(155e) A Discrete-Continuous Population Balance Approach for the Nanoparticle Precipitation in Microemulsions

The formation of nanoparticles in microemulsion droplets is a promising technology for the control of the particle properties, e.g. the particle size distribution or particle shape [1]. Due to the time consuming and expensive experiments in this field (e.g. complex phase behavior [2] and TEM analysis) a reasonable modelling strategy is an indispensable step for the process analysis.

Some stochastic and a few deterministic modelling approaches can be found in the literature (see overview in [3]). Most of these approaches have a very high computational demand because of the high number of internal coordinates which are necessary for a reliable description of the microemulsion system [3]. At least 3 internal coordinates (the two reactant concentrations inside the droplets and the particle size) have to be considered. Modelling approaches which combine the need of fast computational solutions, e.g. for online process control or CFD studies, and the high dimension of system can not be found in the literature so far. A novel discrete-continuous population balance approach [4] allows a very fast computational solution within a few seconds. The main assumption is a equilibrium distribution of the two reactants inside the droplets. Within in this approach the numbers of molecules/ions of the two reactants inside the droplets are described by a two-dimensional, discrete and time-dependent Poisson distribution [5]. The third internal coordinate of the droplet population, the particle size, is a partially discrete-continuous coordinate. The splitting of the coordinate in a discrete part for the small nuclei (nucleation and growth kinetics simultaneously) and a continuous part for bigger particles (only growth kinetics) enables a very accurate mass conservation of the whole system and a significant reduction of the model equations.

The presented model was validated with barium sulfate microemulsion based precipitation experiments in a semi-batch rushton tank reactor [6]. A good agreement between experimental and simulated particle size distributions was obtained for a set of experiments where the initial reactant concentrations inside the droplets have been used as a control parameter for the particle size.

[1] Kumar, P.; Mittal, K. L. (Eds): Handbook of Microemulsion Science and Technology, Marcel Dekker Inc., New York, 1999

[2] Rauscher, F.; Veit, P.; Sundmacher, K.: Analysis of a technical-grade w/o microemulsion and its application for the precipitation of calcium carbonate nanoparticles. In: Colloid Surf. A-Physicochem. Eng. Asp. 254 (1-3), p. 183-191, 2005

[3] Niemann, B.; Rauscher, F.; Adityawarman, D.; Voigt, A.; Sundmacher, K.: Microemulsion-assisted precipitation of particles: Experimental and model-based process analysis. In: Chem. Eng. & Proc., 2005, accepted

[4] Niemann, B.; Recksiedler, J.; Adityawarman, D.; Sundmacher, K.: Nucleation and growth kinetics for the nanoparticle precipitation of barium sulfate in microemulsions. AIChE 2005 Annual Meeting, Cincinnati, OH

[5] Bandyopadhyaya, R.; Kumar, R.; Gandhi, K. S.; Ramkrishna, D.: Modeling of precipitation in reverse micellar systems. In: Langmuir 13 (14), p. 3610-3620, 1997

[6] Adityawarman, D.; Voigt, A.; Veit, P.; Sundmacher, K.: Precipitation of barium sulfate nanoparticles in a non-ionic microemulsion: Identification of suitable control parameters. In: Chem. Eng. Sci. 60 (12), p. 3373-3381, 2005