Pore transport-controlled shrinking-core systems involving diffusion, migration, and homogeneous reactions: Part I. Formulation of model and rate equation for PbSO4-carbonate system

Previous efforts to generalize the applicability of pore transport-controlled shrinking-core models have been extended further in formulating a model for the conversion of PbSO₄ to lead carbonate in sodium carbonate solutions. It consists of a comprehensive set of equations for transport of eight species in the lead carbonate product layer, which incorporates diffusion, migration, and homogeneous reactions in addition to the heterogeneous reaction of PbSO₄ at the shrinking-core interface. Through a mathematical transformation to reduce the number of independent variables to a single one, it has been shown that the rate equation for the time dependence of the extent of conversion (α) of PbSO₄, for even such a complicated system, has the familiar form 1−2/3 α−(1−α)^2/3=k _p t, in agreement with experimental findings. In this case, however, the value of the parabolic rate constant (k _p) must be determined by the numerical solution of the set of transport equations defining the system. This result is general for many reaction systems other than the one analyzed here. The mathematical criteria for shrinking-core models to yield a rate equation with the aforementioned form are also described.