Definition of Darci Numbers
Definition 1
In fluid mechanics, when dealing with a porous medium with permeability $k$, the following dimensionless quantity is called the Darcy number. $$ \mathrm{Da} := {\frac{k}{L^2}} $$ Here $L$ is the characteristic length.
Explanation
Darcy number is the permeability itself divided by the square of a characteristic length, so that it represents permeability independent of the system scale in the context of porous media and Darcy’s law.
Intuitively, in diffusion problems for heat or mass transport, a larger Darcy number suggests higher transport efficiency. Simulations used to investigate this typically assume that the Darcy number is uniform throughout the domain.
Nouri-Borujerdi, A., Noghrehabadi, A. R., & Rees, D. A. S. (2008). Influence of Darcy number on the onset of convection in a porous layer with a uniform heat source. International Journal of Thermal Sciences, 47(8), 1020-1025. https://doi.org/10.1016/j.ijthermalsci.2007.07.014 ↩︎