Approximate analytical solution of the integro-differential model of
bulk crystallization in a metastable liquid with mass supply (heat
dissipation) and crystal withdrawal mechanism
Abstract
This paper is devoted to an approximate analytical solution of an
integro-differential model describing the process of nucleation and
growth of particles in crystallizers, taking into account the
thermal-mass exchange with the environment and the removal of product
crystals from the metastable medium. The method developed in this work
for solving model equations (kinetic equation for the particle size
distribution function and balance equations for temperature/impurity
concentration) is based on using the saddle point method for calculating
the Laplace-type integral. It is shown that the degree of metastability
of the liquid decreases with time at a fixed value of the mass inflow
from the outside (heat flow to the outside). The crystal size
distribution function has the form of an irregular bell-shaped curve,
which increases with the intensification of heat and mass exchange with
the environment.
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