Abstract
The validity of Darcy’s law at very low Reynolds numbers is discussed controversially in literature, as some authors propose a pre–Darcy flow regime below some critical Reynolds number. The scope of this work is to investigate this problem experimentally. Therefore, a packing of glass spheres is perfused by different glycerin–water solutions. A linear behaviour between the flow velocity and the pressure drop through the packed spheres is found in the complete investigated range of Reynolds number {Re}_{d'}, based on the mean-pore diameter d' and mean-pore velocity v' with 10^{-9} le {Re}_{d'} le 10^{-1}. This contradicts the results of different authors like Fand et al. (1987) or Kececioglu and Jiang (1994), postulating a pre–Darcy regime for {Re}_{d'} le 2.8 cdot 10^{-6} or {Re}_{d'} le 0.13, respectively.Graphical abstract
Highlights
For the flow of a fluid through a porous medium, a pressure gradient is necessary
We have investigated the onset of the pre–Darcy flow regime experimentally
Mixtures of Glycelrol and water are used as working liquids, in order to obtain a wide range of Reynolds numbers, namely 1.6 ⋅ 10−9 ≤ Red ≤ 0.19
Summary
For the flow of a fluid through a porous medium, a pressure gradient is necessary. A creeping flow can be described by the law of Darcy (1856). The pressure loss due to the friction at the pore walls proves to be proportional to the speed of the flow. For sufficiently large Reynolds numbers, inertial effects come into play. Darcy’s law loses its validity, and the
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