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When water flows through the soil it will carry contaminants along with it in solution, this process is called advection. The amount of contaminant mass transported by advection is proportional to the groundwater (seepage) velocity, v, and the concentration, c, of the contaminant. This mass can be measured in a plane perpendicular to the direction of groundwater flow during a unit of time, this is called the flux, f . The flux is then the mass of contaminant transported per unit area per unit time and is given by:
f = n v c = va c
where,
n = effective porosity of the soil,
v = groundwater (seepage) velocity,
va = Darcy velocity = n v.
c = concentration of the contaminant at the time of interest.
The total mass of contaminant transported from a contaminant source into the ground can then be obtained by integrating the flux over the time period of interest viz.
ma = A ʃ n v c dt
where,
ma = total mass of contaminant transported,
A = cross-sectional area of the landfill.
It is should be noted that the velocity that the contaminant moves through the soil is the groundwater velocity and not the Darcy velocity. If the groundwater velocity is zero (i.e., there is no flow) then there would
be no advection.