A filter comprises porous material that traps contaminants when fluid passes through under an applied pressure difference. One side effect of this applied pressure, however, is that it compresses the filter. This changes the permeability, which may affect its performance. As the applied pressure increases, the flux of fluid processed by the filter will also increase but the permeability will decrease. Eventually, the permeability reaches zero at a point in the filter and the fluid flux falls to zero. In this paper, we derive a model for the fluid transport through a filter due to an applied pressure difference and the resulting compression. We use this to determine the maximum operating flux that can be achieved without the permeability reaching zero and the filter shutting down. We determine the material properties that balance the desire to maximize flux while minimizing power use. We also show how choosing an initial spatially dependent permeability can lead to a uniformly permeable filter under operation and we find the permeability distribution that maximizes the flux for a given applied pressure, both of which have desirable industrial implications. The ideas laid out in this paper set a framework for modelling more complex scenarios such as filter blocking.

中文翻译：

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可压缩性对过滤介质性能的影响

过滤器包括多孔材料，当流体在施加的压差下通过时，该多孔材料会捕获污染物。但是，这种施加压力的一个副作用是它会压缩过滤器。这会改变渗透率，这可能会影响其性能。随着施加压力的增加，过滤器处理的流体通量也将增加，但渗透率将降低。最终，渗透率在过滤器中的某个点达到零，流体通量下降到零。在本文中，由于所施加的压力差和所产生的压缩力，我们导出了通过过滤器的流体传输模型。我们用它来确定在磁导率不为零和过滤器关闭的情况下可以达到的最大工作通量。我们确定的材料特性可以平衡通量最大化和功耗最小化的需求。我们还展示了如何选择初始的空间相关渗透率如何在运行中产生均匀渗透性的过滤器，并且发现了在给定施加压力下可使通量最大化的渗透率分布，这两者均具有理想的工业意义。本文提出的想法为建模更复杂的场景（例如过滤器阻塞）设置了框架。