Investigating Salt-Finger Convection Under Time-Dependent Gravity Modulation in Micropolar Liquids

Abstract

This paper investigates how gravity modulation affects salt-finger convection in a micropolar liquid layer confined between two parallel, infinitely long plates separated by a thin gap. The system is heated and has solute added from above. The study uses linear stability analysis to examine when and how salt-finger convection, driven by the salt-finger process, begins. To analyze this, the partial differential equations governing the system are solved numerically using normal mode analysis. The Venezian approach is applied to find the critical Rayleigh number and the solutal Rayleigh number, which are key to understanding the onset of convection. Also, the paper explores how different micropolar fluid parameters—such as the coupling parameter, micropolar heat conduction parameter, couple stress parameter, and inertia parameter—affect the system when gravity modulation is present. It is found that gravity modulation can either stabilize or destabilize convection, depending on its frequency. At very high frequencies (approaching infinity), the effect of gravity modulation becomes minimal, having little impact on the convection process. The paper also examines the relationship between the critical Rayleigh number and the solutal Rayleigh number, which are related to heat and solute concentration, respectively.