Significant errors can result in modeling dissolution processes if the polydispersity of the solid particles is ignored and the sample is treated as a collection of monodisperse spheres having the average size of the mixture. Population balance modeling provides an effective analytical means of predicting the effect of polydispersity on a wide variety of heterogeneous reaction systems including dissolution processes.

Few studies have examined the effect of polydispersity on dissolution processes. A thorough review of the pertinent literature has already been presented (LeBlanc and Fogler, 1987). Mixed regime refers to kinetics in which the mass transfer and intrinsic surface reaction rates are of the same order of magnitude. Polydisperse mineral systems which have some particles dissolving simultaneously in both rate limiting regimes can be analyzed with this method (i.e., for broad initial distributions, the large particle dissolution may be mass transfer limited, while the smaller particles are surface reaction rate limited. Model DevelopmentFor purposes of illustration, first order surface reaction kinetics which yield an analytically solvable population balance, will be considered. More complex kinetics, such as second or nth) order or Langmuir kinetics, can also be handled using the mixed regime technique, however, the resulting population balances must be solved numerically. The surface reaction dissolution rate for first order kinetics may be set equal to the surface mass transfer rate, to obtain a general expression for the particle dissolution kinetics. Single particle shrinkage rateFor small spherical particles which "move with the flow," the Reynolds No. is small, the Sherwood No. is 2, and the expression for the particle shrinkage rate becomes: where 0, is the diameter at which the surface reaction and mass transfer resistances are equal. Once calculated, Do may then be compared to the initial particle size distribution, and the rate S. E. LeBlanc is currently at the University of Toledo. controlling regime(s) governing the dissolution behavior of the distribution can be determined. From our definition, we can form the following dimensionless quantity:The magnitude of this dimensionless term indicates the rate controlling regime. For example, if the particle diameter is much less than Do (i.e., D << Do and K , << K,,,), then the surface reaction rate is controlling.We shall soon see that if one tries to make predictions using only single particle information, the results may be directly opposite to those observed experimentally for polydisperse systems.

T h e dissolution kinetics of a number of m a n g a n e s e o x i d e s in acidic solutions were studied. Using a slurry r e a c t o r , r a t e l a w s were d e t e rmined for e a c h of t h e m a n g a n e s e o x i d e s in t h e hydrohalogen a c i d s . Significant variations in t h e reaction r a t e s (up t o five o r d e r s of magnitude over t h e HCI b a s e rate) were obtained with different a c i d s . T h e addition of anions a s neutral salts to acidic solutions is s h o w n t o p r o d u c e t h e same rate-accelerating effect as a c i d s containing t h a t anion. T h e effect of t h e different a c i d s on t h e o x i d e dissolution r a t e s is explained using semiconductor band theory a n d e n e r g y diagrams.

A set creative problem-solving tools for instructional purposes is discussed. The tools include a problem-solving text which presents the heuristic, a set of slides in electronic form that can be used to enhance classroom presentations, and interactive computer modules that reinforce and develop the students' problem-solving skills.

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