Silica Gel as a Surrogate for Biogenic Silica in Batch Dissolution Experiments at pH 9.2: Further Testing of the Shrinking Object Model and a Novel Approach to the Dissolution of a Population of Particles

Abstract

Recently, the increase in dissolved concentration in the batch dissolution of various salts or sucrose has been successfully modelled with three equations, one a cubic in time. However, from three separate earlier investigations with ocean sediments and phytoplankton frustules, there is residual suspicion that biogenic silica does not follow this behaviour. This paper shows that the Shrinking Object Model applies to the dissolution of sieved silica gel particles, as well as to a sample of unsieved, freeze-dried frustules of Odentella sp. Silica gel, being readily available in quantities that can be sieved, is a useful surrogate for biogenic silica in allowing problems of experimental design to be overcome. The dissolutions covered three possible analytic integrations that arise from the model: an exponential for approach to saturation with excess solid silica; the approach to near saturation with either a slight excess or deficiency of silica; dissolution at high under-saturation. Good agreement was found between experimental results and mathematical modelling. The paper provides template calculations by which future raw results can be parameterized. Nevertheless, the reasons for non-linear kinetics reported in earlier work have not been identified, and so controversy over non-linear dissolution kinetics is enhanced. Stirring regime was found to be important with silica gel dissolution, and so biogenic silica dissolution is therefore likely to be 'transport limited' at low stirring rate. Accordingly, all archived and future data should be scrutinized for stirring effects before being applied to the oceanic environment. A rigorous test for determining whether a substance's dissolution deviates from the model is recommended as a preliminary to any future dissolutions, whether in batch or with the chemostat. A fixed amount of frustule sample is added to a series of buffered mixtures containing increasing background silicic acid concentrations. Absence of any problem is marked by a linear plot between the increase in silicic concentration accruing over a fixed reaction period and that of the background silicic acid. A novel mathematical proof is provided to justify the test's use. The reasons for the earlier deviations from expected behaviour of, for example, oceanic sediments, are discussed. Lastly, the paper provides a novel approach to the dissolution of a population of particles of mixed sizes which will probably find ready future application in oceanography.

Generic Issues of Batch Dissolution Exemplified by Gypsum Rock

“…1 Introduction Greenwood et al (2001), Truesdale et al (2005a, b) and Truesdale (2007Truesdale ( , 2008Truesdale ( , 2009Truesdale ( , 2010 studied batch (closed system) dissolution partly to understand the dynamics of biogenic silica dissolution in the oceans (e.g., Yool and Tyrell 2003;Kamatani 1982;Trégur et al 1989), but increasingly for its own sake. Hence, these dynamics are of interest in the dissolution of a vast range of substances as well as silica, involved for example in industrial and other applications, e.g., mineral extraction (Sohn and Wadsworth 1979), radioactive-waste disposal (Ichenhower et al 2008) and drug delivery (Balbach and Korn 2004).…”

“…After illuminating this, Truesdale et al (2005a, b) confirmed that the exponential approach only applies to dissolving loads which are in excess of saturation and where loading remains essentially constant throughout dissolution; that is, the condition generally used with investigations based upon TST. Meanwhile, through deeper study of Kamatani et al's (1980) shrinking sphere model, Truesdale et al (2005a) and Truesdale (2007Truesdale ( , 2008Truesdale ( , 2010 derived equations for the batch dissolution of either mono-dispersed or poly-dispersed particles (populations of particles of either one size or many sizes, respectively) at high under-saturation. From this, it could be seen that the earlier progress by Kamatani et al (1980) probably stalled because the populations of diatom frustules which they studied would have been poly-, not mono-dispersed.…”

“…Truesdale (2008Truesdale ( , 2009) extended this work to dissolutions of particles of mixed-size, and generally to shrinking objects rather than just shrinking spheres. A key understanding of this (Truesdale 2010) is that the shrinking object model is more simply posited as an object shrinking at a constant rate in one of its linear dimensions. Truesdale (2010), concerned that 'nonlinear kinetics' can so easily be the result of inadequate experimental design, suggested an experiment that could be adopted as a universal prerequisite to determine their presence or absence in any dissolution system.…”

“…A key understanding of this (Truesdale 2010) is that the shrinking object model is more simply posited as an object shrinking at a constant rate in one of its linear dimensions. Truesdale (2010), concerned that 'nonlinear kinetics' can so easily be the result of inadequate experimental design, suggested an experiment that could be adopted as a universal prerequisite to determine their presence or absence in any dissolution system. This paper develops the recent improvements to modelling of the dynamics of batch dissolution even further by testing the equations on gypsum about which, anyway, much is already known from other approaches (e.g., Barton and Wilde 1971;Christoffersen and Christoffersen 1976;Liu and Nancollas 1971;Gobran and Miyamoto 1985;Lebedev and Lekhov 1990;Raines and Dewers 1997;Jeschke et al 2001;Kuechler et al 2004).…”

“…Also, conductimetry provides virtually continuous analytical output with time. As gypsum is a natural mineral, it provides a suitable working material with which to test Truesdale's (2010) assertion that working at very low solid loadings with the Truesdale (2007) equation should be preferable to using the high loadings conventional in the TST approach. This would certainly circumvent problems with secondary mineral precipitation (Tole et al 1986).…”