Dynamics of three immiscible and miscible fluids in a rectangular enclosure: Influence of surface tension and diffusion on bubble-droplet behavior

The transient dynamics of three immiscible and miscible fluids confined within a vertical rectangular enclosure are investigated numerically. A circular fluid region is initially placed at the center of the domain, while the upper and lower halves are occupied by fluids of different densities, resulting in six density arrangements that encompass droplet-falling, bubble-rising, and hybrid bubble-droplet configurations. The Navier–Stokes equations coupled with multiple volume-fraction transport equations are solved using a finite-volume framework to capture the complex multi-interface structures. For immiscible systems, variation of the Weber number (We) revealed transitions from capillary-dominated regimes with smooth, stable interfaces to inertia-dominated regimes characterized by strong deformation, filamentation, and fragmentation. In gravitationally unstable configurations, Rayleigh–Taylor instability interacts with the motion of the circular region, producing complex bubble–spike structures, enhanced vortex activity, and pronounced oscillations in the center-of-mass evolution. A hybrid bubble–droplet regime is identified when competing buoyancy mechanisms coexist, leading to intensified flow motion and asymmetric interface dynamics. In contrast, gravitationally stable configurations exhibit more orderly behavior, with limited deformation and smoother interface evolution even at high We. For miscible systems, a reduction of the Schmidt number leads to thicker interfacial layers, weaker buoyancy forces, reduced velocity magnitudes, and damped oscillations in the fluid motion, indicating a transition from capillary-dominated and instability-dominated dynamics to diffusion-controlled regimes. The study provides new physical insight into the coupled roles of buoyancy, surface tension, inertia, and diffusion in three-fluid systems and offers benchmark data for validating numerical models of immiscible–miscible multi-fluid flows in confined geometries.