Ellis number leads to destabilization. The results obtained in the limiting cases are found to be consistent with those reported in previous studies.