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gwnow@amu.pl

Department of Physical Chemistry Faculty of Chemistry, UAM, Poznań. The filling up tetrahedral nodes in the monodisperse foams and emulsions with Reuleaux-like tetrahedra. Waldemar Nowicki, Grażyna Nowicka. gwnow@amu.edu.pl. Model: The three phase fluid system: A, B and C phase

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gwnow@amu.pl

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  1. Department of Physical Chemistry Faculty of Chemistry, UAM, Poznań The filling up tetrahedral nodes in the monodisperse foams and emulsions with Reuleaux-like tetrahedra Waldemar Nowicki, Grażyna Nowicka gwnow@amu.edu.pl

  2. Model: The three phase fluid system: A, B and C phase A and B fluids form droplets/bubbles dispersed into liquid C The volume of the dispersion medium C is so low that the dispersion is a system of space-filling polyhedra organized into a network.

  3. The aim of the study: Are 3D patterns stable in three-phase bidisperse cellular fluids? Can these patterns be formed spontaneously? Do the transition states associated with local energy minima?

  4. 2-phase cellular fluids (foams) • Plateau’s laws: • Films meet at triple edges at 2/3  (120°) • Edges meet at tetrahedral vertices at arccos(1/3) (109.5°) • Laplace’s law: • The curvature of a film separating two bubbles balances the pressure difference between them

  5. 3-phase cellular fluids • The energy and structure of cellular fluid are dominated by interfacial tension. • The structure can be found by the interfacial energy minimization.

  6. Monodisperse foams Arystotle –tetrahedra fill the space (On the Heavens) Kelvin – the best partition –slightly curved 14-sided polyhedra (tetrakaidecahedra). Thomson W. (Lord Kelvin), On the division of space with minimum partitional area, Phil. Mag., 24, 503 (1887) Weaire-Phelan –two kinds of cells of equal volume: dodecahedra, and14-sided polyhedra with two opposite hexagonal faces and 12 pentagonal faces (0.3% in areabetter than Kelvin's partition) Weaire D., Phelan R., A counterexample to Kelvin’s conjecture on minimal surfaces, Phil. Mag. Lett., 69, 107 (1994) Experiment – the light tomography of foams Thomas P.D., Darton R.C., Whalley P.B., Liquid foam structure analysis by visible light tomography, Chem. Eng. J., 187 (1995) 187-192 Garcia-Gonzales R., Monnreau C., Thovert J.-F., Adler P.M., Vignes-Adler W., Conductivity of real foams, Colloid Surf. A, 151 (1999) 497-503

  7. 2D bidisperse cellular fluids SURUZ 2003

  8. Surface Evolver by Keneth Brakke (Susquehanna University)

  9. 3 dimensional bi-disperse cellular fluids

  10. tetrahedron (343–6) Interfacial energy vs. curvature radius

  11. tetrahedron (343–6) Interfacial energy vs. curvature radius

  12. sphere (11) Interfacial energy vs. curvature radius

  13. lens (121–1) Interfacial energy vs. curvature radius

  14. trihedron (232–3) Interfacial energy vs. curvature radius

  15. Minimum curvature radius vs. relative interfacial tension

  16. The mixing energy – the change in the interfacial energy which accompanies the transfer of A cell from the A-C network to the B-C network

  17. tetrahedron (343–6) Mixing energy vs. volume fraction

  18. R=Rmin tetrahedron (343–6) Mixing energy vs. volume fraction

  19. sphere (11) Mixing energy vs. volume fraction

  20. R=Rmin lens (121–1) Mixing energy vs. volume fraction

  21. R=Rmin trihedron (232–3) Mixing energy vs. volume fraction

  22. 5.1013.39 11 121–1 232–3 343–6 Mixing energy vs. relative interfacial tension

  23. 0.1 5.1013.39 11 121–1 232–3 343–6

  24. Small cells introduced to the monodisperse network produce the stable highly-organized patterns at any  values. At =1 patterns cannot be formed spontaneously. For small values patterns are able toself-organize.

  25. Thank you for your attention ???

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