Leaching has potential for clean up of toxic waste sites, but there must be no dispersal of the contaminants to adjacent areas. If the toxic material is soluble in water, it may already be dispersed by the percolation of rain water or by flow of groundwater. The penetration of wastes down into the soil has been modeled by several groups.
Movement depends on convection with the solvent, diffusion, and exchange with the soil solids.
This is much more complicated than batch or countercurrent leaching where we neglected any binding of the solute because the equilibria are complex and the motion is in three dimensions. Problems of this type require considering many elements that interact. The term for this approach is finite element analysis , and linear algebra with matrices aids the solutions. If contaminated soil were flushed by pumping water through it, the pumped water under pressure would escape to the surroundings. This is unacceptable because the toxic wastes would be diluted to make treatment more difficult and dispersed to make collection more costly.