SURFACE TENSION A-LEVEL PHYSICS

SURFACE TENSION

Some observation due to surface tension

1. A drop of water, on closing a tap remained dinging on the tap, as if the water was held in a bag.
2. A thin needle can be made to float on the surface though it is denser than water.
3. Mercury gathers in small spherical drops when poured on a smooth surface
4. When a capillary tube is dipped in water, water is seen rising up in a tube.
5. Insects can walk on the water surface

All the above observations show that a liquid surface behaves as if it was or it is in a state of tension. The phenomenon is called surface tension.

Surface Tension or Co-efficient of surface tension (γ)

This is the force per unit length acting in a liquid surface at right angle to an imagining drawn tangentially to the liquid surface.

Molecular Theory of Surface Tension

The force F(r)  between two molecules of a liquid varies with their separation r as shown below

At the average equilibrium separation, r_0,     

 F(r) = 0

For r > r_o = the force is attractive.

For r <r_o = the force is repulsive.

The corresponding potential energy variation with molecular separation is shown below

• The molecule within the body of the liquid (built molecule) is attracted equally by neighbors in all directions, hence the force on the bulk molecule is zero, so the intermolecular separation for bulk molecules is r_o.
• For a surface molecule, there is a net inward force because there are no molecules above the surface. Hence to bring a molecule from inside the liquid.
• To the surface, work must be done against the inward attractive force, hence a molecule in the surface of the liquid has a greater potential energy than a molecule in bulk. The potential energy stored in the surface is called free surface energy.
• Molecules at the surface have their separation r > r_o The attractive forces experienced by surface molecules due to their neighbours put them in a state of tension and the liquid surface behaves as a stretched skin.

Surface energy and shape of a drop of a liquid                                                                      

All systems arrange themselves in such a way that they have the minimum possible potential energy. The number of molecules that resides in the surface has to be minimum, and to minimize the number of molecules on the surface, the surface area must be reduced, hence liquid surface contract to the smallest possible area.

So free liquid drops are spherical for any given volume because it is the shape which gives the minimum surface area. A large drop flattens out in order to minimize the gravitational potential energy which tends to exceed the surface energy.

Due to its large weight, gravitational force distorts the spherical shape of large droplets however a small drop takes on a spherical shape to minimize the surface energy, which to be greater than gravitational potential energy. Therefore the gravitational force can not distort the spherical shape due to very small mass of tiny droplets.

Angle of contact

The angle between the solid surface and the tangent to the liquid surface at the point of intersection with the solid surface as measured through the liquid.

A liquid makes an acute angle of contact with the solid surface if the adhesive forces between the liquid and solid molecules are greater the cohesive forces between the liquid molecules themselves. The angle of contact is zero on a clean glass for pure water. If a liquid makes an acute angle of contact, it is said to wet the solid surface.

A liquid makes an obtuse angle of contact with the solid surface if the cohesive forces between the liquid molecules themselves are greater than the adhesive forces between the solid and liquid molecules. Such a liquid is said not to wet the solid surface.   The angle of contact of mercury on a glassurface is 140⁰. Addition of detergent to a liquid reduces the angle of contact and therefore helps in washing.

Excess pressure inside an air bubble

Consider the equilibrium of one half of an air bubble of radius r, in a liquid of surface tension γ

This half of the bubble is in equilibrium under the action of force F₁ which is due to pressure P₁, F₂ which is due to the pressure p₂ and force F

P₁= pressure outside the bubble

P₂ = pressure inside the bubble

For equilibrium, F₁+F = F₂

Excess pressure inside a soap bubble                                                                                          

For a soap bubble, it has two surfaces

Note. The pressure on the concave side of a liquid surface is always greater than that on a convex side e.g.

Flat surface        P_A = P_B

Hence excess is equal o zero on a flat surface.

Concave meniscus

Capillary Rise

Consider the care of a liquid wets glass.

The radius of curvature of the meniscus is related to the radius of the capillary and angle of contact as shown

Effects of temperature on surface tension

When the temperature of a liquid is raised, the mean kinetic energy of the molecules of the liquid raises on the average of the force of attraction between the molecules decreases since the molecules spend less time in the neighbourhood of the given molecules as a result the intermolecular separation rises hence surface tension of the liquid decreases with rising temperature.

Relationship between surface energy and surface tension

Suppose a film is stretched isothermally (at constant temperature) so that the edge BC moves through a distance x to B’C’.

The work done to stretch the film = F₀x

Hence surface tension can also be defined as the work done to increase surface area of a liquid by 1m² under isothermal condition.

A pin is attached to the capillary tube with its tip just touching the liquid in the beaker. A traveling microscope is focused on the meniscus M. The reading S₁, on the scale is recorded. The beaker is carefully removed and the traveling microscope is focused on the tip of the pin P. The reading S₂ on the scale is recorded.

The radius, r of the capillary tube is determined measuring its diameter by using a traveling microscope. The angle θ of contact is measured and since the density, ρ of the

The pressure in the flask is increased gradually by allowing drops to fall down the funnel. Bubbles formed at the tip of the capillary tube dipping in the specimen liquid are observed. When the bubble has grown to a hemispherical shape, the tap T is closed and the reading h2 on the manometer is recorded. The depth, h1 of the end of the capillary

The radius, a of the capillary tube is determined measuring its diameter by using a traveling microscope. The angle θ of contact is measured and since the density, ρ₁, ρ₂ of the liquids are known, then γ can be calculated.

Examples

1) Mercury is poured into a glass U- tube with vertical limbs of diameters 20mm and 12.00mm respectively. If the angle of contact between mercury and glass is 140⁰and the surface tension of mercury is 0.152 Nm^-2. Calculate the difference in the levels of mercury. (Density of  mercury = 1.35 x 10⁴ kgm^-3).

A droplet of mercury of radius 2.0mm falls vertically and on hitting the ground it splits into two droplets each of radius 0.50mm. Calculate the change in surface energy.

Account for the change in (i) above.

1c) Energy of a large droplet

Change in energy

The energy reduces because some of it is lost in overcoming  air resistance.

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