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Analytical travelling wave solutions of a dental plaque model with nonlinear sorption
We study a theoretical model of the progress of carious lesion of tooth enamel as a result of the diffusion of organic acids from the dental plaque through the enamel to react with static hydroxyapatile. The process is modeled by an advective-reaction-diffusion equation that is coupled with nonlinear sorption. The concentration profile of the mobile, or diffusing, reactant can be obtained exactly in the form of a travelling wave front. We describe the method for finding the analytical solutions using the travelling wave coordinate when the wave is assumed to be moving at constant speed. Numerical solutions are then found in order to compare with the exact solution in the context of experimental data reported in the literature.