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Advective skew dispersion is a natural Markov process defined by a diffusionwith drift across an interface of jump discontinuity in a piecewise constantdiffusion coefficient. In the absence of drift, this process may be representedas a function of $\alpha$-skew Brownian motion for a uniquely determined valueof $\alpha=\alpha^*$; see Ramirez et al. [Multiscale Model. Simul. 5 (2006)786--801]. In the present paper, the analysis is extended to the case ofnonzero drift. A determination of the (joint) distributions of key functionalsof standard skew Brownian motion together with some associated probabilisticsemigroup and local time theory is given for these purposes. An application tothe dispersion of a solute concentration across an interface is provided thatexplains certain symmetries and asymmetries in recently reported laboratoryexperiments conducted at Lawrence--Livermore Berkeley Labs by Berkowitz et al.[Water Resour. Res. 45 (2009) W02201].

Occupation and local times for skew Brownian motion with applications to dispersion across an interface