1. DROPS IN LOW REYNOLDS NUMBER FLOW Maria L. Ekiel-Jeżewska Eligiusz Wajnryb Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw, Poland COST ``Physics of droplets’’, December 12, 2006, Darmstadt

2. DEPARTMENT OF MECHANICS AND PHYSICS OF FLUIDS DIVISION OF VISCOUS AND THERMAL FLOWS Head: Tomasz A. Kowalewski 6 researchers, 5 PhD students POLISH ACADEMY OF SCIENCES Warsaw Poland INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH

3. OUR DROPLETS

4. DROP BREAK-UP S. Błoński, T. A. Kowalewski movie

5. MD: OIL DROPS IN WATER A. Słowicka, Z. Walenta

6. TURBULENCE IN CLOUDS P.M. Korczyk, S.P. Malinowski, T.A. Kowalewski moviemovie

7. VAPOUR BUBBLES S. Błoński, R. Trzciński, T. A. Kowalewski moviemovie

8. MICROFLOWS S. Błoński, T.A. Kowalewski movie

9. PARTICLES CLOSE TO INTERFACE B. Cichocki, M.L. Ekiel-Jeżewska, G. Naegele, E. Wajnryb

10. SUSPENSION DROPS S. Alabrudziński, D. Chehata, M.L. Ekiel- Jeżewska, T.A. Kowalewski

11. VISCOSITY OF EMULSIONS J. Bławzdziewicz E. Wajnryb, P. Vlahovska

12. LOW REYNOLDS NUMBER

13. Drops in low Reynolds number flows THEORY: Stokes equations, multipole expansion, mobility of friction problems NUMERICAL CODE: non-deformable surfaces, up to hundred of spheres (solid, liquid or gas), infinite fluid or periodic boundary conditions or flat interface or two parallel flat interfaces EXPERIMENT: 3D particle tracking

14. Particles close to interface J. Bławzdziewicz M. L. Ekiel-Jeżewska E. Wajnryb in progress

15. Particles at a free surface B. Cichocki M. L. Ekiel-Jeżewska G. Nägele E. Wajnryb

16. Particles at a free surface Rotne-Prager

17. Ink drop M. Kolanowski S. Błoński M. L. Ekiel-Jeżewska Michelson movie

18. Suspension drops: experiment S. Alabrudziński D. Chehata M. L. Ekiel-Jeżewska T. Kowalewski Re << 1 g

19. Suspension drops: theory ASSUMPTIONS - Stokes flow - random distribution of N point forces F inside a sphere of radius R QUESTION Particle + fluid flows? M. L. Ekiel-Jeżewska B. Metzger E. Guazzelli

20. Result: ``perfect drop’’ fluid particles

21. Effective viscosity of emulsions J. Bławzdziewicz E. Wajnryb P. Vlahovska high frequency

22. Effective viscosity of emulsions

23. Conclusions: our tools + interests LOW REYNOLDS NUMBER FLOWS NUMERICAL CODE (MULTIPOLE EXPANSION ) Mobility and dynamics of spherical non-deformable drops and solid particles close to an interface EXPERIMENT (PARTICLE TRACKING) Motion of solid particles, drops and bubbles