Shrinking Sphere Kinetics for Batch Dissolution of Mixed Particles of a Single Substance at High Under-Saturation: Validation with Sodium Chloride, but with Biogenic Silica in Mind

Abstract

The cubic equation recently derived for the increase in concentration of a solute with time, as the solid dissolves in batch according to the shrinking sphere model at high under-saturation, is extended to dissolutions of mixtures of differently sized particles. This problem needs to be solved if batch dissolutions are to play their part in the proposed amelioration of global warming and associated climate change by accelerated ‘re-burial’ of excess CO₂ in ocean sediment. The upgraded model was tested using sodium chloride dissolved in 50% aqueous propanone, whence the model fitted two separate runs with 500 and 212 μm, and 212 and 38 μm, diameter crystals, respectively. The key to simulating dissolution in this way lies in the dissolutions being independent of each other. It is further shown that although this condition was implicit in the recent derivation of the cubic equation, it was not recognised at the time. The work should be applicable to any batch dissolution of mixed particles at high under-saturation, and hence, may find use in many industrial and laboratory dissolutions. Simulations show how agglomerated mixtures can yield a straight line on the plot of ln(1 − C/C _T) versus time, as was reported to occur recently with sodium chloride taken ‘straight from the bottle’. It is shown that this probably explains why exponential dissolutions may have seemed appropriate to the dissolution of biogenic silica in earlier literature. This study suggests that a new round of biogenic silica dissolutions, but with sieved samples, would be worthwhile, with the likelihood that shrinking sphere behaviour might well be found to characterise the kinetics. The opportunity is taken to investigate a number of aspects of the shrinking sphere model not generally discussed before, e.g. the graph for the change in surface area with time. The limitations of using cubic salt crystals with the shrinking sphere model are discussed.