Photochemical reactors use natural or artificial light to activate a catalyst. This Demonstration analyzes the behavior of a photocatalytic reactor consisting of two concentric cylinders. The reactant and product of the reaction flow in a fluid in the cylindrical annulus formed by an ultraviolet lamp and an outer cylinder that has a wall coated by a catalyst. We assume the properties of the fluid are constant, that the fluid is in laminar flow that is independent of axial location, and that in the inlet region the reactant concentration is uniform. Photocatalytic reactors are mostly used for degrading contaminants in aqueous solutions; they are also used for contaminant removal from air and wastewater treatment.
The mass balance for the reactant is:
with boundary conditions:
The velocity of the fluid in the annulus is :
and the maximum velocity is
Here stands for the reactant specific density, is the concentration of reactant , is the reactant diffusivity, is the pressure difference, is the radius of the outer cylinder, is the length of the reactor, is the ratio of the UV lamp radius to the radius of the outer cylinder, is the fluid viscosity, and the axial and radial variables are and , respectively.
The average (cup) concentration of the reactant is:
This system of equations is solved with the built-in Wolfram Language function NDSolve and plots of the velocity profile, contours of the reactant concentration and the average (cup) conversion of the reactant are shown.
 R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena, 2nd ed., New York: J. Wiley, 2002.