Analytical solution of advective mixing in a conduit.

The permeable conduit wall in a karst aquifer allows for water and solute to be exchanged between conduits and the limestone matrix. Contaminant sequestered in the limestone matrix is flushed into conduits following flood events. The contaminant released from the permeable wall will then mix with conduit water and will be transported downgradient in the conduit. A one-dimensional advection-dispersion equation is presented to describe this mixing-transport incorporating water flow and solute flux through the conduit wall. An analytical solution ignoring conduit dispersion is derived using the method of characteristics. Scale analysis is performed to provide a general guideline to estimate when conduit dispersion can be neglected. The solution also can be used to compute the distribution of solute in the matrix before flushing.