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The role of eddies inside pores in the transition from Darcy to Forchheimer flows

We studied the role of intra‐pore eddies, from viscous to inertial flows, in modifying continuum‐scale flow inside pores. Flow regimes spanning Reynolds NumberRe∼ 0 to 1350 are divided into three zones – one zone follows Darcy flow, and the other two zones describe non‐Darcy or Forchheimer flow. During viscous flows, i.e.,Re < 1, stationary eddies occupy about 1/5 of the pore volume. Eddies grow when Re > 1, and their growth leads to the deviation from Darcy's law and the emergence of Forchheimer flow manifested as a characteristic reduction in the apparent hydraulic conductivity Ka. The reduction in Ka is due to the narrowing of the flow channel which is a consequence of the growth in eddies. The two zones of Forchheimer flow correspond to the changes in rate of reduction in Ka, which in turn are due to the changes in eddy growth rate. Since the characteristics of Forchheimer flow are specific to pore geometry, our results partly explain why a variety of Forchheimer models are expected and needed for different porous media.