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 |
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| Authors: | Victor W Truesdale |
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| Institution: | (1) School of Life Sciences, Oxford Brookes University, Gipsy Lane, Headington, Oxford, OX3 0BP, UK |
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| 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 chemo-stat. 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. |
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