Simulation of crystal size and shape by means of a reduced two-dimensional population balance model

Morphological population balance for modeling crystal growth in face directions

“…A splitting method was employed to decompose the 2-D PB equation into a pair of 1-D equations, and each of them was then solved using a high-resolution descritization scheme via implementing a hybrid of the upwind scheme, and the Lax-Wendroff method through a flux limiter function, with the kinetic parameters being determined from experimental data. Briesen 57 used the same potassium dihydrogen phosphate system and the same kinetic parameters 56 to illustrate the numerical results of a reduced 2-D PB model. Coordinate transformation was performed to model the system by introducing two characteristic parameters: the crystal volume and a shape factor.…”

Measurement of particle size and shape by FBRM and in situ microscopy

“…In most studies two-dimensional PSDs and PBEs have been used (Briesen, 2006;Ma et al, 2002;Oullion et al, 2007a,b;Puel et al, 1997Puel et al, , 2003a, the main reason being the difficulty of measuring particle size and growth in multiple directions, especially in situ during growth, as well as the computational difficulties commonly encountered in solving multi-dimensional PBEs. In the 2-D PSD case a crystal is typically described as a 3-D parallelepiped, with length L 1 , height L 2 and width L 3 , where one geometrical constraint is imposed to reduce the number of independent descriptors to two, e.g.…”

“…In the 2-D PSD case a crystal is typically described as a 3-D parallelepiped, with length L 1 , height L 2 and width L 3 , where one geometrical constraint is imposed to reduce the number of independent descriptors to two, e.g. by setting L 3 = L 2 (Briesen, 2006;Ma et al, 2002;Puel et al, 1997Puel et al, , 2003a or by assuming that the width L 3 has the same constant value for all crystals (Oullion et al, 2007a,b).…”

Multi-Impurity Adsorption Model for Modeling Crystal Purity and Shape Evolution during Crystallization Processes in Impure Media

“…The crystallization of KDP (potassium dihydrogen phosphate) from solution was taken as the model system, for which multidimensional kinetic parameters are available in the literature 11,47,49,50,72,73 . As it is shown on Fig.…”