Surface tension

# Surface tension

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## Surface tension

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1. Surface tension Oct2013

2. Dispersed liquids in nature

3. Artificiallly dispersed liquids http://www-math.mit.edu/~bush/gallery.html http://lmlm6-62.univ-lille1.fr/lml/perso/pbrunet/page_perso.html http://www.dolomite-microfluidics.com/products/system-solutions

4. There is an extra energy associated with a surface Molecules on the surface are less bounded than molecules in the bulk. There is therefore an energy associated with a free surface. More rigorously: there is a free energy associated with an interface. This energy is the surface tension g

5. Solids have a surface tension too • More about this later

6. How many molecules are on the surface of a 10-nm droplet ? D = 100 Ǻ The molar volume of liquid nitrogen is 34.6 cm³/mol, which converts to a molecule « diameter » of 4.8 Ǻ Consider a drop of diameter D = 100 Ǻ The total volume is 4/3*p*(D/2)3, and that of the surface layer is 4/3*p*[ (D/2)3 – (D/2-t)3] A droplet of 10 nm in diameter has therfore 25 % of the molecules on the surface! t ~ 4.8 Ǻ

7. The surface tension can be thought of as a force F A The energy per unit area is g It can often be thought of as a force http://www.funsci.com/fun3_en/exper2/exper2.htm

8. A didactic setup(Cf. Wilhelmy plate) http://www.funsci.com/fun3_en/exper2/exper2.htm

9. Values of g for some usual liquids Values from Butt, Graf & Kappl, Physics and Chemistry of Interfaces, Wiley, 2006

10. A rough estimation of gfrom the energy of vaporization Cyclohexane @ 25°C Uevap = 30.5 kJ/mol r=773 kg/m³ M=84.16 g/mol Assuming a cubic structure (6-coordinated), Uevap converts to 5.08 kJ/mol for each bond. Each molecule on the surface has one missing bond. All is left to determine is the area of each molecule on the surface. This can be estimated as a² with NA a³ r = M, i.e. a = 0.565 nm The final estimate is about 26 mJ/m² (the experimental value is ~ 25 mJ/m²)

11. Stefan’slaw Jozef Stefan 1835-1893 From K.S. Birdi, Surface and ColloidChemistry, Principles and Applications 2010, CRC Press

12. There is an entropic contribution to sin addition to the energeticcontribution The surface tension vanishesat the criticaltemperature with n ~ 1 P solid liquid The correspondingMaxwell’s relation reads gas Tc T

13. Surfactants Surfactant classification according to the composition of their head: nonionic, anionic, cationic, amphoteric.

14. Effect of surfactants on surface tension Criticalmicellar concentration

15. Minimal surfaces Costa’s minimal surface (1982)

16. Minimal surfaces in materials sciences Micron, Volume 38, July 2007, Pages 478–485

17. Young-Laplace equation Pext Pin The mechanical equilibrium of a half-droplet requires R g g For a more complex interface, the relation is with R1 & R2 being the principal radii of curvature

18. Laplace Pierre-Simon de Laplace (1749-1827) Nous devons donc envisager l’état présent de l’univers comme l’effet de son état antérieur et comme la cause de celui qui va suivre. Une intelligence qui, pour un instant donné, connaîtrait toutes les forces dont la nature est animée, et la situation respective des êtres qui la composent, si d’ailleurs elle était assez vaste pour soumettre ces données à l’Analyse, embrasserait dans la même formule les mouvements des plus grands corps de l’univers et ceux du plus léger atome : rien ne serait incertain pour elle et l’avenir, comme le passé serait présent à ses yeux.  (Laplace, Essai philosophique sur les probabilités, 1795) Géomètre de première catégorie, Laplace n’a pas tardé à se montrer un administrateur plus que médiocre ; de son premier travail nous avons immédiatement compris que nous nous étions trompés. Laplace ne traitait aucune question d’un bon point de vue : il cherchait des subtilités de partout, il avait seulement des idées problématiques et enfin il portait l’esprit de l’infiniment petit jusque dans l’administration.  (Napoléon Bonaparte, à propos du passage de Laplace au ministère de l’intérieur)

19. Thomas Young Thomas Young 1773-1829 • Optics: the double-slitinterferenceexperiments • Mechanics: Young’smodulus • Wettingphenomena: Young-Laplace & Young-Dupré relations • Vision and colortheory: Young-Helmholtz, 3-dimensional colorspace • Physiology: pulse speed • Linguistics: heintroduced the idea of « Indo-Europeanlanguages » • Egyptology: hedecyphered the hieroglyphs (before Champollion) • Music: Young temperament

20. What happens now? A small and a large droplets lie on a fiber wetted by a thin liquid film. How does the system evolve?

21. Laplace equation applies to solid particles as well Lattice Contraction and Surface Stress of fcc Nanocrystals J. Phys. Chem. B, 2001, 105 (27), pp 6275–6277

22. Ostwald ripening Wilhelm Ostwald 1853-1932 New Journal of Physics Volume 7 2005 D G A L Aartset al 2005 New J. Phys.7 40 doi:10.1088/1367-2630/7/1/040 Interfacialdynamics in demixingsystemswithultralowinterfacial tension http://iopscience.iop.org/1367-2630/7/1/040/media/movie1_SD.mpg

23. What is the pressure in a soap bubble ? « Amusons nous sur la terre comme sur l'onde, Malheureux celui qui se fait un nom Richesses, Honneurs, Faux éclat de ce monde  Tout n’est que boules de savon. » Taken from the Nobel lecture of P.-G. de Gennes Rev. Modern Phys. 64 (1992) 645

24. And in an anti-bubble? http://www.youtube.com/watch?v=6r_8Pp9WkF0

25. Some menisci configurations Think about the pressure difference between 1 and 2 1 2

26. Plateau-Rayleigh instability

27. Plateau-Rayleigh instabilities in materials science PMMA in pores Cu nanowires Nano Lett., 2007, 7 (1), pp 183–187 Appl. Phys. Lett. 85, 5337 (2004)

28. Joseph Plateau Doctoral thesisat the University of Liège (1829) Professor of experimental physics in Ghent University (1835) Joseph Plateau1801-1883 Plateau’slaws The phenakistiscope (“phenakizein” means “to deceive”)

29. John Strutt (1842-1919-3rd baron Rayleigh • Second Cavendish professor of physicsat Cambridge (following Maxwell) • Dynamicsoaring (flying of birds) • Rayleigh scattering (whyis the skyblue) • Rayleigh waves (acoustics and mechanics) • Rayleigh-Jeans law (blackbody radiation) • Discovery of Argon with Ramsay (Nobel Prize for physics 1904) • Etc.

30. Other types of capillaryinstabilities Rayleigh-Taylor instability http://www.physicscentral.com/explore/pictures/cup.cfm Soft Matter, 2008,4, 1403-1413

31. Sessile drop or bubble Tate’slaw is a rough approximation. More accurate measurements are obtained by analyzing the shape of droplet using Laplace’s law. Can you do that? New J. Phys. 5 (2003) 59

32. The spinningdroplet for small values of s (mostlyintefacial tensions) Optics and Lasers in Engineering Volume 46, Issue 12, December 2008, Pages 893–899

33. Capillary forces Whatis the force betweentwospheres?

34. A more accurateanalysis of forces involved in gmeasurement

35. Surfactants in nature Pulmonary surfactants

36. Whatcanyou tell about the pressure in a liquidfrom the shape of a risingbubble? http://people.rit.edu/andpph/exhibit-bubbles.html