Hydrodynamic instability of miscible fluids in a vertical porous column

A series of experiments have been conducted at a constant temperature on the intrusion of salt from a reservoir containing a fixed volume of solution into an underlying long vertical column of porous material, initially saturated with pure water and sealed at the bottom. The variation with time of the salt concentration in the reservoir was measured for different types of porous materials, different initial concentrations, and different mechanical treatments of the solution. The experimental results, substantiated by the theoretical analyses, indicate that the main contributor to the influx of salt into the porous material is the convective dispersion arising from the onset of horizontal variations of the salt concentration and of the vertical velocity component. The rate of this process is governed by a characteristic time where ρU and ρL are the initial densities in the reservoir and in the porous material, respectively; K is the hydraulic conductivity of the porous material with respect to the liquid initially saturating it; and H is a characteristic head of the solution. Approximate expressions have been derived for the rate of decrease of the salt concentration in the reservoir, for the influx of salt into the porous material, and for the advances of the salt front within it.