Comment on “Frequency-dependent dispersion in porous media” - Davit, Y; Quintard, M (2011)
In a recent paper, Valdes-Parada and Alvarez-Ramirez [Phys. Rev. E 84 031201 (2011)] used the technique of volume averaging to derive a frequency-dependent dispersion tensor, D*(w), the goal of which is to describe solute transport in porous media undergoing periodic processes. We describe two issues with this dispersion tensor that become particularly apparent in the time domain. Firstly, we demonstrate that the definition of D*(w), and equivalently of D*(t), is erroneous, and derive its correct counterpart, D*c(t). With this modification, the approach becomes strictly equivalent to the one devised by Moyne [Adv. Water Res. 20 63 (1997)]. Secondly, we show that the term "frequency-dependent dispersion" is misleading in this case, because D*(t) and D*c(t) do not depend on the process operating frequency. The study carried out by Valdes-Parada and Alvarez-Ramirez represents a frequency-analysis of the relaxation of the dispersion coefficients towards their steady-state, independently of any periodic operation or excitation.