where is the tracer's dimensionless concentration, time (T), dispersivity (L 2 T -1 ) that covers all forms of transport, and axial coordinate (L). The axial domain was [0, ], where corresponds to the height (L) of the liquid column. The domain boundaries were insulated, or in other words, they adhered to the zero-gradient or symmetry condition (no mass transfer across boundaries). The initial condition was a point-addition of tracer at 0 . By definition, the dimensionless concentration's mean is equal to 1 regardless of the injected tracer quantity. The solution to eq 2 with the described boundary and initial conditions is