A mathematical model for bacterial self-healing of cracks in concrete

In the current research, a mathematical model for bacterial self-healing of a crack is considered. The study is embedded within the framework of investigating the potential of bacteria to act as a catalyst of the self-healing process in concrete, which is the ability of concrete to repair occurring cracks autonomously. Spherical clay capsules containing the healing agent (calcium lactate) and nutrients for bacteria are embedded in the concrete structure. Water entering a newly appearing crack initiates the release of the capsule content and activates the bacteria to convert calcium lactate to calcium carbonate (limestone). The crack is sealed through the metabolically mediated limestone precipitation. The model of the self-healing process is based on a moving boundary problem in which two fragments of the boundary move resulting from calcium carbonate precipitation and the dissolution of the capsule content, respectively. A Galerkin finite element method is used to solve the diffusion equations. The moving boundaries are tracked using a level set method.