Size-Independent Nucleation and Growth Model of Potassium Sulfate from Supersaturated Solution Produced by Stirred Crystallization

Abstract

This paper explores the kinetics of the crystallization of potassium sulfate in a stirred bed crystallizer through experimental investigation. Employing classical nucleation theory, the homogeneous and heterogeneous nucleation mechanisms of potassium sulfate were investigated. The induction time and critical nucleation parameters, including the surface tension (γ), critical nucleation radius (r*), critical nucleation free energy (ΔG*), and critical nucleation molecule number (i*), were meticulously determined under varying temperatures and supersaturation ratios. The experimental findings revealed that as the temperature and supersaturation ratio increased, the induction time, critical nucleation free energy, critical nucleation radius, and critical molecule number decreased whereas the nucleation rate increased. The crystalline shape remains relatively unaltered with respect to temperature and supersaturation ratio, yet the particle size (D₁₀, D₅₀, D₉₀) increases as the supersaturation and temperature increase. The variations in the measured nucleation parameters align well with the predictions of classical nucleation theory. Furthermore, the kinetic equations of crystal nucleation and the growth rate in a stirred crystallization system were fitted using population balance equations. The results demonstrate that the growth rate increases with increasing supersaturation and stirring rates. Additionally, the effects of the parameters in the nucleation rate equation suggested that the suspension density exerted the greatest influence, followed by the supersaturation ratio and stirring rate. This extensive research provides invaluable theoretical guidance for optimizing the crystallization process and designing industrial crystallizers.

Keywords: growth; nucleation; population balance equation; potassium sulfate; stirred crystallization.

Figure 1

SEM images of K₂SO₄ crystallized from different supersaturation at 328 K (a) 1.20; (b) 1.22; (c) 1.25; (d) 1.28.

Figure 2

SEM of K₂SO₄ crystallized from different supersaturation ratios at 328.15 K (a) 1.20; (b) 1.22; (c) 1.25; (d) 1.28.

Figure 2

SEM of K₂SO₄ crystallized from different supersaturation ratios at 328.15 K (a) 1.20; (b) 1.22; (c) 1.25; (d) 1.28.

Figure 3

The experimental XRD patterns of K₂SO₄. (T: 328 K; S: 1.20).

Figure 4

(a) Effects of supersaturation on CSD. (b) Particle size changes with varying supersaturation at 328 K.

Figure 5

(a) Effects of temperature on CSD. (b) Particle size changes with varying temperatures at S = 1.2.

Figure 6

The relationship between the supersaturation ratio and induction period at various temperatures.

Figure 7

The plots of ln($t_{ind}$) versus 1/ln²S.

Figure 8

The relationship between the supersaturation ratio and nucleation parameters at various temperatures (a) critical nucleation free energy; (b) the number of formula units in the critical nucleus; (c) the radius of the critical nucleus; (d) nucleation rate.

Figure 9

The γ and f for homogeneous nucleation of K₂SO₄.

Figure 10

The relationship between crystal particle number density and particle size.

Figure 11

The relationship between nucleation rate and suspension density.

Figure 12

The relationship between nucleation, growth rate, and supersaturation ratio.

Figure 13

The relationship between crystallization kinetic rate and stirring rate.

Figure 14

Comparison between experimental and theoretical kinetics rate for K₂SO₄ crystallization: (a) nucleation rate and (b) growth rate.

Figure 15

Experimental setup for stirred crystallization. (1) Jacketed crystallizer; (2) Thermostatic circulating water; (3) Thermoelectric couple; (4) Agitator; (5) Laser Particle Size Analyzer.