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- W2019961221 abstract "Flow through preferential pathways can be a significant contribution to the total flow through a porous medium. Analytical strategies for specifying conditions on preferential pathway flow boundaries are considered. A new analytical solution is presented based on Brinkman's extension of Darcy' s law for flow in and around a preferential pathway through a porous medium. Nondimensional analysis is presented to quantify the solution's predicted impact compared to solutions based on Darcy's law as the pathway boundary condition. Analysis is also presented to quantify the magnitude of essential parameters required to produce significant results. These results indicate that for some parameter values, Brinkman's extension of Darcy's law predicts a significantly higher volumetric flux within the preferential pathway, and predicts that velocities in excess of the Darcy velocity will be induced for a significant distance into the porous medium. There has been a struggle to develop appropriate boundary conditions for this problem. Brinkman's extension of Darcy's law is clearly not an ideal solution. However, the approach has an interesting experimental and analytical history, has conceptual merit, responds in a way that is intuitively plausibility, and provides predictions that can be tested experimentally. It is hoped that presenting this new analytical solution will help to advance the scientific discourse on this subject and may provide insights that lead to new kinds of physical experimentation." @default.
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- W2019961221 date "1999-03-01" @default.
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- W2019961221 title "The impact of Brinkman's extension of Darcy's law in the neighborhood of a circular preferential flow pathway" @default.
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