  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.
