Sonofragmentation of Rectangular Plate-like Crystals: Bivariate Population Balance Modeling and Experimental Validation

Abstract

The use of multidimensional population balance equations in predicting ultrasound-assisted sonocrystallization processes is curbed by the unavailability of physically motivated macroscopic mathematical kernels. This study develops a comprehensive population balance modeling of the ultrasound-assisted sonofragmentation of thin rectangular plate-type pyrazinamide crystals. A new bivariate breakage selection function is presented, which takes care of the time dependence in particle selections along with the size dependence. Furthermore, a new mathematical formulation of the bivariate breakage distribution function is introduced to predict the outcomes of the sonofragmentation experiments of Bhoi et al. (Chem. Eng. Sci.20192031227). Finally, the results obtained from solving the developed population balance model are successfully validated against the experimental results. The developed population balance model accurately captures the effects of variations in ultrasonic amplitude and sonication time.

Investigating Chemical Heterogeneity in Inclusion Populations: A Multivariate Population Balance Model Study in Gas-Stirred Ladles

“…To further evaluate the appropriate level of discretization for the FVS model, L 1 and L 2 errors are calculated along with the computer simulation time for different numbers of cells. The results from the CAT with 60 grid points are chosen as the reference case and compared with other schemes and different numbers of cells.…”

Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model

“…To quantify the prediction errors, the relative L 1 and L 2 errors are calculated using the following formula [23,28]:…”

“…To quantify the prediction errors, the relative L1 and L2 errors are calculated using the following formula [23,28]: L1=∑i=1I|u^i−ui|Δvi∑i=1Iui Δviand L2=∑i=1Ifalse[|u^i−ui|Δvifalse]2∑i=1Iui Δvi,where ui and u^i denote the concentrated number density functions calculated from the analytical solutions and either of the proposed FVS. Moreover, numerical computations are performed to investigate the experimental order of convergence (EOC) of the proposed schemes, using the following formula given in Kumar & Warnecke [29] and Kumar & Kumar [30].…”

Two-dimensional population balance modelling and validation of combined cooling and antisolvent crystallization of l-asparagine monohydrate

“…20 Recently, two-dimensional population balance model has been proposed for ultrasound assisted crystallization and breakage of a plate-like crystal pyrazinamide. [21][22][23] The L-asparagine monohydrate (LAM) is an important nonessential amino acid that plays a pivotal role in the metabolic processes of the human body. It also shows a nonlinear optical property due to the presence of pi bonds.…”