Approximate semianalytical solution for nonlinear surface diffusion in a batch reactor

A semianalytical solution for carbon adsorption process with a nonlinear boundary condition has been derived. A unit-step function was utilized to represent adsorbed-phase adsorbate concentration at solid-liquid interface. An expression for q(r,t) in terms of a unit-step function was derived, which was substituted into boundary and mass balance equations. Finally, three nonlinear simultaneous algebraic equations were derived for calculating the bulk liquid concentration. The linear iterative method is recommended to solve nonlinear algebraic simultaneous equations. The results from the semianalytical solution were verified by comparison with those obtained from numerical solution using experimental data reported by other investigators