A coupledly multiscale nucleation-diffusion model and well-posedness analysis

To address the coupled mechanisms of crystallisation and heat diffusion during the preparation of iron-based catalysts at various concentrations, this paper proposes a novel multiscale model for crystal nucleation, growth and aggregation. By coupling the population balance model with the heat equation, the model describes the dynamic evolution of crystal number density and the temperature field. Well-posedness analysis is first established for the population balance model using the method of characteristics and fixed-point theory. Subsequently, leveraging the global well-posedness of the PBM, the local existence and uniqueness of strong solutions to the coupled nucleation-diffusion model are proved via analytic semigroup theory. Furthermore, small perturbations in initial temperature, boundary flux and nucleation rate have bounded influences on the temperature distribution with Lipschitz continuity. Numerical simulations verifies the theoretical findings.