1. ©2002 Regents of University of Minnesota Simulation of surfactant mechanics within a volume-of-fluid method Ashley James Department of Aerospace Engineering and Mechanics University of Minnesota John Lowengrub School of Mathematics University of Minnesota Mike Siegel Department of Mathematics New Jersey Institute of Technology

2. ©2002 Regents of University of Minnesota Motivation - Tip Steaming Four roll mill 40  m x 140  m bubble air filament fiber 1.3 mm Simpkins & Kuck. Nature. 2000. 403. 641 - 643.

3. ©2002 Regents of University of Minnesota Volume of Fluid Method The interface is captured via the volume fraction, F F is convected with the fluid The solution algorithm minimizes numerical diffusion

4. ©2002 Regents of University of Minnesota Continuum Surface Force Method Surface tension is added to the momentum equation, distributing it over a thin volume near the interface

5. ©2002 Regents of University of Minnesota Interfacial Surfactant Evolution Equations Surfactant concentration Surfactant mass in a cell Diffusion depends upon concentration

6. ©2002 Regents of University of Minnesota Surfactant Convection Surfactant is convected with the volume fraction The concentration is updated with smoothing

7. ©2002 Regents of University of Minnesota Surfactant Diffusion

8. ©2002 Regents of University of Minnesota Axisymmetric Verification Convection with an expanding sphere  No diffusion  Includes stretching Diffusion on a stationary sphere  Static interface

9. ©2002 Regents of University of Minnesota No diffusion Marangoni Convection Concentration Initial Final

10. ©2002 Regents of University of Minnesota Conclusions Variable surface tension effects due to surfactant are included The numerical method accurately models the evolution of interfacial surfactant Surfactant convection and diffusion were verified separately Non-uniformly distributed surfactant leads to Marangoni convection

11. ©2002 Regents of University of Minnesota Future Work Extend from axisymmetric to three dimensions Add surfactant solubility Simulate tip streaming Investigate drop coalescence