Question: The rate at which a solute diffuses through a membrane is proportional to the area and to the concentration difference across the membrane. A solution

The rate at which a solute diffuses through a membrane is proportional to the area and to the concentration difference across the membrane. A solution of concentration C flows down a tube with constant velocity v. The solute diffuses through the wall of the tube into an ambient solution of the same solute of a lower fixed concentration C₀. If the tube has constant circular cross-section of radius r, show that at distance x along the tube the concentration C(x) satisfies the differential equation

dC dx 2k rv (C-Co)

where k is a constant.

dC dx 2k rv (C-Co)

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