A two-component lattice Boltzmann model for solute transport in bubbly flows

The mass transfer of soluble gas into and out of a solvent is an essential mechanism in processes such as oxygenation, aeration, and stripping of carbon dioxide. An effective tool to understand such systems is numerical simulation of the applicable transport equations coupled with the relevant thermodynamics of the solvent-solute mixture. This allows for determination of mass transfer rates and shape changes of dissolving/growing bubbles at different flow regimes.

We present a (diffuse interface) free energy lattice Boltzmann model for a binary system that consists of a gaseous solute and a solvent that coexists in liquid and vapor form. In this model, the thermodynamic pressure and chemical potential are derived from the free energy functional of the binary system. The solvent obeys a non-ideal (vapor-liquid) equation of state, and the solute is ideal. Due to the free energy of the mixture, the solute partitions between the liquid and vapor phases.  Bubbles that rise under gravity for varying Reynolds and Eötvös numbers are validated by their shape and terminal rise velocity in two and three dimensions. Examples of nucleation, coalescence and breakage of bubbles will also be presented.