A stochastic interpretation of the tailing effect in solute transport

 The advection-dispersion equation (ADE) is inadequate for describing tails in solute breakthrough curves. Re-examination of solute breakthrough curves from one-dimensional experiments in porous media and channel flow literature shows a consistent discrepancy compared with solutions to the ADE. The leading tail of breakthrough curves is sharper, and the trailing tail is longer and smoother, than best fitting, least-squares ADE solutions. A random particle simulation exercise shows that the ADE may firstly be erroneous because of the assumption of time steps over which random solute movements are considered independent. Definition of such time steps hinges upon the slowest random movements, such as those predominantly by molecular diffusion. A second potential source of error is the highly skewed nature of the inverse distribution of underlying, micro-scale velocities, which causes slow convergence to normality under the central limit theorem.