Simulation of mass transfer in circulating drops with applications to liquid-liquid extraction

SEBASTIÁN UBAL; CARLOS H. HARRISON; PAUL GRASSIA; WALTER J. KORCHINSKY

Borovets

Conferencia; 8th European Conference on Foams, Emulsions and Applications (EUFOAM 2010); 2010

Department of Chemical Engineering, Faculty of Chemistry, Sofia University

Liquid-liquid extraction is a common chemical engineering process in which solute is transferred between two solvent phases prepared in a bi-liquid emulsion. Circulation of liquid within emulsion droplets can help to accelerate the rate of mass transfer, by bringing solute from deep within the drop interior to the surface, where it can transfer to the continuous phase. Determining the extent to which mass transfer is enhanced by the droplet circulation requires knowledge of the microfluidic circulation patterns within and around droplets. It is found that simulating the solute mass transfer is inherently expensive because mass transfer is typically much slower than the circulation, typically by a factor of 10000. Simulations must still resolve the rapid streamline orbits, even though the mass transfer processes of interest are orders of magnitude slower. An alternative semi-analytic boundary layer theory of mass transfer in the presence of circulation is developed, but is found to agree poorly with full numerical simulations on the time scales of primary interest. Instead a streamline-averaged theory of mass transfer (in which solvent concentration is uniform along streamlines, but varies both from streamline to streamline and over time) shows much better agreement with the full simulations.