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A mathematical model describing the snow-plow effect, i.e. the removal of adsorbed ions from soil particles by an incoming solution with relatively high solute concentration, is analyzed. It is shown that an accurate numerical solution to the model must be obtained to investigate the influence of the parameters entering the problem. The numerical solution helps generate simple rules that allow for straightforward but accurate construction of snow plows in practical situations. The numerical results are also used to evaluate an earlier analytical approximation and are compared to experimental observations.