We formulate a model for the dynamic growth of a membrane developing in a flow as the result of a precipitation reaction, a situation inspired by recent microfluidic experiments. The precipitating solid introduces additional forces on the fluid and eventually forms a membrane that is fixed in the flow due to adhesion with a substrate. A key challenge is that, in general, the location of the immobile membrane is unknown a priori . To model this situation, we use a multiphase framework with fluid and membrane phases; the aqueous chemicals exist as scalar fields that react within the fluid to induce phase change. To verify that the model exhibits desired fluid–structure behaviours, we make simplifying assumptions to obtain a reduced form of the equations that is amenable to exact solution. This analysis demonstrates no-slip behaviour on the developing membrane without requiring fluid–membrane interface boundary conditions. The model has applications towards precipitate reactions where the precipitate greatly affects the surrounding flow, a situation appearing in many laboratory and geophysical contexts including the hydrothermal vent theory for the origin of life. More generally, this model can be used to address fluid–structure interaction problems that feature the dynamic generation of structures.

中文翻译：

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沉淀诱导膜形成的多相模拟

我们为沉淀反应的结果在流动中发展的膜的动态生长制定了模型，这种情况受最近微流体实验的启发。沉淀的固体会在流体上引入额外的力，并最终形成膜，由于与基材的粘附，该膜固定在流动中。一个关键的挑战是，一般来说，固定膜的位置是先验未知的。为了模拟这种情况，我们使用具有流体和膜相的多相框架；水性化学物质以标量场的形式存在，在流体中发生反应以引起相变。为了验证模型表现出所需的流固性行为，我们进行了简化假设以获得适合精确解的方程的简化形式。该分析表明，在不需要流体-膜界面边界条件的情况下，发展中的膜具有无滑移行为。该模型适用于沉淀物反应，其中沉淀物极大地影响周围的流动，这种情况出现在许多实验室和地球物理环境中，包括生命起源的热液喷口理论。更一般地说，该模型可用于解决以结构动态生成为特征的流固耦合问题。