Analytical solution for the effective time lag of a membrane in a permeate tube collector in which Knudsen flow regime exists

Gas permeation in a simplified constant volume system, in which the outflow volume consists of a cylindrical collector tube, initially at high vacuum, has been modeled. Assuming a Knudsen flow regime in the permeate collector the analytical solution for the effective time lag of a membrane has been obtained by using the concept of linear asymptotes and Laplace transformation of the governing partial differential equation. The solution indicates that the effective time lag is different from the actual time lag of the membrane; the magnitude and the sign of the difference between the two time lags depends on the location where the pressure rise in the permeate tube collector is monitored, as well as, on the length and the Knudsen diffusion coefficient in the tube.