Modelling of the rise and absorption of a fluid inclusion

Abstract

The buoyancy-driven rise of a small single fluid inclusion in a viscous liquid that is enclosed in a container of the cylindrical shape is numerically modelled. It is additionally assumed that the inclusion is slowly absorbed by the surrounding liquid. The phase-field approach is used as a physics-based model for the description of the thermo- and hydrodynamic evolution of a miscible heterogeneous binary mixture. The interplay of the effects of absorption and inclusion’s motion are investigated. We found that the dissolution of a nearly spherical inclusion does not occur evenly over its surface. The interfacial diffusion is stronger at the inclusion’s top cap. The matter absorbed by the liquid does not quickly penetrate into the bulk of the ambient phase, it accumulates behind the inclusion forming a concentration wake. We found that during the rise the inclusion’s speed grows. The speed and the acceleration of the inclusion strongly depend on the absorption rate, so the inclusion rises faster at the higher absorption rates. This effect is explained by the action of the Marangoni stress that is developed due to non-uniform mixture composition along the inclusion’s surface. We also found that the rise of the inclusion in a closed container is accompanied by the recirculation flow that is developed near the inclusion and that rises upwards with the inclusion. In the limit of negligible absorption (higher Peclet numbers) the convergence to a constant terminal speed of an immiscible inclusion is observed.