The flow through a porous medium strongly depends on the boundary conditions, very often assumed to be static. Here, we consider changes in the medium due to swelling and erosion and extend existing lattice–Boltzmann models to include both. We study two boundary conditions: a constant pressure drop and a constant flow rate. For a constant flow rate, the steady state depends solely on the erosion dynamics while for a constant pressure drop it depends also on the timescale of swelling. We analyze the competition between swelling and erosion and identify a transition between regimes where either swelling or erosion dominate.

中文翻译：

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流经随时间变化的多孔介质：膨胀和侵蚀

通过多孔介质的流动在很大程度上取决于边界条件，通常被认为是静态的。在这里，我们考虑了由于溶胀和腐蚀而引起的介质变化，并扩展了现有的格-玻尔兹曼模型以将两者都包括在内。我们研究了两个边界条件：恒定的压降和恒定的流量。对于恒定的流量，稳态仅取决于腐蚀动力学，而对于恒定的压降，则还取决于溶胀的时间尺度。我们分析了膨胀和侵蚀之间的竞争，并确定了以膨胀或侵蚀为主的各种制度之间的过渡。