ABSTRACT
This chapter outlines the Laplace transform development of the solutions. The solutions giving the mobile phase concentration profile and surface flux rate for several semi-infinite systems. The chapter considers the fate and transport mechanisms of diffusion, adsorption, and first-order reactive decay. It describes various cases where chemical dynamics are due to diffusion and adsorption processes. The chapter also describes cases that include the additional fate process of decay, which is modeled using simple first-order kinetics. Numerical evaluation of the concentration profile and some of the surface flux expressions requires the calculation of the error function or the complimentary error function. As the diffusion equation is linear, if a problem with the same linear boundary conditions may be decomposed into simpler sub-problems, the overall solution is the sum of the solutions to the constituent sub-problems. The numerical evaluation of an unbounded system is much simpler compared to those in which the lower boundary condition plays a role.
