# A familiar equation for Fick's first law

**Fick's Law again:** Flux is directly proportional to the steepness of the gradient.

So now we know that the gradient is represented by dC/dx, but what does “directly proportional” mean? Use your mouse to see how the steepness of the gradient affects the amount of diffusion:

When we have a small gradient, there is not much diffusion going on, but when
the gradient is BIG, then diffusion can be substantial. But how can we represent
this mathematically? Well, **if two quantities are directly proportional, they
are related to each other through an equation like y = mx**. Hmmm.... this equation
should sound familiar -- it's the equation for a line which goes through (0,0).

So, FINALLY, a mathematical equivalent to Fick's law, in both a continuous (calculus) and discrete version. Notice that they both have the same basic form that is directly analogous to the basic equation for a straight line that intersects the origin (y=mx):

Continuous version |
Discrete Version |

**So for both equations, "y" is the flux (or more correctly, the flux density), and is dependent (and therefore
called the dependent variable) on two quantities:** 1) the **steepness** of the gradient
(in red) and 2) a coefficient based on the particular substance being measured
(the **Diffusion coefficient**, "D" - more on that later).

One last note ... **Why the negative sign in front of the diffusion coefficient???** Remember that diffusion always goes DOWN the concentration gradient -- its direction
is opposite the concentration gradient. So the the diffusion coefficient has a
**Movement always occurs in a direction OPPOSITE to that of the gradient**.

Copyright University of Maryland, 2007

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