Medical Sciences Interview
Scientific Reasoning Skills
Sample Problem

Scientific reasoning skills

Linking your sciences together

New Court and the Bridge of Sighs

In this test of your scientific reasoning you will be linking together ideas which you have studied in your different subjects at school.
The aim is to see if you can apply concepts which you have already studied in ways which you have not met before.

You should try to answer the questions in italics before moving to the next page.

Do not worry if the problem seems unfamiliar: this is intentional, to test your reasoning!

Stability of soap bubbles

Where physical chemistry meets biology

By Brocken Inaglory. The image was edited by user:Alvesgaspar
[CC-BY-SA-3.0], from Wikimedia Commons

We will consider how forces act upon a soap bubble to maintain its stability, and then apply these ideas to a biological problem.

But first, let us begin with a specific situation...

Two interconnected soap bubbles

What happens when two bubbles of different sizes are connected?

Two interconnected bubbles

Imagine two bubbles of different sizes joined together by a hollow tube so that the gas spaces inside are interconnected.

What would you expect to happen next?

Two interconnected soap bubbles

Imagine that we conduct the experiment

When the valve is opened, air passes from the small bubble to the large bubble. Consequently the large bubble expands and the small bubble shrinks, until it ultimately collapses altogether.

Was this what you expected? Why might this occur?

Stability of a single soap bubble

What forces act on the bubble wall?

To solve this problem we need first to understand what keeps a single bubble at a constant size.

What forces are acting upon the wall of the bubble?

Stability of a single soap bubble

What forces act on the bubble wall?

The wall of the bubble is under tension, causing the bubble to collapse. This tendency is balanced by the air pressure inside the bubble, which keeps it inflated. If the bubble is to remain at a constant size, then these two forces must balance.

Why does the soap film of the bubble wall behave as if it is under tension?

Surface tension at the air-water interface

Surface tension results from cohesive forces

At the air-water interface, surface tension results from the greater cohesion of water molecules to each other than adhesion to the molecules in the air. The overall effect is an inward force at its surface that causes the water to behave as if the water were covered with a stretched elastic membrane.
It is this surface tension force that allows water striders to walk on water!

So how would surface tension be affected by adding soap to the water?

Surface tension in a soap film

Surface tension provides a force per unit length

Soap intereferes with cohesion between water molecules, reducing the surface tension force.
Surface tension in a soap film provides a constant force (T), per unit length of interface. You can imagine the cohesive forces acting across a cut in the soap film. If the length of the cut were doubled, the forces would double also.

So how can these ideas be applied to the stability of a soap bubble?

Stability of a single soap bubble

What are the forces on the bubble wall?

To understand the soap bubble, we must calculate individually the surface tension and pressure forces.
Imagine that a bubble of radius r made from a soap solution with surface tension T has been cut into two hemispheres across the equator.

How large is the surface tension force on the lower hemisphere and which way does it act?

Stability of a single soap bubble

Surface tension acts upwards on the lower hemisphere

Surface tension forces will act around the perimeter of the cut in the bubble wall. This force will act upwards on the lower hemisphere.
At the equator the length of the perimeter is:
2 * pi * r
Since surface tension exerts a force of T per unit length, the total force acting upward is:
2 * pi * r * T
As the soap film has two surfaces, the force would actually double, but ignore this for now.

How large is the force on the lower hemisphere due to the pressure (P) within the bubble and which way does it act?

Stability of a single soap bubble

Pressure exerts a force downwards on the lower hemisphere

The resultant force due to the pressure inside the bubble will act downwards on the lower hemisphere, perpendicular to the plane of section across the equator. The area subtended by the lower hemisphere is:
pi * r * r
Since pressure exerts a force of P per unit area, the total force acting downward is:
pi * r * r * P

So how can we calculate whether the bubble will be stable?

Stability of a single soap bubble

The bubble will be stable when the forces are balanced

For stability, the surface tension forces and pressure forces, which act in opposite directions, must balance:
2 * pi * r * T = pi * r * r * P
Cancelling and rearranging:
P = 2 * T / r
which is known as the Law of Laplace

So why when two bubbles of different sizes were connected did the smaller bubble collapse?

Two interconnected soap bubbles

Why does the smaller bubble collapse?

Two interconnected bubbles

For stability the Law of Laplace requires that:
P = 2 * T / r
This means that the pressure is higher in the smaller bubble than in the larger bubble, since its radius is smaller.
So air flows from the smaller bubble into the larger bubble: this continues until the smaller bubble collapses completely.

So how is this relevant to biology? Do we have bubbles anywhere within our body?

The lung contains alveoli for gas exchange

Alveoli are lined with a thin fluid film and so obey the Law of Laplace

Alveoli of the lung. By Patrick J. Lynch, medical illustrator
[CC BY 2.5], via Wikimedia Commons

For stability the Law of Laplace requires that:
P = 2 * T / r
If alveoli were to differ in size and all have the same surface tension, then small alveoli would collapse completely, inflating larger ones, just like the connected bubbles.
This would impair gas exchange and make the lung harder to inflate!

So how could the lung prevent alveolar collapse?

The lung contains alveoli for gas exchange

The Law of Laplace causes small alveoli to collapse if surface tension is constant

Small and large alveoli

For stability the Law of Laplace requires that:
P = 2 * T / r
The problem is caused by our assumption that surface tension is the same in both large and small alveoli. But we have already seen how surface tension can be reduced by interfering with water cohesive bonds. Somehow we need to make the surface tension lower in the smaller alveoli than the larger ones.

How might this be achieved?

Surfactant disrupts water cohesion

Surface tension is reduced by surfactant at the air-water interface

Pulmonary surfactant

Cells in the lung secrete a substance known as pulmonary surfactant which reduces the surface tension in alveoli.
Surfactant molecules have a polar head and a non-polar tail. So they sit in the air-water interface and disrupt water cohesion.
This lowers the surface tension of the fluid film lining the alveoli.

But how does this help stabilise small alveoli?

Surfactant disrupts water cohesion

Surface tension is reduced more when surfactant is crowded together

Surfactant in small and large alveoli

Surfactant is crowded together more in small alveoli, reducing surface tension more than in large ones.
As alveoli expand during inspiration, the surfactant becomes more spread out in the fluid film. This increases surface tension in the larger alveoli and slows their rate of expansion, ensuring that all alveoli inflate at about the same rate.

When might surfactant be absent clinically and what could you do about it?

Infant respiratory distress syndrome

Surfactant is absent in premature babies

Synthetic pulmonary surfactant.
By Bobjgalindo [CC BY-SA 4.0], from Wikimedia Commons

Pulmonary surfactant is expressed late in pregnancy. So premature babies can have insufficient surfactant to prevent partial alveolar collapse.
This results in fast breathing, a fast heart rate and difficulty in breathing, accompanied by pronounced blue colouring of the skin during breathing efforts. If not treated, ventilatory failure may result.
Artificial surfactant can be used to treat respiratory distress syndrome, but it remains the most common single cause of death in the first month of life in the developed world.

The End