Sharp interface models from homogeneous reaction systems

• Main Author: Fernandez Fonseca, Andrea
• Other Authors: Evans, Jonathan
• Published: University of Bath 2013
• Subjects: 510
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607473

This thesis investigates the fast-reaction limit for a one dimensional reaction-diffusion system describing the penetration of the carbonation reaction in concrete. Three conceptually different scaling regimes of the effective diffusivities of the driving chemical species are explored using matched asymptotics. The limiting models include one-phase and two-phase generalised Stefan moving boundary problems as well as a nonstandard two-scale (micro-macro) moving boundary problem. These sharp interface models are studied to uncover the mechanisms at the free boundary. A power law for the concentration of the chemical species at the interface is derived, as well as the large and small time asymptotic behaviour of the free boundary and the concentration profiles. Numerical results, supporting the analytical results, are presented throughout this thesis, including the application of the method of lines to solve the limiting Stefan problems. To conclude, numerical illustrations of different two-dimensional geometries are included.