On the Theory of Unsteady-State Operation of Bulk Continuous Crystallization

Author:

Makoveeva Eugenya V.,Alexandrov Dmitri V.ORCID,Ivanov Alexander A.ORCID

Abstract

Motivated by an important application in the chemical and pharmaceutical industries, we consider the non-stationary growth of a polydisperse ensemble of crystals in a continuous crystallizer. The mathematical model includes the effects of crystal nucleation and growth, fines dissolution, mass influx and withdrawal of product crystals. The steady- and unsteady-state solutions of kinetic and balance equations are analytically derived. The steady-state solution is found in an explicit form and describes the stationary operation mode maintained by the aforementioned effects. An approximate unsteady-state solution is found in a parametric form and describes a time-dependent crystallization scenario, which tends toward the steady-state mode when time increases. It is shown that the particle-size distribution contains kinks at the points of fines dissolution and product crystal withdrawal. Additionally, our calculations demonstrate that the unsteady-state crystal-size distribution has a bell-shaped profile that blurs with time due to the crystal growth and removal mechanisms. The analytical solutions found are the basis for investigating the dynamic stability of a continuous crystallizer.

Funder

Russian Science Foundation

Publisher

MDPI AG

Subject

Inorganic Chemistry,Condensed Matter Physics,General Materials Science,General Chemical Engineering

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