Multi-scale analysis of freezing process in mining applications: From equilibrium to non-equilibrium

The mining sector is crucial to Canada's economy but faces challenges in transitioning to sustainable practices amid increasing global energy demands and climate change. Dependency on fossil fuels contributes to carbon emissions, while rising temperatures in northern regions accelerate permafrost degradation, threatening critical infrastructure and mining operations. Addressing these challenges requires innovative solutions and a deeper understanding of physical phenomena in cold climates that are unique to Canada, such as solid-liquid phase changes, to ensure the industry's long-term sustainability.This dissertation focuses on advancing our fundamental knowledge of solidification, including both equilibrium and non-equilibrium processes, at multiple temporal and spatial scales through theoretical and experimental analyses. It begins with a state-of-the-art review of freezing processes, outlining recent progress from fundamental, methodological, and applied perspectives. The thesis then addresses macro-scale equilibrium solidification by developing novel analytical solutions to two-phase Stefan problems via singular perturbation and asymptotic analysis, which are both accurate and computationally efficient. These solutions facilitate the thermal estimation of phase change materials (PCMs) for cold thermal energy storage, as well as artificial ground freezing (AGF) for stabilizing ore deposits and protecting permafrost.The thesis advances to the study of multi-stage and multi-scale non-equilibrium solidification, characterized by innovative laboratory experiments and unified mathematical models. Specifically, it examines the five-stage solidification of pure substances and mixtures, including stochastic heterogeneous nucleation, non-linear crystal growth, and coupled heat and mass transport with freeze-point depression. The multi-scale analysis captures temporal and spatial phenomena using novel experimental and mathematical frameworks. Non-equilibrium solidification significantly enhances the development of PCMs for cold thermal energy storage, as well as spray freezing (SF) for heating, cooling, and decontaminating wastewater in mines.The combination of equilibrium and non-equilibrium solidification, investigated through theoretical and experimental frameworks, contributes to our fundamental understanding of complex phase-change processes. The developed analytical solution to two-phase Stefan problems significantly reduces the computational time for equilibrium processes compared to numerical methods. The novel multi-stage and multi-scale frameworks for both pure substances and mixtures accurately characterize non-equilibrium behaviors (e.g., heterogeneous nucleation and non-linear crystal growth) that are otherwise difficult to obtain via conventional approaches.From an applied perspective, the freezing process (both at equilibrium and non-equilibrium) is a key influential factor in the thermal estimation and design of AGF, PCMs, and SF. The developed frameworks delineate practical parameters such as total freezing time, interface movement, thermal storage capacity, freeze concentration, ice quality, and ice production. Accurate analysis of freezing phenomena is of great importance in the innovation, development, and integration of these cutting-edge clean technology solutions, tailored specifically to the unique landscapes and environments of Canadian mines in today's global energy transition and climate crisis

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