Defining the Departure from Darcy Regime
If Reynolds Number represents the ratio of the ‘momentum flux’ to the ‘viscous stress’ (which can also be interpreted to be as the ratio between the inertial forces and the viscous forces), then, Darcy’s law remains valid as long as the viscous stress dominates, where the relation between pressure-drop and velocity remains linear.
In this context, which of the following two dimensionless numbers - would remain - more appropriate – in order to define the departure from Darcy’s regime;
(a) when the fluid flow is associated with weak inertial forces; and
(b) when the fluid flow remains associated with strong inertial forces – in the absence of any turbulence?
Critical Reynolds Number (as a function of porosity);
or,
Critical Forchheimer Number (as the ratio of the pressure-gradient to the viscous resistance)?
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