G.M. van Rosmalen

Induction time and metastability limit in new phase formation

An analysis is made of the induction time ti in new phase formation, i.e. of the time elapsing before the onset of the process. A general formula for ti is proposed which is valid for any number of nuclei appearing and growing in the parent phase and which unites the known expressions for ti only applicable when either one or a large number of nuclei are involved in the process. This formula for ti is used for determination of the metastability limit in new phase formation, i.e. of the critical (or maximum) supersaturation below which the parent phase can stay long enough in metastable equilibrium.

Determination of nucleation and growth rates from induction times in seeded and unseeded precipitation of calcium carbonate

Abstract Theoretical expressions for the supersaturation dependence of the induction time in seeded and unseeded precipitation are derived for different mechanisms of crystallite growth. On the basis of the theory a combined analysis of the induction time in both seeded and unseeded precipitation is presented, which allows separate determination of the nucleation and growth rates. Induction times in both seeded and unseeded precipitation of calcium carbonate in the absence and presence of additives are measured and interpreted in the light of the proposed theory. The analysis provides full information about the growth and nucleation rates in the investigated systems.

Crystal growth of calcium sulphate dihydrate at low supersaturation

Abstract The growth rate of calcium sulphate dihydrate crystals, gypsum, in aqueous suspension has been shown to be screw dislocation controlled in the supersaturation range 1.03 C C s . Constant composition experiments show that the overall rate of growth decreases with increasing mass of the crystals. A combination of normal spiral growth, growth of cooperating spirals with non-parallel Burgers vectors, and growth of grain boundary spirals, together with partial outgrowth of concave parts of the crystals, can explain the rate of growth found for different preparations of gypsum crytals.

The influence of various polyelectrolytes on the precipitation of gypsum

Abstract In order to establish a relationship between the molecular structure of polycarboxylates and their growth retarding influence on gypsum crystals, seeded suspension growth experiments were performed at various growth conditions. Two types of polycarboxylates were studied with a molecular structure based on either polyacrylic or polymaleic acid. The molecular structure of these compounds was varied by partial substitution with monomers containing other functional groups than carboxylic acid groups, like hydroxyl, amino and sulfonic acid groups as well as hydrophobic groups. Besides the type of additional functional groups, also their position in the molecule was varied with respect to their distance from the polymer backbone. Some polymaleic and polyacrylic compounds were also studied at different pH-values. For the mechanism of growth inhibition a model is proposed, which explains why polymaleates are more effective than polyacrylates at high pH-values, and why their inhibitor effectiveness can be increased with additional hydroxyl and amino groups, but not with sulfonic acid groups. By application of various adsorption procedures to the seed crystals it became clear that the adsorption process of the polyelectrolytes onto the gypsum crystal surface is completed within a few minutes. With advancing outgrowth of the seed crystals, adsorbed polyelectrolyte inhibitor molecules are eventually overgrown.

Calcium phosphate precipitation in a fluidized bed in relation to process conditions: A black box approach

The precipitation features of calcium phosphate in a fluidized bed reactor in the concentration range between 5 and 100 mg P 1−1 were studied, and the conditions for optimum phosphate removal efficiency were established. The supply of calcium ions should be such that a Ca/P molar ratio of 3 at the inlet of the reactor is achieved. If the water to be treated does not contain magnesium or carbonate ions, the supply of base should suffice to promote a conversion of 50–65% of the incoming phosphate to the solid phase. In the presence of carbonate and magnesium ions, the base supply should provide a conversion of 80–95%. Magnesium and carbonate ions did not have a detrimental effect on the phosphate removal efficiency for inlet concentrations of up to 4.8 × 10−3 (Mg/P < 2 mol mol−1) and 1.8 × 10−3 kmol m−3, respectively. The feasibility of a process based on the precipitation of magnesium phosphate instead of calcium phosphate was demonstrated for waters with a low calcium content (Ca/P < 0.8 mol mol−1). Finally a method is presented to select process conditions where co-precipitation of unwanted phases can be avoided.

