Theoretical model for diffusion-reaction based drug delivery from a multilayer spherical capsule

Controlled drug delivery from a multilayer spherical capsule is used for several therapeutic applications. Developing a theoretical understanding of mass transfer in the multilayer capsule is critical for understanding and optimizing targeted drug delivery. This paper presents an analytical solution for the mass transport problem in a general multilayer sphere involving diffusion as well as drug immobilization in various layers due to binding reactions. An eigenvalue-based solution for this multilayer diffusion-reaction problem is derived in terms of various non-dimensional quantities including Sherwood and Damköhler numbers. It is shown that unlike diffusion-reaction problems in heat transfer, the present problem does not admit imaginary eigenvalues. The effect of binding reactions represented by the Damköhler numbers and outer surface boundary condition represented by the Sherwood number on drug delivery profile is analyzed. It is shown that a low Sherwood number not only increases drug delivery time, but also reduces the total mass of drug delivered. The mass of drug delivered is also shown to reduce with increasing Damköhler number. The impact of shell thickness is analyzed. The effect of a thin outer coating is accounted for by lumping the mass transfer resistance in series with convective boundary resistance, and a non-dimensional number involving the thickness and diffusion coefficient of the coating is shown to govern its impact on drug delivery characteristics. The analytical model presented here improves the understanding of mass transfer in a multilayer spherical capsule in presence of binding reactions, and may help design appropriate experiments for down-selecting candidate materials and geometries for drug delivery applications of interest.