Fluid dynamics of nonaqueous phase contaminants in groundwater: Analytical solutions and analogy with zhukovsky’s trochoid

An exact solution to a free-boundary, potential, 2-D flow of a Darcian fluid (mathematically equivalent to flow of a heavy irrotational ideal fluid) past a barrier is obtained by the theory of holomorphic functions. A volume of liquid contaminant contrasting in density with the ambient flowing groundwater makes a lens attached to the stoss or lee side of the barrier. The shape of the interface morphs in response to a pressure-velocity field in the dynamic and static liquid phases. The flow net and interface are plotted from explicit expressions found for the complex potential and complex velocity. As a particular case, we obtain a famous Zhukovsky’s gas-bubble contour belonging to the class of trochoids. Serious caveats for remediation projects and artificial recharge of groundwater are inferred: more intensive descending seepage of ponded surface water through a heterogeneous aquifer may worsen the groundwater quality, contrary to what would occur in homogeneous porous media.