Stability analysis of Rayleigh–Bénard–Marangoni convection in fluids with cross-zero expansion coefficient

Abstract

Cross-zero expansion coefficient Rayleigh–Bénard–Marangoni (CRBM) convection refers to the convective phenomenon where thermal convection with stratified positive and negative expansion coefficients in a liquid layer is coupled with the Marangoni convection. In the Bénard convection, fluids with a cross-zero expansion coefficient contain a neutral expansion layer where the expansion coefficient (α) is zero, and the local buoyancy-driven convection is coupled with the Marangoni convection, leading to unique flow instability phenomena. This paper uses linear stability theory to analyze the CRBM convection in a horizontal liquid layer under a vertical temperature gradient and performs numerical calculations for fluids under different Bond numbers (Bd) in both bottom-heated and bottom-cooled models, obtaining the critical destabilization conditions and modes. In the bottom-heated model, different combinations of buoyancy instability mechanism (BIM), tension instability mechanism, and coupled instability mechanism (CIM) appear depending on the dimensionless temperature for the neutral expansion layer (Tα0) and the Bd. In the bottom-cooled model, two mechanisms occur according to the variation of Tα0: BIM and CIM.