Consider two large compartments containing **weak** glycerol
solution at concentrations *A* and *B*. The compartments
are joined by a **small**, asymmetric channel. Glycerol **slowly
diffuses** through the channel at a rate *F*(*A*,*B*).

Since the solutions are weak, the rate will be linearly proportional to the concentration difference:

*F*(*A*,*B*) = *a A* - *b B*

for some *a* and *b*.
This equation holds for any small values of *A* and *B*,
including zero.

If *A*=*B*, the two compartments are in equilibrium, so
there can be no net flow:

*F*(*A*,*A*) = *a A* - *b A* = 0;

*a = b*;

*F*(*A*,*B*) = *a*(*A* - *B*).

Suppose *A* = k, *B* = 0. The rate of flow is *ak*.
If *A* = 0 and *B* = k the rate is similarly -*ak*.

Therefore, the channel conducts equally well in both directions.

One direction is better than the other only if one of the assumptions
is violated: the concentration is **strong**, the channel is
**large** compared to the compartments, or the molecules move
**ballistically**. Any model that explains why one direction is
better than another must show which assumption is violated and how the
rates approach equality in a limiting case.