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# Measuring the Surface Tension of Water by Light Diffraction on Capillary Waves

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The SEENET-MTP Seminar: Trends in Modern Physics
19–21 August 2011, Niš, Serbia

Talk by Ljubisa Nesic (Faculty of Science and Mathetamtics, Univ. of Nis)

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### Measuring the Surface Tension of Water by Light Diffraction on Capillary Waves

1. 1. Measuring the Surface Tension of Water by Light Diffraction on Capillary Waves Balkan Summer Institute 2011 (BSI2011) Seminar for teachers BSS2011: Trends in Modern Physics (BSS2011) Ljubisa Nesic Faculty of Science, Nis, Serbia and Dragisa Nikolic Grammar School, Pirot, Serbia
2. 2. <ul><li>Surface tension </li></ul><ul><li>Capillary waves </li></ul><ul><li>Experiment </li></ul>
3. 3. Surface tension <ul><li>The cohesive forces among the liquid molecules are responsible for this phenomenon </li></ul>
4. 4. Surface tension <ul><li>This creates some internal pressure and forces liquid surfaces to contract to the minimal area </li></ul><ul><li>Surface tension is measured in newton per meter (N/m) or joules per square meter (J/m 2 ) </li></ul>
5. 5. Surface tension and capillarity <ul><li>Capillary action , or capillarity , is the ability of a liquid to flow against gravity where liquid spontaneously rises in a narrow space </li></ul><ul><li>The adhesive forces among the liquid molecules and solid surrounding surfaces are responsible for this phenomenon </li></ul>
6. 7. Surface tension - contraction to the minimal area <ul><li>If the diameter of the tube is sufficiently small, then the combination of surface tension (which is caused by cohesion within the liquid) and forces of adhesion between the liquid and container act to lift the liquid. </li></ul>
7. 9. Measuring of surface tension <ul><li>Static (ordinary) method </li></ul><ul><ul><li>involves the measurement of the force to be exerted on a piece of metal as it is pulled from a liquid. </li></ul></ul><ul><ul><li>But </li></ul></ul><ul><ul><ul><li>it cannot be used to continuously measure the surface tension. </li></ul></ul></ul><ul><ul><ul><li>It is also difficult to use in some environments. </li></ul></ul></ul>
8. 10. Capillary waves <ul><li>Type of the surface waves on water </li></ul><ul><li>Waves - result of a generating force </li></ul><ul><ul><ul><li>blowing wind, vessels moving, volcanic eruptions, submarine earthquakes, …, stones, … </li></ul></ul></ul><ul><li>An additional force - restoring force - acts to return the surface of the water to its original flat level. </li></ul><ul><ul><li>two different restoring forces </li></ul></ul><ul><ul><ul><li>gravity (gravity waves) </li></ul></ul></ul><ul><ul><ul><li>surface tension (capillary waves - ripples) </li></ul></ul></ul>
9. 11. <ul><li>wave energy – NOT the water particles – moves across the surface of the sea </li></ul><ul><li>wave form moves and with it, energy is transmitted </li></ul><ul><li>nearly all water movements are turbulent (non-laminar) </li></ul>Wave direction Wave
10. 12. Traveling Surface Wave
11. 13. Deep- to Shallow-Water Waves
12. 14. <ul><li>As more energy is transferred to the water, the waves will grow in size </li></ul><ul><li>As the waves grow, gravity will become the restoring force and the waves will be gravity waves. </li></ul><ul><li>Speed of the waves u ? </li></ul><ul><li>Many approaches </li></ul><ul><ul><li>Analytical mechanics, conservation of energy, dimensional analysis , … </li></ul></ul>
13. 15. Dispersion relation <ul><li>u g =  / T =  / k is the function of: </li></ul><ul><ul><li>wavelength  , gravitational field strength g, density of water  </li></ul></ul><ul><ul><li>u=const     g  </li></ul></ul>The variation of wave speed with wavelength is called dispersion and the functional relationship is called the dispersion relation .
14. 16. <ul><li>If surface tension is taken as a dominant restoring force, the waves are capillary, and their speed will depend on density, wavelength and the surface tension (  ): u=const       </li></ul>Dispersion relation
15. 17. Capillary and Gravity waves <ul><li>Capillary waves- wavelength < 1.73 cm </li></ul><ul><li>Gravity waves- wavelength > 1.73 cm </li></ul>
16. 18. Wave Sizes- Wave Energy
17. 19. Experiment <ul><li>A laser beam is aimed at a reservoir containing water, with ripples induced by a wire attached to a speaker driven by a function generator. The surface ripples act as a diffraction grating causing the interference spots on the screen. </li></ul>
18. 20. Reflection diffraction gratings
19. 21. Experiment <ul><li> - is the angle of the laser beam measured from horizontal axis, k - is the (capillary) wave vector </li></ul><ul><li>The effective grating spacing in this case is </li></ul>
20. 22. Experiment <ul><li>r is the angle between the incident beam and the direction to the first maximum. </li></ul><ul><li>In the case of first maximum (  is the laser wavelength) </li></ul>
21. 23. Experiment <ul><li>r is the angle between the incident beam and the direction to the first maximum. </li></ul><ul><li>In the case of first maximum (  is the laser wavelength) </li></ul>
22. 24. Experiment
23. 26. <ul><li>He-Ne laser, P=2 mW </li></ul><ul><li> =632,8 nm </li></ul><ul><li>θ=7 0 </li></ul><ul><li>Ŀ=5 m </li></ul>