Percolative Elution

Directed percolation problems have a long history, and have been resistant
to finding exact solutions.

Here I shall present a theory for elution from a random medium, concentrating on
cases where the flow is forced in one direction. Compared to the
standard directed
percolation problem, the model is a more faithful representation of the physics
because it respects mass conservation of flow through a medium.

I argue that the elution process can be slow, with a power-law decay
of the concentration
of the eluted substance. I shall discuss in detail a model for this
process which is exactly solvable,
and explore the relationship between this model and standard models
for directed percolation.

The talk is based upon recent collaborations, including results
obtained with Kyle Kawagoe,
Greg Huber, Alain Pumir, Mar Pradas and Eli Ben-Naim.