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.
In the current research, a mathematical model for the post-damage improvement of the carbonated blast furnace slag cement (BFSC) exposed to accelerated carbonation is constructed. The study is embedded within the framework of investigating the effect of using lightweight expanded clay aggregate, which is incorporated into the impregnation of the sodium mono-fluorophosphate (Na-MFP) solution. The model of the self-healing process is built under the assumption that the position of the carbonation front changes in time where the rate of diffusion of Na-MFP into the carbonated cement matrix and the reaction rates of the free phosphate and fluorophosphate with the components of the cement are comparable to the speed of the carbonation front under accelerated carbonation conditions. The model is based on an initial-boundary value problem for a system of partial differential equations which is solved using a Galerkin finite element method. The results obtained are discussed and generalized to a three-dimensional case.
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