1. Balkan Summer Institute 2011 (BSI2011)
Seminar for teachers BSS2011: Trends in Modern Physics (BSS2011)
Measuring the Surface Tension of Water by Light Diffraction on Capillary Waves
Ljubisa Nesic
Faculty of Science, Nis, Serbia
and
Dragisa Nikolic
Grammar School, Pirot, Serbia

2. Surface tension
Capillary waves
Experiment

3. Surface tension
The cohesive forces among the liquid molecules are responsible for this phenomenon

4. Surface tension
This creates some internal pressure and forces liquid surfaces to contract to the minimal area
Surface tension is measured in newton per meter (N/m) or joules per square meter (J/m2)

5. Surface tension and capillarity
Capillary action, or capillarity, is the ability of a liquid to flow against gravity where liquid spontaneously rises in a narrow space
The adhesive forces among the liquid molecules and solid surrounding surfaces are responsible for this phenomenon

7. Surface tension - contraction to the minimal area
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.

9. Measuring of surface tension
Static (ordinary) method
involves the measurement of the force to be exerted on a piece of metal as it is pulled from a liquid.
But
it cannot be used to continuously measure the surface tension.
It is also difficult to use in some environments.

10. Capillary waves Type of the surface waves on water
Waves - result of a generating force
blowing wind, vessels moving, volcanic eruptions, submarine earthquakes, …, stones, …
An additional force - restoring force - acts to return the surface of the water to its original flat level.
two different restoring forces
gravity (gravity waves)
surface tension (capillary waves - ripples)

11. wave form moves and with it, energy is transmitted
Wave direction
Wave
wave energy – NOT the water particles – moves across the surface of the sea
wave form moves and with it, energy is transmitted
nearly all water movements are turbulent (non-laminar)

12. Traveling Surface Wave

13. Deep- to Shallow-Water Waves

14. As more energy is transferred to the water, the waves will grow in size
As the waves grow, gravity will become the restoring force and the waves will be gravity waves.
Speed of the waves u?
Many approaches
Analytical mechanics, conservation of energy, dimensional analysis, …

15. Dispersion relation ug=  / T =  / k is the function of:
wavelength , gravitational field strength g, density of water 
u=const    g 
The variation of wave speed with wavelength is called dispersion and the functional relationship is called the dispersion relation.

16. Dispersion relation
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      

17. Capillary and Gravity waves
Capillary waves- wavelength < 1.73 cm
Gravity waves- wavelength > 1.73 cm

18. Wave Sizes- Wave Energy

19. Experiment
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.

20. Reflection diffraction gratings

21. Experiment The effective grating spacing in this case is
 - is the angle of the laser beam measured from horizontal axis, k - is the (capillary) wave vector

22. Experiment In the case of first maximum ( is the laser wavelength)
r is the angle between the incident beam and the direction to the first maximum.

23. Experiment In the case of first maximum ( is the laser wavelength)
r is the angle between the incident beam and the direction to the first maximum.

24. Experiment

26. He-Ne laser, P=2 mW
=632,8 nm
θ=70
Ŀ=5 m