ShrinkingcoreModell

The shrinking core model, sometimes written shrinking-core model, is a mathematical framework used to describe heterogeneous gas-solid reactions in which a solid particle reacts with a fluid and the unreacted core shrinks as the reaction proceeds. It is widely used in hydrometallurgy, mineral processing, catalysis, and environmental engineering to interpret leaching, reduction, oxidation, and solid-gas interactions. In German-language sources the term appears as Shrinking-Core-Modell.

The model assumes a single, homogeneous particle with a fixed initial shape, commonly spherical. The reaction starts at the outer surface and proceeds inward, forming a solid product layer that surrounds an unreacted core. Depending on the system, the overall rate can be controlled by the chemical reaction at the core–product interface, diffusion of the reactant through the product layer, or diffusion of the product through that layer. The unreacted core shrinks over time as the reaction progresses.

Let X denote the fraction of solid that has reacted, r the radius of the unreacted core, and R0 the initial radius. For a spherical particle, X = 1 − (r/R0)^3. Three limiting cases are typically distinguished: (1) chemical reaction at the interface (surface-reaction control); (2) diffusion of the reactant through the product layer (product-layer diffusion control); and (3) diffusion of the product through the layer (product-layer diffusion). Each case yields a different time dependence of X, which is used to fit experimental data and identify the dominant resistance.

Applications include ore processing, leaching, and catalytic or environmental processes involving solid particles. Limitations involve assumptions of constant particle size, fixed geometry, and negligible pore evolution; extensions address non-spherical shapes, porous pellets, and coupled heat and mass transfer.