404 Not Found


nginx/1.14.0 (Ubuntu)

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.

404 Not Found

404 Not Found


nginx/1.14.0 (Ubuntu)