Curvature effects on a simplified reaction-diffusion model of biodegradation

Abstract

The biodegradation process of some types of polymers occurs due to many different factors including their morphology, structure and chemical composition. Although this is a complicated process, most of its important stages like the diffusion of monomers and the hydrolysis reactions have been modeled phenomenologically through reaction-diffusion equations, where the properties of the polymers were encompassed. Using a simplified reaction-diffusion model for the biodegradation of polymers, in this contribution we study the possible effects of the curvature of the system’s geometry in the degradation process, which is characterized by the interaction of the corresponding reaction rate and the diffusion coefficient. To illustrate the problem of diffusion on a curved surface we consider the surface of a cylinder and of the so-called Gaussian bump. We show how the degradation process is affected by the curvature of the system for the simplified model.