The dissolution/crystallization rate of suspended particles is a substantial parameter in particle/fluid systems. Frequently, the mass transfer is accompanied by chemical reactions, which affect the mass transfer in the boundary layer surrounding the particles. Additionally, in particular in liquids, the physical interactions between the species dissolved in the suspension have to be considered.In the modeling of such systems one has to differentiate between fast chemical reactions, which instantaneously attain chemical equilibrium, and reactions, which are slow with respect to mass transfer. An important example for the influence of fast and slow reactions on the mass-transfer rate is the dissolution of limestone in aqueous electrolyte solutions, where solid limestone (CaCO 3 ) particles dissolves under formation of calcium (Ca 2 + ), carbonate (CO 3 2± ) and hydrogencarbonate ions (HCO 3 ± ):(1)While the reactions (1) and (2) are instantaneous, the hydrolysis of the dissolved CO 2 ,is slow. Moreover, the limestone dissolution rate is affected by other dissolved species, e.g. soluble salts (physical effect), as well as by reactions, which change the pH (chemical effect). Since also gaseous CO 2 affects the dissolution rate of limestone, for the calculation of the dissolution process a three-phase system consisting of the gas phase, the liquid and the suspended solid particles has to be modeled which, in addition to the dissolution/crystallization of the particles, also considers the absorption/desorption processes between the gas and the liquid phase.The general model for the limestone dissolution is developed in three steps. First, under consideration of the mass transfer, the reaction kinetics and the thermodynamic equilibrium a reaction diffusion model for single limestone particles is set up. In the second step, an universal dynamic mass-transfer model for the three-phase system gas/liquid/ solid is developed. Subsequently, the single-particle model is combined with the population balance and integrated into the dynamic model. After adjustment and validation the model enables the simulation of instationary dissolution and crystallization processes with polydisperse solids. A Reaction-Diffusion Model of the Limestone Dissolution RateThe flux of the calcium ions, which corresponds to the dissolution rate of the limestone particles, can be expressed by

The dissolution rate of limestone was measured by the pH‐stat method. In the measurements the influence of pH, particle size, kind of limestone, sparging and stirrer speed was first examined for particle fractions with narrow size distributions. Under the assumption that each particle size distribution is adequately represented by its mean particle size, the monodisperse model presented in Part I was adjusted to these data. The adjusted model was combined with the population balance and the three‐phase model described in Part I to a general simulation model for the dissolution of polydisperse solids.

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Die Messung der Kalksteinauflösungsgeschwindigkeit wurde nach der ¹pH-Stat Methodeª durchgeführt [1]. Dabei wird die instationäre Auflösung von Kalkstein bei einem durch Titration mit HCl-Lösung konstant gehaltenen pHWert und einer annähernd gleich bleibenden Lösungs-zusammensetzung gemessen. Der Prozess wird durch folgende Bruttoreaktionsgleichung beschrieben: CaCO 3 (s) + 2HCl D CaCl 2 + H 2 O + CO 2 (g)