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Fluid extraction across pumping and permeable walls in the viscous limit

机译：在粘性极限范围内穿过泵送壁和渗透壁的流体抽取

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摘要

In biological transport mechanisms such as insect respiration and renal filtration, fluid travels along a leaky channel allowing material exchange with systems exterior to the channel. The channels in these systems may undergo peristaltic pumping which is thought to enhance the material exchange. To date, little analytic work has been done to study the effect of pumping on material extraction across the channel walls. In this paper, we examine a fluid extraction model in which fluid flowing through a leaky channel is exchanged with fluid in a reservoir. The channel walls are allowed to contract and expand uniformly, simulating a pumping mechanism. In order to efficiently determine solutions of the model, we derive a formal power series solution for the Stokes equations in a finite channel with uniformly contracting/expanding permeable walls. This flow has been well studied in the case in which the normal velocity at the channel walls is proportional to the wall velocity. In contrast we do not assume flow that is proportional to the wall velocity, but flow that is driven by hydrostatic pressure, and we use Darcy's law to close our system for normal wall velocity. We incorporate our flow solution into a model that tracks the material pressure exterior to the channel. We use this model to examine flux across the channel-reservoir barrier and demonstrate that pumping can either enhance or impede fluid extraction across channel walls. We find that associated with each set of physical flow and pumping parameters, there are optimal reservoir conditions that maximize the amount of material flowing from the channel into the reservoir. Published by AIP Publishing.
机译：在诸如昆虫呼吸和肾脏过滤之类的生物运输机制中，流体沿着泄漏通道行进，从而允许与通道外部的系统进行物质交换。这些系统中的通道可能会进行蠕动泵送，这被认为可以增强物料交换。迄今为止，很少进行分析工作来研究泵送对跨过通道壁的材料提取的影响。在本文中，我们研究了一种流体抽取模型，其中流经泄漏通道的流体与储层中的流体交换。模拟泵送机制，使通道壁均匀收缩和膨胀。为了有效地确定模型的解，我们导出了具有均匀收缩/扩展可渗透壁的有限通道中Stokes方程的形式幂级数解。在通道壁处的法向速度与壁速度成比例的情况下，已经对该流动进行了很好的研究。相反，我们不假定流量与壁速成正比，而是假定流体压力是由静水压力驱动的，并且我们使用达西定律为正常壁速关闭系统。我们将流动解决方案合并到一个模型中，该模型可跟踪通道外部的物料压力。我们使用此模型来检查通道-水库屏障之间的通量，并证明泵送可以增强或阻止通道壁上的流体提取。我们发现，与每组物理流量和泵送参数相关联，存在最佳的储层条件，可使从通道流入储层的物料量最大化。由AIP Publishing发布。

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