Estimation of aggregation kernels based on Laurent polynomial approximation

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.

Subjects

Aggregation

Aggregation kernel

Inverse methods

Polynomial approximation

Funding(s)

SPP 1679: Teilprojekt "Numerische Lösungsverfahren für gekoppelte Populationsbilanzsysteme zur dynamischen Simulation multivariater Feststoffprozesse am Beispiel der formselektiven Kristallisation"

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Estimation of aggregation kernels based on Laurent polynomial approximation