Abstract We investigate the spherically symmetric dissolution of an initially cold alumina particle in a bath of molten cryolite. The cryolite initially freezes on the particle, forming a shell that must melt before the particle can dissolve. We derive asymptotic solutions valid in the limits of small-superheat and of small Stefan number. In the small-superheat limit, the evolution of the boundary exhibits a two-scale behaviour. In the small Stefan number limit, we find that the behaviour of a particle could be limited by either the dissolution (in the case where the temperature differences are small) or by heat transfer (when the latent heat is large and the temperature gradients are large). Our asymptotic predictions are validated by a front fixing numerical scheme that we initiate using the early-time asymptotics.

中文翻译：

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冰晶石浴中氧化铝颗粒溶解的传热传质问题

摘要 我们研究了初始冷的氧化铝颗粒在熔融冰晶石浴中的球对称溶解。冰晶石最初在颗粒上冻结，形成必须在颗粒溶解之前熔化的壳。我们推导出在小过热度和小 Stefan 数限制下有效的渐近解。在小过热极限下，边界的演变表现出两尺度行为。在小的 Stefan 数限制中，我们发现粒子的行为可能受到溶解（在温差很小的情况下）或传热（当潜热很大且温度梯度很大时）的限制）。我们的渐近预测通过我们使用早期渐近启动的前端固定数值方案进行验证。