Dissolution of powdered minerals: The effect of polydispersity

Abstract

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.

Nonisothermal dissolution and crystallization of ellipsoidal particles in liquid solutions

“…Note that, if bϭ0, 10 represents an oblate spheroidal surface, if aϭbϾ0, it denotes a prolate spheroidal surface, and if aϭbϭ0, it reduces to a spherical surface. For dissolution, the parameter is the time required to dissolve a particle; for crystallization, the initial linear sizes of a crystal on the x, y, and z axes are (1/2)ͱ 10 2 Ϫa 2 , (1/2)ͱ 10 2 Ϫb 2 , and ͑1/2͒ 10 , respectively.…”

Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties

“…In order to describe the particle size distribution of powders, basically, four formulas are used in practice [22]: the Gorden-Andreev [22,23], the Rozin-Rammlar-Bennett [24], [22], the normal [25][26][27][28][29] or lognormal [25][26][27][28][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] distributions. In other research [27,36,37], it is considered the issue that distributions with only two parameters are insufficient.…”

Managing Solids in Microreactors for the Upstream Continuous Processing of Fine Chemicals

“…An important consideration in any such case is the dissolution time (and/or the mixing time) relative to the reaction time scale. The rate of dissolution of a solid material in a solvent is controlled by the surface area per unit mass. , Several classes of reactions are highlighted in Table that may require the dissolution or the handling of solid starting compounds in continuous manufacturing. Palladium-catalyzed C–C and C–N bond-forming reactions are widely used to prepare pharmaceuticals and fine chemicals.…”