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- Title
Sucrose Dissolution Studies Leading to a Generic Shrinking Object Model for Batch Dissolution of Regular-Shaped Particles.
- Authors
Victor Truesdale
- Abstract
Abstract The dissolution of sieved sucrose crystals has been studied spectrophotometrically by observing the increase in dissolved sucrose concentration with time. Equations recently derived from the shrinking sphere model for the batch dissolution of a solid in under-saturated conditions tested successfully on both single crystal-size and mixtures of two sizes of sucrose crystals. Single-sized crystals provided a straight line for the plot of the fraction of un-dissolved solid to the power one-third, versus time ($$ f_{\text{u}}^{ 1/ 3} $$ vs. t). The dissolution of mixtures of two crystal sizes fitted the non-linear equation tested earlier on sodium chloride in water-propanone mixtures. Together, these two sets of tests on ionic and covalent substances verify that many simple dissolutions will be easily modelled using this physical model based on shrinkage, where the chemical composition of the solids is very much of secondary importance. Consequently, there is an increased chance that the equations will describe the dissolution of biogenic silica in seawater, the problem which originally inspired this study. More than this, though, the equations are discovered to be mathematically generic; very many geometries other than the sphere satisfy the same equations, and the “shrinking object dissolution model” is thereby defined. The approach should also apply even to non-aqueous dissolutions. A prototype plot of shrinking object rate constant (obtained from numerical fitting of the model to sucrose) versus particle size is presented, and it is shown how analogous treatments for other substances will be central to collection and use of much dissolution data in the future. The study is placed in context with much earlier solid phase decomposition studies, concluding that the key characteristic of the simplest of all dissolutions is that the interface between solid and liquid should advance at a uniform linear rate. It is shown how this approach leads to equations of the same mathematical forms already discussed above.
- Subjects
SOLVATION; SUCROSE; CRYSTAL models; MIXTURES; NONLINEAR differential equations; MATHEMATICAL models; SPECTROPHOTOMETRY; SOLID-phase analysis; GEOCHEMISTRY
- Publication
Aquatic Geochemistry, 2009, Vol 15, Issue 3, p421
- ISSN
1380-6165
- Publication type
Article
- DOI
10.1007/s10498-008-9059-7