Fluids at Rest and in Motion: Surface Tension – SS1 Physics Lesson Note (Third Term)

Surface tension is the force per unit length acting along an imaginary line drawn on the surface of a liquid at rest.

Behavioural objectives

By the end of the lesson, students should be able to:

1. define surface tension and state its SI unit and dimensional formula;
2. describe a simple demonstration of surface tension;
3. list ways of reducing surface tension and give examples of its effects;
4. calculate surface tension using T = F/L;
5. define viscosity and state the factors that affect it and its applications.

What is surface tension?

Surface tension is the force that makes the surface of a liquid behave like a stretched elastic skin.

• Skin effect: the liquid surface acts as if it were covered with an elastic skin in a state of tension.
• Type of quantity: it is treated as a scalar quantity.
• Unit: it is measured in N/m (or N m^-1).
• Temperature: the value depends on the liquid and on its temperature.

The table shows the surface tension of some liquids.

How can surface tension be demonstrated?

Surface tension can be shown by floating a needle on still water, or by watching a drop form at a tap.

Floating needle experiment

1. Fill a beaker with water and let the surface come completely to rest.
2. Place a dry needle on a small piece of blotting paper.
3. Gently lay the paper and needle on the water surface without disturbing it.
4. After some time, the paper becomes wet and sinks, but the needle stays afloat.
5. The water surface acts as a skin that supports the weight of the needle.

Drop at a tap

• Observation: water gathers into a large ball at the spout without falling at once.
• Explanation: the water surface acts like a bag (skin) holding the drop.
• Result: the drop breaks off only when it becomes too heavy for the skin.

Other surface tension phenomena

• Soap bubble: a bubble forms when a ring is dipped into soapy water and lifted out.
• Paintbrush in water: the hairs spread out while the brush is in the water.
• Paintbrush out of water: the film of water between the hairs pulls them tightly together.

What causes surface tension?

Surface tension is caused by the attractive forces between liquid molecules, which pull surface molecules towards the inside of the liquid.

• Inside the liquid: a molecule is pulled equally in all directions, so the forces balance.
• At the surface: there are no liquid molecules above, so the molecule is pulled inward.
• Intermolecular forces: forces such as the Van der Waals force draw the particles together.
• Effect: the surface tends to shrink to the smallest possible area, which is why drops are round.

What is the formula for surface tension?

Surface tension is the ratio of the surface force F to the length L along which the force acts.

T = F/L

• T: the surface tension of the liquid, in N/m.
• F: the force acting along the surface, in newtons (N).
• L: the length along which the force acts, in metres (m).

Worked example

Calculate the surface tension of a liquid when the dragging force is 7 N and the length along which it acts is 2 m.

1. Write the given values: F = 7 N, L = 2 m.
2. Write the formula: T = F/L.
3. Substitute: T = 7/2.
4. Answer: T = 3.5 N/m.

What is the unit and dimensional formula of surface tension?

The SI unit of surface tension is the newton per metre (N/m), and its dimensional formula is MT^-2.

1. Start with the formula: T = F/L.
2. Since F = ma, write T = ma/L.
3. Replace force with its dimensions: F = MLT^-2.
4. Write T = MLT^-2 × L^-1.
5. Simplify: T = MT^-2.

How can surface tension be reduced?

Surface tension of a liquid such as water can be reduced by adding certain substances or by raising its temperature.

• Oil: adding oil to the water.
• Grease: adding grease.
• Kerosene: adding kerosene.
• Soap or detergent: adding either to the water.
• Heat: heating or boiling the water.
• Camphor: adding camphor to the water.
• Alcohol: adding alcohol to the water.

What are examples of surface tension in everyday life?

Surface tension explains the behaviour of rainproof materials, soaps, bubbles and drops.

• Rainproof tent materials: the surface tension of water bridges the pores in the material, so water does not pass through.
• Clinical test for jaundice: the test uses the lowering of surface tension of urine by bile salts.
• Disinfectants: they are solutions of low surface tension, so they spread easily.
• Washing clothes: soaps and detergents lower the surface tension of water.
• Round bubbles and drops: surface tension provides the wall tension that gives bubbles and liquid droplets their round shape.

What is viscosity?

Viscosity is the internal friction between layers of a moving fluid, and it measures how much the fluid resists flow.

• Definition by ratio: it is the ratio of the shearing stress to the velocity gradient in the fluid.
• Type of quantity: it is treated as a scalar quantity.
• Unit: pascal-second (Pa s).

Viscosity (η) = Force / (Area × Velocity gradient)

Velocity gradient = Velocity / Length

Which liquids have low or high viscosity?

What is the relationship between weight, upthrust and viscous force?

A body falling steadily through a fluid is acted on by its weight, the upthrust and the viscous force.

• W: the weight of the body, acting downwards.
• U: the upthrust, acting upwards.
• V: the viscous force, acting upwards against the motion.

When the body moves at constant velocity: W = U + V, so W – U – V = 0.

Hence V = W – U, which is the apparent (effective) weight of the body in the fluid.

What are the factors affecting viscosity?

The viscosity of a fluid depends on the material, its temperature and, for liquids, very high pressure.

• Material: viscosity is a property of the material, so each fluid has its own value.
• Liquids and temperature: viscosity of simple liquids decreases as temperature increases.
• Liquids and pressure: viscosity of simple liquids increases under very high pressure.
• Gases and temperature: viscosity of gases increases as temperature increases.
• Gases and pressure: viscosity of gases is independent of pressure and density.

What are the effects of viscosity?

• Rate of flow: viscosity is responsible for different rates of fluid flow.
• Motion of bodies: viscosity affects the motion of a body moving through a fluid.

What are the applications of viscosity?

1. Lubricants: viscous liquids reduce friction between moving parts.
2. Ships and aircraft: knowledge of viscous drag (drag force) is applied in their design.
3. Particle size: it is used to estimate the size of small particles moving through a fluid.

What is the difference between surface tension and viscosity?

Surface tension acts along the surface of a liquid at rest, while viscosity acts between layers of a fluid in motion.

Evaluation

1. Define surface tension and state its SI unit.
2. State the dimensional formula of surface tension.
3. List three ways of reducing the surface tension of water.
4. A force of 12 N acts along a length of 3 m on the surface of a liquid. Calculate the surface tension.
5. State two factors that affect the viscosity of a liquid.

Assignment

Define viscosity, state two substances with high viscosity, and explain how temperature affects the viscosity of a liquid and of a gas.