Polar molecules possess a weak electromagnetic field which is shared with their neighbours (known as the Van Der Waals or cohesive force). At the surface there are fewer neighbours (the Van Der Waals force is also present in non-polar molecules). Molecules on the surface of a liquid will experience a net downward force simply due to the absence of neighbours above. As the surface is pulled downward, the surface area is minimised and the density in the layer increases until limited by Coulomb repulsive forces. The energy density in the surface layer is higher than in the body of the liquid (where viscous forces reign). Surface tension produces effects such as a pin, of density much higher than water, floating if placed on the surface carefully.

Another force to consider in determining how the surface of a liquid will shape itself is the adhesive force between the liquid and a solid with which it is in contact. Water adheres strongly to glass. The water molecules in contact with the glass will tend to be attracted upwards. The surface tension effect will simultaneously rearrange the shape of the surface of the water until it is again in the lowest energy configuration. This process (obviously over a very short time-scale) will continue until the angle that the surface of the water makes with the wall of the vessel reaches a certain critical angle. This turned up at the edges shape is known as the meniscus. Water does not adhere well with wax, explaining why rain falling on the waxed surface of a car will curl up into droplets while that falling on the windscreen will spread all over the surface.

Reducing the surface tension of water will increase the degree to which it will spread over a surface (i.e. its 'wetness'). Raising the temperature of water or adding cleaning agents (surfactants) such as detergent will reduce surface tension. A washing machine is a surface tension reducer! A third method is to physically create turbulence on the surface so that the membrane is broken. Water is sprayed on the spot where a diver will enter the water so that a less painful impact results. OK, since I know by now you will be dying to know how to calculate the surface tension of a liquid, I present to you-

**How to determine surface tension by the capillary tube method**

What you will need-

- 1 capillary tube
- Some liquid (avoid mercury)
- 1 PC microscope (available for under 100 dollars)
- 1 PC with printer (most probably you have these)
- 1 ruler
- 1 micrometer screw gauge
- 1 beaker (a transparent cup would do)
- You will need to know the density of the liquid.

If you don't have a

micrometer screw gauge you could try your best with the ruler. First start up your image

capture software and

clamp the capillary tube into the beaker full of water. Notice the liquid rise up the tube due to a combination of surface tension and adhesive forces with the glass. Now the surface tension (which I will henceforth call Gamma) is the force per unit length along the

circumference of the liquid in the tube.

Gamma= F/2*Pi*R

where R is the radius of the tube. This force is balanced out by the force due to

gravity, namely the mass of the liquid that has risen multiplied by the acceleration due to gravity g (9.8 ms

^{-2}). This mass is the product of volume of liquid in the tube and the

density of the liquid (water= 1000 kg m

^{-3}). So lets write that out in equation form. Furthermore, the tension force acts parallel to the surface of the liquid where it meets the glass. It is its vertical component which balances gravity. We take care of this by multipying Gamma by Cos(theta) where theta is the angle made between the liquid and the glass.

2*Pi*R*Gamma*Cos(theta)=Volume*density*g

The volume of liquid is best calculated in two parts. First, there is the liquid beneath the lowest part of the

meniscus which is at a height h above the level of the main body of water. This is simply given by the volume of a

cylinder Pi*R

^{2}h. Next there is the water above the lowest part of the meniscus. In a narrow tube such as this the surface of the water assumes a

hemispherical shape of radius R. The volume of this hemisphere is 2/3*PI*R

^{3}, while the total cylindrical volume of this section (of height R) is PI*R

^{3}. This means the water in this section has volume 1/3*PI*R

^{3} which is equivalent to the volume of a cylinder of height R/3. Thus the total volume of the water in the capillary tube is PI*R

^{2}(h+R/3) (it might be helpful to draw a diagram of this). Finally, plug this expression for the volume into the equation above and one has

Gamma=(1/2*Cos(theta))*density*R(h+R/3)

or if you have are using browser that supports such symbols

γ=(1/2Cos(θ))*ρR(h+R/3)

So thats the theory and the

apparatus has been set up. Better get on with the experiment in that case. We need to find R, h and theta in order to obtain a value for Gamma.

- Measure the outer diameter of the capillary tube using the micrometer screw gauge. The accuracy of this device is a fraction of a millimeter.
- Take image of capillary tube using microscope. The image should include the level of the main body of liquid and the meniscus in the tube.
- Print out image.
- Measure outer diameter on capillary tube using your trusty 12".
- Calculate ratio of the outer diameter as it is represented on the printed page and the one measured more accurately in step 1. This is your scale factor between reality and image.
- From the image measure the height of the liquid in the tube. The position of the base of the liquid may be difficult to ascertain due to the pulling up of the water at the edge of the beaker. Scale down using ratio determined in previous step to find h.
- Measure the inner diameter on the image. Scale down and divide by two to find the radius R of the liquid in the tube
- Get out your long lost protractor and measure theta on the printed image. Remember this is the angle the surface of the liquid makes with the tube at the glass/liquid interface.
- Plug figures for R, h and theta and the known value of density into the formula for the sought after surface tension

Now you are equipped to test the claims of laundary detergent manufacturers. First find the surface tension of tap water. Next add your favourite non-Bio to test if Gamma is reduced. Try replicating conditions in washing machine by raising the

temperature of water. Remember any contaminants in the liquid or on the surface of the capillary tube will severely skew the results.

*Sources*

Undergrad Physics

tdent clarified the physics for me.