A third-order approximate solution of the reaction–diffusion process in an immobilized biocatalyst particle

Abstract

A third-order polynomial model was suggested to describe the reaction–diffusion process of substrate in the immobilized biocatalyst particles and further to estimate their effectiveness factors. Both the numerical solution of the differential equation using the shooting method and the third-order approximate solution have been obtained. They were in good agreement for describing the substrate concentration distribution inside the particles when β= C s/ K m was larger than or equal to 0.75 φ 2−1 and φ=(R/3) r m /DK m . The relative errors of effectiveness factors obtained by the two methods were found less than 10% in a wide range of φ 2 and β except for the high values of φ 2. Some published practical systems were also examined. The results have indicated that the method proposed here could be of value for a quick estimation of substrate distribution and effectiveness factor of some systems such as dynamic oxygen transfer into natural mycelial pellets in submerged cultures.