Table of Contents

• Prequiz...
• Just Plain Movement
• 1: Measuring movement
• 2: Directed vs. undirected movement
• 3: Measuring movement using flux
• Introducing Gradients
• 4: Gradients and diffusion
• 5: Watching diffusion happen (applet)
• 6: Visualising 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: Graphing Fick's First Law
• 11: How does flux depend on distance?
• 12: A fragrant example
• 13: General transport equations and Fick's First Law
• Review
• 14: Summary

Measuring Movement Using Flux

Since we are interested in a specific process (movement), we need a good way to measure that process. As scientists, we love to measure things. In fact, if we can't measure something, we're probably not very interested in it. As it turns out, there are all sorts of ways to measure movement, but we are going to focus on the quantity known as flux.

Flux is an unusual concept for many people because its ordinary (conversational) meaning is rather different from its scientific meaning. For most people (meaning the two people we just asked!) flux means changes in conditions, similar to “ebb and flow” or “fluctuations”. Mathematically, however, flux means “the net rate at which particles move through a certain area”.

In other words, flux is the net movement of particles across a specified area in a specified period of time. The particles may be ions or molecules, or they may be larger, like insects, rabbits or cars. The units of time can be anything from milliseconds to millennia. Here are some examples of flux:

The number of cars that pass through a toll booth every day.	The net number of rabbits that cross a fence every hour.	The net number of salt ions that pass out of a cell membrane every minute.

Flux is not the same thing as velocity or speed, which are measured in the units of distance per time, rather than number per time. Individual oxygen molecules may be moving very fast, but since they are going in a variety of directions (they are undirected), there may be no net movement of oxygen from one place to another.

Likewise, flux is also not the same thing as density or concentration, which are measured as particles per volume. A cell may be chock-full of oxygen, but if none of the oxygen molecules are going anywhere, there is no flux. Or there may be only a little oxygen, but what is there is quickly leaking out, so in that case, flux is high.

Finally, movement itself is not enough. If (like some cats I know) you continually go in and out of the same door, we wouldn’t say there was high flux through the door. Instead, flux is a measure of net movement, where ‘net’ is only taking into account the remaining ‘gain’ after all positives and negatives have been accounted for or cancelled out.

So what is flux? First, we need the flow rate, which is the number of particles moving in a specified time (mol s^-1).  Flux is the flow rate divided by the area through which the substance is moving. Therefore, the units of flux are mol m^-2 s^-1 or mol cm^-2 s^-1.

flux = flow rate/area, and

flow rate = flux × area