Analytical expressions of the effectiveness factor of a biocatalytic membrane reactor, and its asymptote as the Thiele modulus becomes large, are presented. The evaluation of the effectiveness factor is based on the solution of the governing equations for solute transport in the two regions of the reactor, i.e. the lumen and the matrix (with the biofilm immobilized in the matrix). The lumen sol...

We consider a mathematical model that describes the release of heparin-binding growth factors from an affinity-based delivery system. In the delivery system, heparin binds to a peptide which has been covalently cross-linked to a fibrin matrix. Growth factor in turn binds to the heparin, and growth factor release is governed by both binding and diffusion mechanisms, the purpose of the binding be...

Integration factor (IF) methods are a class of efficient time discretization methods for solving stiff problems via evaluation of an exponential function of the corresponding matrix for the stiff operator. The computational challenge in applying the methods for partial differential equations (PDEs) on high spatial dimensions (multidimensional PDEs) is how to deal with the matrix exponential for...