Online microscopy has received much attention in the field of crystal shape control over recent years, since commonly used measurement techniques cannot provide enough information for this purpose. In this work, we present an estimation scheme that serves to reconstruct the 3D crystal shape from the measured 2D crystal projection. The boundary curves of the crystal projections are parametrized by Fourier descriptors, which are subsequently compared with a precomputed database. The procedure is evaluated in comparison with various effects that might impair the estimation. A good agreement between the true and estimated values is found in all cases. The presented methods are applied to batch cooling crystallizations of potassium dihydrogen phosphate (KDP) dissolved in water. As a result, the face specific growth rates are determined as a function of supersaturation. To validate the performance of this scheme, the calculated face specific growth rates are used in a model-based prediction of the supersaturation profiles, which agrees well with the experimental data.
The final shape distribution of crystalline
materials is an important
product quality that is controlled by the growth and possibly also
by the dissolution rates of individual crystal facets. Knowledge of
the kinetics under batch process conditions allows optimal process
design with regard to desired shape distributions. In this work, potassium
dihydrogen phosphate (KDP) was chosen as a model substance, for which
face-specific growth and dissolution rates were determined in a batch
crystallizer. The temporal evolution of the crystal population was
tracked with a flow-through microscope using a shape estimation procedure
presented by C. Borchert et al. (Image-Based in Situ Identification
of Face Specific Crystal Growth Rates from Crystal Populations. Cryst. Growth Des. 2014, 14, 952–971). Effects of concentration and temperature on the
kinetics were separately investigated. It was found that crystal growth
is strongly affected by impurities at low supersaturation, whereas
impurity effects are diminishing at higher supersaturation. The dissolution
rates were found to be linearly dependent on the applied undersaturation,
and no impurity effects were visible. The effects of temperature on
both growth and dissolution kinetics were found to obey the Arrhenius
law, and corresponding activation energies for growth and dissolution
of KDP were determined.
The control of the
evolution of the crystal size and shape distribution
(CSSD) during crystallization processes is an important task in crystallization,
as the final CSSD decisively influences the physical and solid state
properties of crystalline material. This work utilizes sequential
growth and dissolution cycles, which turn out to result in an essentially
enlarged region of attainable crystal sizes and shapes. Using potassium
dihydrogen phosphate as a model substance, such a cyclic crystallization
process is realized in a batch scale and in a novel, fully automated,
and controlled manner. To this end, a novel observer setup is presented,
which is based on video microscopy, and facilitates the real-time
monitoring of the evolution of the crystal size and shape distribution.
Given this information, optimal strategies for the control of supersaturation
profiles as well as CSSD are experimentally successfully implemented,
proving a reliable and high-precision generic control scheme for crystal
shape manipulation. The proposed theoretical and experimental research
results are expected to be of use in targeted crystal size and shape
manipulation in chemical and pharmaceutical industries.
The dynamics of particulate processes can be described by population balance equations which are governed by the phenomena of growth, nucleation, aggregation and breakage. Estimating the kinetics of the latter phenomena is a major challenge particularly for particle aggregation because first principle models are rarely available and the kernel estimation from measured population density data constitutes an ill-conditioned problem. In this work we demonstrate the estimation of aggregation kernels from experimental data using an inverse problem approach. This approach is based on the approximation of the aggregation kernel by use of Laurent polynomials. We show that the aggregation kernel can be well estimated from in silico data and that the estimation results are robust against substantial measurement noise. The method is demonstrated for three different aggregation kernels. Good agreement between true and estimated kernels was found in all investigated cases.
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