A population balance model for ultrasound-assisted unseeded batch cooling crystallization of L-asparagine monohydrate (LAM) from its aqueous solution is developed and validated. The model considers nucleation, growth, and breakage phenomena and is solved by high resolution finite volume discretization with a flux limiter. An additional kinetic expression is introduced for induced nucleation due to ultrasound irradiation. The kinetics are extracted using a nonlinear optimization technique that uses solute concentration data measured by high performance liquid chromatography and mean crystal size measured by laser diffraction. The developed model shows good quantitative agreement with experimental observations on solute concentration and final crystal size distribution (CSD). Experimental data and model simulations show that ultrasound significantly reduces the metastable zone width for LAM, enhances the nucleation rate, and induces early nucleation.
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