FLOW IN POROUS-MEDIA .1. A THEORETICAL DERIVATION OF DARCYS-LAW
FLOW IN POROUS-MEDIA .1. A THEORETICAL DERIVATION OF DARCYS-LAW
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DOI：
10.1007/bf01036523
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发表时间：
1986-01-01
影响因子：
2.7
通讯作者：
WHITAKER, S
中科院分区：
文献类型：
--
作者：
WHITAKER, S
采用体积平均法分析了穿过刚性多孔介质的斯托克斯流。传统的平均过程产生运动方程和以体积平均压力和速度表示的连续性方程。运动方程包含涉及压力和速度的空间偏差、布林克曼校正和其他低阶项的积分。该分析清楚地表明了为什么不应该使用布林克曼校正来适应多孔介质和边界固体表面之间界面处的无滑移条件。体积平均运动方程中压力和速度的空间偏差的存在引起了闭合问题，并且导出了空间偏差的表示，从而导出了达西定律。理论发展并不局限于均质或空间周期性多孔介质；然而，没有考虑多孔介质结构突变的问题。
Stokes flow through a rigid porous medium is analyzed in terms of the method of volume averaging. The traditional averaging procedure leads to an equation of motion and a continuity equation expressed in terms of the volume-averaged pressure and velocity. The equation of motion contains integrals involving spatial deviations of the pressure and velocity, the Brinkman correction, and other lower-order terms. The analysis clearly indicates why the Brinkman correction should not be used to accommodate ano slipcondition at an interface between a porous medium and a bounding solid surface.The presence of spatial deviations of the pressure and velocity in the volume-averaged equations of motion gives rise to aclosure problem, and representations for the spatial deviations are derived that lead to Darcy's law. The theoretical development is not restricted to either homogeneous or spatially periodic porous media; however, the problem ofabrupt changesin the structure of a porous medium is not considered.