The second-order reaction by which a species is transferred fromsolution to a fixed site in aporous solid is considered. A web of the porous solid moves undera reservoir of the solution,which saturates as liquid percolates downward. The saturated webthen passes through a zonein which there is no downward flow and on to a pair of rollers where anarbitrary fraction of thesolution is physically expressed and the reaction continues in time.The salient behavior ofthis class of reactors is described in the hodograph plane.Accommodating optimized designsare detailed under constraints which arise naturally. Comparisonis made with experiment forthe application to chelation of sodium pyrithione to zinc sites incellulose sponge.