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# Surface tension Oct 2013. Dispersed liquids in nature.

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Surface tension Oct 2013

Dispersed liquids in nature

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

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

How many molecules are on the surface of a 10-nm droplet ? 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* *(D/2) 3, and that of the surface layer is 4/3* *[ (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 D = 100 Ǻ

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

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

Values of for some usual liquids SubstanceSurface tension (mN/m) Water (10°C)74.2 Water (25°C)72.0 Water (50°C)67.9 Mercury (25°C)485.5 Acetone (25°C)23.5 Ethanol (25°C)23.2 Formamide (25°C)57.0 Nitrogen (77°K)8.85 Values from Butt, Graf & Kappl, Physics and Chemistry of Interfaces, Wiley, 2006

A rough estimation of from the energy of vaporization Cyclohexane @ 25°C U evap = 30.5 kJ/mol =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 N A a³ = M, i.e. a = 0.565 nm The final estimate is about 26 mJ/m² (the experimental value is ~ 25 mJ/m²)

Stefans law From K.S. Birdi, Surface and Colloid Chemistry, Principles and Applications 2010, CRC Press Jozef Stefan 1835-1893

There is an entropic contribution to in addition to the energetic contribution T P Tc gas liquid solid with n ~ 1 The surface tension vanishes at the critical temperature The corresponding Maxwells relation reads

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

Effect of surfactants on surface tension Critical micellar concentration

Minimal surfaces Costas minimal surface (1982)

Minimal surfaces in materials sciences MicronMicron, Volume 38, July 2007, Pages 478–485Volume 38,

Young-Laplace equation R P ext P in The mechanical equilibrium of a half-droplet requires For a more complex interface, the relation is with R1 & R2 being the principal radii of curvature

Laplace Nous devons donc envisager létat présent de lunivers comme leffet 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 dailleurs elle était assez vaste pour soumettre ces données à lAnalyse, embrasserait dans la même formule les mouvements des plus grands corps de lunivers et ceux du plus léger atome : rien ne serait incertain pour elle et lavenir, comme le passé serait présent à ses yeux. (Laplace, Essai philosophique sur les probabilités, 1795) Géomètre de première catégorie, Laplace na 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 dun bon point de vue : il cherchait des subtilités de partout, il avait seulement des idées problématiques et enfin il portait lesprit de linfiniment petit jusque dans ladministration. (Napoléon Bonaparte, à propos du passage de Laplace au ministère de lintérieur) Pierre-Simon de Laplace (1749-1827)

Thomas Young Thomas Young 1773-1829 Optics: the double-slit interference experiments Mechanics: Youngs modulus Wetting phenomena: Young-Laplace & Young-Dupré relations Vision and color theory: Young-Helmholtz, 3-dimensional color space Physiology: pulse speed Linguistics: he introduced the idea of « Indo-European languages » Egyptology: he decyphered the hieroglyphs (before Champollion) Music: Young temperament

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

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

Ostwald ripening Wilhelm Ostwald 1853-1932 http://iopscience.iop.org/1367-2630/7/1/040/media/movie1_SD.mpg New Journal of Physics Volume 7 2005 D G A L Aarts et al 2005 New J. Phys. 7 40 doi:10.1088/1367-2630/7/1/040doi:10.1088/1367-2630/7/1/040 Interfacial dynamics in demixing systems with ultralow interfacial tension

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 nest que boules de savon. » Taken from the Nobel lecture of P.-G. de Gennes Rev. Modern Phys. 64 (1992) 645

Some menisci configurations 12 Think about the pressure difference between 1 and 2

Plateau-Rayleigh instability

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

Joseph Plateau Joseph Plateau 1801-1883 Doctoral thesis at the University of Liège (1829) Professor of experimental physics in Ghent University (1835) The phenakistiscope (phenakizein means to deceive) Plateaus laws

John Strutt (1842-1919- 3rd baron Rayleigh Second Cavendish professor of physics at Cambridge (following Maxwell) Dynamic soaring (flying of birds) Rayleigh scattering (why is the sky blue) Rayleigh waves (acoustics and mechanics) Rayleigh-Jeans law (blackbody radiation) Discovery of Argon with Ramsay (Nobel Prize for physics 1904) Etc.

Other types of capillary instabilities Soft Matter, 2008,4, 1403-1413 Rayleigh-Taylor instability http://www.physicscentral.com/explore/pi ctures/cup.cfm

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

The spinning droplet Optics and Lasers in Engineering Volume 46, Issue 12Volume 46, Issue 12, December 2008, Pages 893–899 for small values of (mostly intefacial tensions)

Capillary forces What is the force between two spheres?

A more accurate analysis of forces involved in measurement

Surfactants in nature Pulmonary surfactants

What can you tell about the pressure in a liquid from the shape of a rising bubble? http://people.rit.edu/andpph/exhibit-bubbles.html

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