Diffusion Factors

Diffusion Factors

A flea has no lungs, no heart and no blood, and it manages perfectly well. Oxygen simply diffuses in through its surface and reaches everything inside. You cannot do that. You need lungs with a surface area the size of a tennis court, a pump, and five litres of blood, all to achieve the same result. Nothing about the chemistry is different. What changed is the size, and this module is about why size alone forces that entire apparatus into existence.

Small against large

Every cell in a body needs oxygen delivered and waste taken away. How that is achieved depends entirely on the ratio between the surface available and the volume to be served:

Surface area to volume

A cube has sides of 2 cm. Work out its total surface area and its volume, then divide the first by the second to get its surface area to volume ratio.

Why does the ratio fall?

That cube of side 2 cm has a surface area to volume ratio of 3. Double it to a cube of side 4 cm and the ratio drops to 1.5. Why does growing always lower the ratio, for any shape?

• Surface area depends on length squared while volume depends on length cubed, so volume grows faster than surface every time the object gets bigger. The inside outruns the outside
• The surface of a larger organism is thicker, so less can get through it
• Larger organisms tend to be rounder, and a sphere has the worst ratio of any shape
• Larger organisms have larger cells, and large cells exchange less efficiently

What sets the rate

Four things change how fast diffusion happens across a surface:

What is each adaptation for?

Fick's law

The three factors combine into one relationship. The rate of diffusion is proportional to: (surface area × concentration difference) ÷ thickness Read it as a fraction and it tells you the direction of every effect at once. Surface area and concentration difference are on top, so increasing either raises the rate. Thickness is underneath, so increasing it lowers the rate. Worked example. A surface with an area of 10, a concentration difference of 6 and a thickness of 5 gives a relative rate of (10 × 6) ÷ 5 = 12. Halve the thickness to 2.5 and the rate doubles to 24. Double the area instead and it also doubles. Neither number means anything on its own; the point is the comparison. Most exam questions do not want a number at all. They want you to name which factor changed and say whether the rate goes up or down.

Find the relative rate

An exchange surface has a surface area of 12, a concentration difference of 5 and a thickness of 3. Calculate its relative rate of diffusion.

Two changes at once

A section of exchange surface doubles in area. At the same time, scar tissue makes it twice as thick. What happens to the rate of diffusion across it?

• It stays roughly the same. Doubling the area doubles the top of the fraction and doubling the thickness doubles the bottom, so the two changes cancel out
• It doubles, because the increase in surface area is the larger effect
• It falls to a quarter, because the two changes compound
• It halves, because thickness has more effect on diffusion than surface area does

Why diffusion needs help

Diffusion is not slow. Across the width of a cell it is essentially instant, and across an alveolar wall it takes a fraction of a second. The problem is how badly it scales. The time diffusion takes rises with the square of the distance, so making the journey ten times longer makes it a hundred times slower. Over micrometres that is nothing. Over the width of a human body it would take years, and you would be dead long before the oxygen arrived. So a large organism splits the job in two. Diffusion does the short hop across the exchange surface, where it is superb, and mass transport in the blood does the long haul, where diffusion would be hopeless. And notice what the blood is also doing while it travels: by carrying oxygen away the instant it arrives, it keeps the concentration on that side low, which keeps the gradient steep. The transport system is not just a delivery service; it is half of what makes the exchange surface work at all.

Why keep breathing?

Sitting completely still, you use very little oxygen, and the air in your lungs already contains far more oxygen than your blood does. So why does breathing carry on regardless?

• To keep replacing the air. If the same air stayed in the alveoli, its oxygen would diffuse into the blood and its concentration would fall towards the blood's, the gradient would flatten, and diffusion would slow towards nothing however much oxygen was left
• Only to remove carbon dioxide, since oxygen would be sufficient without it
• To keep the lungs inflated, since they would otherwise collapse under their own weight
• To warm the incoming air, which speeds up diffusion

Two failing lungs

Two patients are breathless on climbing stairs, and their lungs have failed in different ways.

• In the first patient, emphysema has broken down the walls between alveoli, so many small sacs have merged into fewer large ones. Which term of Fick's law has changed, and how?
• The second patient has fluid collecting in the alveoli, so oxygen must now cross a layer of liquid before it reaches the wall. Which term has changed here?
• Both patients are given oxygen-enriched air to breathe. Why does that help in both cases, even though the underlying faults are different?

Why big things need lungs

Put the argument into order, from being small to needing a circulatory system.

• An organism grows larger
• Its volume increases faster than its surface area, because one depends on length cubed and the other on length squared
• Its surface area to volume ratio therefore falls
• The outer surface can no longer supply the whole of the interior by diffusion alone
• A specialised exchange surface evolves, folded to regain the lost area
• And a transport system evolves to carry the gases between that surface and the tissues, since diffusion cannot cover the distance

Diffusion summary

As an organism grows, its volume rises faster than its surface area, so its surface area to volume ratio _____. Beyond a certain size the body surface can no longer supply the interior, and a specialised exchange surface is needed. Fick's law says the rate of diffusion is proportional to surface area times concentration difference, divided by the _____, so a thicker barrier makes diffusion _____. Ventilation and blood flow both work by keeping the concentration _____ steep, since a gradient left undisturbed flattens itself.