Darcy's experiments and the deviation to nonlinear flow regime

Many important technological and natural processes involving flow through porous media are characterized by large filtration velocity It is important to know when the transition from the linear flow regime to the quadratic flow regime actually occurs to obtain accurate models for these processes. By interpreting the quadratic extension of the original Darcy equation as a model of the macroscopic form drag, we suggest a physically consistent parameter to characterize the transition to quadratic flow regime in place of the Reynolds number, Re. We demonstrate that an additional data set obtained by Darcy, and so far ignored by the community, indeed supports the Darc equation. Finally, we emphasize that the cubic extension proposed in the literature, proportional to Re-3 and mathematically valid only for Re much less than1, is irrelevant in practice. Hence, it should not be compared to the quadratic extension experimentally observed when Re greater than or equal toO(1). [S0098-2202(00)01703-X].