Model of buoyancy-driven motion of a liquid shows role of surface tension in droplet dynamics

From oil recovery to remediating aquifers, many industrial endeavors rely on leveraging the miscibility of two liquids to use one to displace another. The classical representation of miscible liquids, however, fails to fully capture the behavior of moving droplets, such as tendency to form spherical shapes, in a miscible environment.

Vorobev et al. report results from a direct numerical study aimed at modeling the buoyancy-driven motion of a liquid droplet in an ambient miscible liquid. Applying a phase-field model that incorporates the concept of dynamic surface tension, the group was able to better understand the factors leading to moving miscible droplets remaining intact without breaking or dispersing into an ambient fluid.

“We have developed a novel approach for the accurate description of evolving miscible liquids by taking into account the dynamic surface tension forces,” said author Anatoliy Vorobev. “We argue that even a simple everyday problem, such as dissolution of a honey droplet in tea, cannot be accurately solved with the use of currently available commercial software.”

With the exception of a very slow rise, the group found the motion of a miscible droplet results in its instant dispersion. Dispersion occurs on a short hydrodynamic time scale, over which time the droplets surface tension plays a major role in its dynamics, even more so than the interfacial diffusion.

Vorobev said he hopes the paper will spark greater interest in their theoretical approach. The group looks to adapt their model for carbon dioxide-rich binary mixtures with compressible gaseous phases as well as the effects of high-frequency vibrations on the dynamics of heterogeneous binary mixtures.

Source: “Shapes of a rising miscible droplet,” by Anatoliy Vorobev, Timofey Zagvozkin, and Tatyana P. Lyubimova, Physics of Fluids (2019). The article can be accessed at https://doi.org/10.1063/1.5141334 .