There are many reports on the flow through a straight channel filled with a porous medium. However, the flow through a tortuous channel has not been investigated. The present paper considers a channel of arbitrary curvature filled with a fluid-saturated porous medium. Using intrinsic coordinates, the Darcy-Brinkman equation is perturbed about the small centerline curvature. The effect of curvature enters the first order which shifts the velocity maximum towards the inner wall, where the shear stress is also higher. The second order gives the effect of curvature on the net flow rate, which may or may not be increased by curvature. The results are illustrated with a channel with a single bend and a channel with sinusoidal curvature. These results are important for the study of channels with bends, rock crevices, and catalytic converters.

中文翻译：

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任意曲率通道中的 DARCY-BRINKMAN 流

有许多关于流过充满多孔介质的直通道的报道。然而，尚未研究通过曲折通道的流动。本文考虑了一个充满流体饱和多孔介质的任意曲率通道。使用内在坐标，Darcy-Brinkman 方程在小中心线曲率附近受到扰动。曲率的影响进入一阶，将最大速度移向内壁，那里的剪切应力也更高。二阶给出曲率对净流量的影响，可能会或可能不会因曲率而增加。结果用单弯曲通道和正弦曲率通道说明。这些结果对于研究具有弯曲、岩石裂缝和催化转化器的通道很重要。