Comparative study of thermal Marangoni convection in shallow rectangular cavities with single-free-surface and two-free-surface configurations

A comprehensive three-dimensional numerical study is conducted to investigate thermal Marangoni convection in a shallow rectangular cavity, focusing on the fundamental differences between the single-free-surface and two-free-surface configurations. Simulations are performed over a range of thermal Marangoni numbers (Ma) and two aspect ratios (As = 1 and ∞). The results reveal that the flow structure is significantly altered by the presence of a second free surface. At a lower Ma, the two-free-surface system exhibits a symmetric and double-layered counter-circulation pattern driven by Marangoni stresses on both interfaces, distinct from the single recirculation roll observed in the single-free-surface case. This configuration reduces the effective vertical confinement and attenuates local temperature gradients near sidewalls. Once Ma exceeds a critical value, the flow transitions to a three-dimensional oscillatory state characterized by hydrothermal waves (HTWs) and stationary longitudinal rolls. The two-free-surface system shows higher oscillation frequencies but lower amplitudes compared to its single-free-surface counterpart under identical conditions, attributed to the underlying interplay between effective fluid inertia and spatial constraint in the two configurations. Furthermore, longitudinal wall confinement (As = 1) significantly influences wave pattern development, promoting standing-wave-type oscillations, while removing longitudinal confinement (As = ∞) facilitates the direct formation of oblique HTW. A universal transition sequence from periodic oscillation to quasi-periodic oscillation, and finally to chaos, is observed with increasing Ma for all configurations. The present study would provide more insights into the critical role of geometric confinement and interfacial conditions in governing the stability and pattern formation of thermal Marangoni convection.