Table of Contents

• Prequiz...
• Just Plain Movement
• 1: Measuring Movement
• 2: Directed vs. Undirected Movement
• 3: Measuring Movement Using Flux
• Introducing Gradients
• 4: What is a gradient?
• 5: Watching diffusion happen (applet)
• 6: Visualizing the Gradient
• Fick's Laws, Part I
• 7: Fick's First Law
• 8: The gradient in Fick's First Law
• 9: A familiar equation for Fick's first law
• 10: The diffusion coefficient is the slope
• 11: What are the units for D?
• 12: How does flux depend on distance?
• 13: A fragrant example
• 14: General Transport Equations and Fick's First Law
• Fick's Laws, Part II
• 15: Fick's Second Law ...
• 16: ... is about "time to diffuse"
• 17: A Very Useful Formula
• 18: Time-to-diffuse "explodes"
• 19: General Functions and Diffusion
• Biological Applications
• 20: Biological Applications
• 21: Why do rhinos have lungs and amoebas don't?
• 22: Diffusion is efficient in small organisms, but not big ones
• 23: Diffusion within lungs
• 24: How many macrophages does it take to kill a virus?
• 25: You need a lot of macrophages - or one smart one!
• Review
• 26: Final Review

Visualizing

Fundamentally, the word "gradient" means that in one place, there are a lot of particles, and in another place, there are few particles -- and in between those places, the number of particles changes gradually.

Now imagine all these particles moving around. In fact, small particles like atoms are in constant motion and this is what causes diffusion. How? Well, at the left, where there are lots of particles, none of them will travel very far without bumping into another particle. So, they will keep bouncing around, back and forth, up and down, and not get very far. On the other hand, on the right, where are few particles, they can move a long distance without any bounces. In particular, once a particle is heading for an empty area, it keeps going -- there's nothing there to stop its progress.

More succinctly, we say that:

• When the concentration is high,
  mean displacement (average distance moved) is small.
• When the concentration is low,
  mean displacement is high

The applet below will help you visualize diffusion. Before you start the applet you should realize that the particles in the box are not distributed randomly and not spread out evenly. Instead, they are clustered at the center of the box. We say there is a steep gradient between the center and the sides of the box. Now start the simulation. Notice that although each particle is moving randomly, the net effect is that the clumped particles get spread out evenly. In the other words, there is a flux of particles from the center to the edges at least until the particles are spread out evenly. After that, there is no net movement - no flux.

Applet based on original Java simulation by N. Betancourt, 1999

You can also click off the trace function so that you can watch the particles moving about randomly.

If you start the simulation over several times with different numbers of particles. You will see that the particles always move from a state of high order (all particles in the center of the screen) to a state of disorder (all particles distributed rather evenly throughout the screen).

You can also see that diffusion only occurs when there is a gradient. After the gradient is gone, then the continual movement no longer results in a net change in distribution. In other words, without a gradient there is no flux.