An analysis of growth experiments of gypsum crystals in suspension

Abstract Experiments on the growth of gypsum crystals in suspension have been analysed by three methods. The most adequate description of the growth process has been obtained by applying a method, based on the relationship between the overall growth rate, the linear growth rates of the different crystals faces and the normalized volume of the crystals. The overall growth rate has been factorized into a concentration dependent function R and a function depending on the normalized volume of the crystals. Introduction of an expression for R , derived from the spiral growth model, has given a good fit with the experimental data. At constant concentration of the bulk solution the growth rate decreases with increasing normalized volume of the crystals. The results from the fitting procedure and the microscopic observations together indicate that the growth of gypsum occurs by a combined spiral growth and layer growth mechanism.

Eutectic freeze crystallization : Application to process streams and waste water purification

Abstract Two case studies are presented using eutectic freeze crystallization (EFC) as an alternative for evaporative crystallization: a 7.8 ton day −1 35 w% aqueous sodium nitrate and a 24 ton day −1 12 w% copper sulfate stream. The proposed crystallizer is a cooled disk column crystallizer (CDCC), using indirect cooling for heat transfer. In single stage operation, the formed ice crystals are used to pre-cool the feed stream. A two stage refrigeration unit utilizes the formed ice crystals in the condensation of refrigerant. Expressed as a thermal equivalent energy requirement, EFC requires 1282 kJ kg −1 NaNO 3 and 1037 kJ kg −1 CuSO 4 ·5H 2 O. Compared to conventional multi-step evaporation, the energy reductions are 30% for sodium nitrate and 65% for copper sulfate.

Effect of additives on nucleation rate, crystal growth rate and induction time in precipitation

Abstract A theory is proposed and general expressions are derived for the nucleation rate, the rate of crystal growth by two-dimensional nucleation and the introduction time in unseeded precipitation in the presence of additives. According to the theory, the additives behave as active centres for nucleation and do not alter the surface free energy and edge free energy of the nuclei by adsorption on them, because of the short lifetime of the nuclei and/or their small surface area. The surface free energy and edge free energy of the nuclei formed on the additives, however, can be different from the surface free energy and edge free energy of the nuclei on the original active centres in heterogeneous nucleation. Induction times in unseeded barium sulphate precipitation are measured as a function of the concentration of an additive, a co-polymer of maleic acid and vinyl sulphonic acid, and interpreted by the proposed theory. It is concluded that this theory describes fairly well the obtained experimental data, which show a stimulation of the precipitation process at very low additive concentrations and a change-over into retardation at an additive concentration of ≈ 0.005 ppm.

Influence of mixing on the product quality in precipitation

Precipitation of barium sulfate has been studied in a rectangular flat reactor with jet mixing, both experimentally and with Computational Fluid Dynamics (CFD) modeling. The precipitation kinetics and mass balances were implemented in the CFD software (Fluent® version 4.25). The influence of the hydrodynamics on the quality of the precipitate has been studied by changing the inlet velocity ratio while keeping the residence time and species concentration in the reactor constant. The CFD model was able to predict the influence of the inlet velocity ratio on the area mean particle size, the coefficient of variation of the particle size distribution, and the degree of conversion. Flow visualization experiments show that the simulated flow pattern was in good agreement with the experiments. A non-symmetric flow pattern was found, which was in agreement with the study of Murai e.a., 1989.

Phosphate removal in a fluidized bed—II. Process optimization

The aggregation of fine primarily formed calcium phosphate particles with sand grains in a fluidized bed for phosphate removal was studied experimentally by means of a set-up which isolated aggregation from other processes during calcium phosphate precipitation, as well as through experiments under normal operation of the fluidized bed. The net aggregation process was described by means of a mathematical model which takes into account two competing mechanisms: orthokinetic aggregation and breakage. The net aggregation process was found to account for ∼ 60% of the phosphate removed by the fluidized bed. It was found that the orthokinetic aggregation can be improved by spreading the supersaturation more evenly throughout the reactor, and breakage can be diminished by a low energy dissipation rate in the bed. Optimization of the phosphate removal efficiency was therefore achieved by selecting sand grains of small sizes (0.1–0.3 mm) and a low superficial velocity (7·10−3 m/s), and by spreading the addition of the NaOH solution (reactant) over two dosage points. Under these conditions the phosphate removal efficiency was ∼ 80%.