Solute transport across an interface: A Fickian theory for skewness in breakthrough curves

[1] This paper provides a mathematical treatment of solute transport when the mean velocity is perpendicular to a sharp interface. For this case, the resident and flux-averaged concentrations can be derived from Fickian laws of convection-dispersion. In a recently reported approach to (deterministic) Fickian convection-dispersion equations it was shown that the concentration field describing solute transport parallel to a sharp interface could be equivalently expressed in terms of the distribution of a particular skew Brownian motion. The present paper is an extension of this theory to the case of Fickian convection-dispersion for solute transport in the direction of flow orthogonal to a sharp interface. Just as in the case of parallel interface, this is significant in that it leads to an explicit formula for the concentration field as well as providing some guidance to the further development of particle tracking methods for representing solute transport in discontinuous media. As an application of this theory we obtain specific results to explain the interesting types of symmetries and asymmetries in the breakthrough curves of a conservative tracer across an sharp interface recently reported by Berkowitz et al. (2009).