Physiology > Gases > Diffusion & Fick's law
Diffusion and Fick's Law
In order for oxygen to be useful to you, it must be dissolved in the aqueous fluid in your cells. For an air-breathing animal, the O2 molecules must diffuse from the air in your lungs into the blood in your alveolar capillaries (the tiny blood vessels surrounding the small air sacs in your lungs). Likewise, CO2 is produced in your tissues, carried in your blood, and ultimately diffuses out of the blood into the air in the alveoli. Your blood carries these gases effectively, but the critical rate-limiting step is often the diffusion between the air and the blood.
The rate of diffusion depends on two things:
- The surface area of the lungs. More area means more chances for gas molecules to diffuse across.
- The rate of diffusion across each centimeter of surface area. This rate can be called the flux density.
The flux density itself depends on two factors:
- The concentration gradient of the gas. For example, the difference in O2 concentration between the air in the alveoli and the blood in the capillaries surrounding the alveoli. If there is a strong concentration gradient (high O2 concentration in the air and low O2 concentration in your blood), diffusion is fast.
- The "easiness" of movement of the gas between the air and the blood. In other words, how quickly the molecules can diffuse across the surface of the lungs at a given concentration gradient. The "easiness" is sometimes called diffusivity, and it can be expressed with a diffusion constant, described below.
Since there are only a few factors affecting the overall rate of gas diffusion into or out of an organism's body, it's possible to express the rate in a fairly simple equation, known as Fick's Law.
Fick's Law of Diffusion
The rate of diffusion of a gas across a permeable membrane can be described with Fick's law of diffusion. There are various forms of this equation, but this one has been adapted for use in physiology:
- m/t: the amount of gas (m) diffusing from one place to another in a given time (t). For example, this might be the number of O2 molecules per second passing across the surface of your lungs. This is also called the oxygen flux.
- D: the diffusion constant, a measure of how easily a gas passes through a particular material (such as a cell membrane). There would be a specific D for O2 diffusing through water, a different D for O2 diffusing through air, and a different D for CO2 in water or air. In most biological situations, the diffusion constant is, in fact, constant, and we won't need to quantify it for this class. We'll be more concerned with the variables that change over time.
- S: the surface area for diffusion. In the case of an air-breathing mammal, this means the surface area of the alveoli in your lungs. For a fish, it would be the surface area of the gills. This surface area is a critical aspect of any animal's morphology, but it can't normally be changed quickly as a response to changing oxygen use.
- ΔC/x: the concentration gradient. The concentration gradient is the difference in concentration between two places ΔC, divided by the distance distance between those places (x). For example, ΔC could be the difference in O2 concentration between the air in your lungs and the blood in your alveolar capillaries. The short distance between air and blood (a couple of cells thick) would be x. For our purposes, it makes sense to express the O2 concentration in terms of partial pressure (PO2).
This equation says two important things about O2 uptake:
Oxygen flux is proportional to the O2 concentration gradient. Since the concentration gradient is the difference in concentration between air in the alveoli and blood in the alveolar capillaries, it can be changed by changing either of these quantities.
Oxygen flux is proportional to the surface area of the lungs or gills. This is important when comparing different animals, but it normally remains constant for a single individual (unless it's growing).
Fick's Law in Practice
You don't always consume oxygen at the same rate. If you exercise, your oxygen consumption rate (m/t) goes up. What changes on the other side of the equation? Not the diffusion constant (D); it remains constant. Not the surface area of your lungs (S); your lungs can't change that fast. (Breathing deeply might increase the volume of air in your lungs, but the surface area doesn't change much.) The only thing left to change is the concentration gradient, ΔC/x. The concentration gradient increases because the oxygen level in your blood decreases when you use the O2; therefore the the difference in concentration between air and blood is greater. Oxygen diffuses into your blood more quickly when you need it. Normally, any changes in your oxygen uptake rate can be explained by changes in the PO2 of blood, alveolar air, or both.
When you are comparing different animals (whether different species or different-sized individuals of the same species), the surface area for gas exchange (A) also becomes an important variable.
Fick's law applies whenever substances move by diffusion: CO2 moving out of a cell and into the bloodstream, water moving through the soil, etc. In all these cases, we are at the mercy of diffusion, and Fick's law tells us that the rate will depend on the surface area and the concentration gradient. Fick's law doesn't apply to oxygen being circulated in the blood, though; that's bulk flow, not diffusion.
To learn more:
Comparative Biomechanics: Life's Physical World (2003), by Steven Vogel, of Duke University. This book is the best overall source for learning about how organisms interact with the physical world, and I used it as a reference for these pages including the formulation of Fick's equation. I also highly recommend Vogel's other books, such as Life in Moving Fluids, Life's Devices, or Glimpses of Creatures in Their Physical Worlds.
This page updated September 22, 2011