To enhance the effective surface, and hence the chemical reaction rate, catalytic surfaces often take the form of porous solids. One such solid may be visualized as consisting of a larger number of cylindrical pores, each of diameter D and length L.

Consider conditions involving a gaseous mixture of A and B for which species A is chemically consumed at the catalytic surface. The reaction is known to be first order k1CA. Under steady state, flow over the porous solid is known to maintain a fixed value of the molar concentration CA0 at the pore mouth.
Beginning from fundamentals, obtain the differential equation that governs the variation of CA with distance x along the pore. Applying appropriate boundary conditions, solve the equation to obtain an expression for CA(x).