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

This study presents analytical and numerical investigations of Marangoni interfacial instability in a two-liquid-layer system with constant solute transfer across the interface. While previous research has established that both diffusivity and viscosity ratios affect hydrodynamic stability via the Marangoni effect, the specific nonlinear dynamics and the role of interfacial deformation remain fully unclear. To address this, we developed a phase-field-based numerical model, validated against linear stability analysis and existing theories. The validated parameter space includes Schmidt number, Marangoni number, Capillary number, and the diffusivity and viscosity ratio between the two layers. Our finding shows that solute transfer from a less diffusive layer triggers short-wave instability, governed by the critical Marangoni number, while solute transfer into a less viscous layer induces long-wave instability, controlled by the critical Capillary number. Nonlinear simulations reveal distinct field coupling behaviors: in the diffusivity-ratio-driven instability, the spatially averaged flow intensity remains symmetric about a flat interface, while solute gradient is uneven. In contrast, in viscosity-ratio-driven instability, a deforming interface separates the two layers, with a uniform solute gradient but asymmetric spatially averaged flow intensity. These results highlight the crucial role of diffusivity and viscosity in shaping Marangoni flows and enhance our understanding of interfacial instability dynamics.