Table of Contents

• Prequiz...
• Fick's Laws, Part II
• 1: Fick's Second Law ...
• 2: ... is about "time to diffuse"
• 3: A Very Useful Formula
• 4: Time-to-diffuse increases dramatically
• 5: General Functions and Diffusion
• Biological Applications
• 6: Biological Applications
• 7: Why do rhinos have lungs and amoebas don't?
• 8: Diffusion is efficient in small organisms, but not big ones
• 9: Why we have lungs
• 10: How many macrophages does it take to kill a virus?
• 11: You need a lot of macrophages - or one smart one!
• Review
• 12: Summary

Time-to-diffuse increases dramatically

How does a graph of time to diffuse as a function of distance look? In other words,

1. Use the equation T = (Δx)² / 2D

2. Put distance (Δx) on the x-axis

3. Put time (T) on the y-axis

4. Assume D = 0.00001 cm²/sec

So, what does the graph look like?

Remember that T = (Δx)² / 2D is a quadratic equation, analogous to y = ax² and so takes the shape of a parabola. In this case, the coefficient “a” is represented by 1/(2D). Here is the graph, using D = 0.00001.

 

Notice that as the distance increases a little, time increases a lot. We say that:

• “time to diffuse increases with the square of distance”, or equivalently,
• “distance diffused increases with the square root of time”.