Title: Marangoni Interfacial Instability Induced by Solute Transfer Across Liquid-Liquid Interfaces

Abstract: This study presents analytical and numerical investigations of Marangoni interfacial instability in a two-liquid-layer system with constant solute transfer across the liquid interface. Previous research has demonstrated that both viscosity ratio and diffusivity ratio can influence the system's hydrodynamic stability via the Marangoni effect, but the distinctions in process and mechanisms are not yet fully understood. To gain insights, we developed a numerical model based on the phase-field method, rigorously validated against linear stability analysis. The parameter space explored encompasses Schmidt number ($Sc \in [0.2, 200]$), Marangoni number ($Ma_c \in [10, 2000]$), Capillary number ($Ca \in [0.01, 1]$), viscosity ratio ($\zeta_\mu \in [0.1, 10]$), and diffusivity ratio ($\zeta_D \in [0.1, 10]$). We identified two key characteristics of Marangoni instability: the self-amplification of triggered Marangoni flows in flow-intensity-unstable case and the oscillation of flow patterns during flow decay in flow-intensity-stable case. Direct numerical simulations incorporating interfacial deformation and nonlinearity confirm that specific conditions, including solute transfer out of a higher viscous or less diffusive layer, amplify and sustain Marangoni interfacial flows. Furthermore, the study highlights the role of interfacial deformation and unequal solute variation in system instability, proposing corresponding instability mechanisms. Notably, traveling waves are observed in the flow-intensity-stable case, correlating with the morphological evolution of convection rolls. These insights contribute to a comprehensive understanding of Marangoni interfacial instability in multicomponent fluids systems, elucidating the mechanisms underlying variations in viscosity and diffusivity ratios across liquid layers.