Single and multi-droplet configurations out of thermodynamic equilibrium: pulsating, traveling and erratic fluid-dynamic instabilities

The peculiar behavior of stable and unstable convection that is produced when a single liquid drop or a periodic array of evenly spaced droplets dissolve in a surrounding liquid is investigated by means of non-invasive optical techniques and computer simulations. Numerical computations are used to capture additional insights into the physics of the problem as well as to discern the role played by buoyancy forces, surface tension gradients and the interaction of both in determining dissolution kinetics and instability mechanisms. The considered system is intended to model the typical phenomena occurring during the thermal processing of liquid-liquid systems exhibiting a miscibility gap (the so-called "immiscible alloys"). These alloys undergo sedimentation of the separated heavier phase to the bottom of the container under normal gravity conditions. Droplets in non-equilibrium conditions on the bottom are responsible for the occurrence of still poorly known phenomena. The present analysis shows that even a single dissolving droplet can behave as an intriguing pattern-forming dynamical system of exceptional complexity leading to a wealth of different spatio-temporal modes of convection when the imposed temperature gradient is increased. The case of a multi-droplet configuration is even more complex; the distribution of solute depends on the multicellular structure of the convective field and on associated ‘pluming phenomena’. Significant adjustments in such patterns take place as time passes. The structure of the velocity field and the number of rising solutal plumes exhibit sensitivity to the number of droplets and to the possible presence of surface Marangoni effects. New classes of possible instability mechanisms (pulsating, traveling, erratic) are identified, described and compared with other canonical phenomena traditionally considered in the literature as reference problems for the study of the evolution a system may exhibit from the stationary state to the fully developed turbulent regime (i.e. the instabilities of pool fires and of gas mixtures, the classical Rayleigh-Bénard problem with the related 'wind of turbulence', etc.).