Stokes flow solutions in infinite and semi‐infinite porous channels
Stokes flow solutions in infinite and semi‐infinite porous channels
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DOI：
10.1111/sapm.12574
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发表时间：
2023-03
影响因子：
2.7
通讯作者：
Francesca Bernardi;S. Chellam;N. Cogan;M. Moore
中科院分区：
文献类型：
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作者：
Francesca Bernardi;S. Chellam;N. Cogan;M. Moore
我们得到了具有透水壁的无限和半无限流道中Stokes流的一类精确解。对于压力和斯托克斯渗流，这些简单、显式的级数表达式对所有渗透率值都有效。在槽壁上，我们对切向流体速度施加了无滑移条件，对法向流体速度施加了基于达西定律的条件。流经流道边界的流体是由流道内部和外部之间的压降驱动的；我们假设外部压力是恒定的。我们展示了在无限信道的情况下基态是如何精确解的。对于半无限通道域，基态解很好地逼近了整体的全精确解，我们推导出了一种在横向壁处提高其精度的方法。这项研究的目的是需要定量地了解适用于各种工程应用的详细的流体动力学，包括基于膜的水净化、热和质量传递以及燃料电池。
We derive a class of exact solutions for Stokes flow in infinite and semi‐infinite channel geometries with permeable walls. These simple, explicit, series expressions for both pressure and Stokes flow are valid for all permeability values. At the channel walls, we impose a no‐slip condition for the tangential fluid velocity and a condition based on Darcy's law for the normal fluid velocity. Fluid flow across the channel boundaries is driven by the pressure drop between the channel interior and exterior; we assume the exterior pressure to be constant. We show how the ground state is an exact solution in the infinite channel case. For the semi‐infinite channel domain, the ground‐state solutions approximate well the full exact solution in the bulk and we derive a method to improve their accuracy at the transverse wall. This study is motivated by the need to quantitatively understand the detailed fluid dynamics applicable in a variety of engineering applications including membrane‐based water purification, heat and mass transfer, and fuel cells.