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

Surface tension Capillary waves Experiment

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

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)

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

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.

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.

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)

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)

Traveling Surface Wave

Deep- to Shallow-Water Waves

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, …

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.

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      

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

Wave Sizes- Wave Energy

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.

Reflection diffraction gratings

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

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.

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.

Experiment

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