Simple Diffusion

In simple diffusion, the substance is driven by concentration difference across a membrane. In the example below, we have a liver compartment that is separated into blood and liver compartments with a passive diffusion membrane for compound A.

For the simple, one-dimensional case shown above, the mass flux through the membrane follows Ficks Law:

\[J = -D \frac{dC}{dx}\]

where,

C:

Concentration at membrane location x

D:

Diffusion coefficient of the molecule

We assume the concentration gradient across the membrane of thickness, x, falls linearly with x leading to:

\[\frac{dC}{dx} = \frac{\Delta C}{\Delta X} = \frac{C_2-C_1}{\Delta x}\]

\[J = -D \frac{\Delta C}{\Delta x}\]

The rate of transfer (f) of a neutral compound across a biological membrane of surface area (S) is:

\[f = JS = -SD\frac{\Delta C}{\Delta x} = -PS(C_2-C_1)\]

where,

PS:

Coefficient of diffusivity

Note: The negative sign on the right side of the equation indicates that the net transfer due to diffusion is in a direction away from the region with higher concentration.