3: 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, how 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”.