The second-order reaction by which a species is transferred from solut
ion to a fixed site in a porous solid is considered. A web of the poro
us solid moves under a reservoir of the solution, which saturates as l
iquid percolates downward. The saturated web then passes through a zon
e in which there is no downward flow and on to a pair of rollers where
an arbitrary fraction of the solution is physically expressed and the
reaction continues in time. The salient behavior of this class of rea
ctors is described in the hodograph plane. Accommodating optimized des
igns are detailed under constraints which arise naturally. Comparison
is made with experiment for the application to chelation of sodium pyr
ithione to zinc sites in cellulose sponge.