Development of a Semi-Empirical Model for Droplet Size Determination of a Three-Channel Spray Nozzle for Pellet Coating Based on the Optical Method Concept
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials: Polymeric Dispersions and Their Rheology
2.1.1. Surface Tension
2.1.2. Viscosity
2.1.3. Density
2.2. Design of Experiment and Dimensional Analysis to Support the Experimental Setup
- -
- Solvents: water, acetone, ethanol, and mixture of ethanol and water
- -
- Polymer used and its w/w%:
- ○
- Hypromellose: 6.5–9.3
- ○
- Ethylcellulose: 4.0
- ○
- Copolymer of acrylic and methacrylic acid: 1.8–10.0
- -
- Viscosity (η): 0.3–225 mPas
- -
- Surface tension (λ): 23.7–72.0 mN/m
- -
- Density (): 790–1030 kg/m3
- -
- Dispersion flow (M): 12–160 g/min
- -
- Atomization air pressure (pa): 1.1–3.1 bar
- -
- Microclimate air pressure (pm): 0.1–2.6 bar
2.3. Droplet Size Measurements
2.3.1. Experimental Setup
2.3.2. Image Analysis
3. Results and Discussion
3.1. Definition of Measuring Conditions
3.2. Statistical Analysis
3.3. Model Construction
3.4. Simplification of Generated Models, Extraction of Basic Physio Chemical Influences, and Comparison with N–T
- The majority of the influences of the parameters are comparable: M and λ exhibit a positive correlation, whereas , pa, and pm show a negative correlation with droplet size.
- The influence of viscosity has a negative correlation with droplet size based on our results and has a positive correlation with droplet size based on the N–T. However, based on the experimental results in this study, the influence of viscosity is much lower compared with the N–T equation, which was also emphasized by other authors [39].
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Ref. | Statistical Approach | No. of Factors | Dispersion Properties | Type of Nozzle | Exp. Scale | No. of Exp. | Method for Droplet Size Determination | Field of Research | Drawbacks |
---|---|---|---|---|---|---|---|---|---|
Thybo et al. (2008) | Least squares analysis | 5 | Newtonian | 2 | Pilot, production | 166 | Malvern laser diffraction, volume-based | Pharmacy, spray drying |
|
Petit et al. (2015) | DA + MLR | 7 (DA) | Newtonian | GEA | No data | 134 | Spraytec laser diffraction, volume-based | Food engineering |
|
Aliseda et al. (2008) | No data | No data | Non-Newtonian | PF28100NB | No data | No data | Phase-Doppler particle analyzer, volume-based | Pharmacy, film coating |
|
Vesey et al. (2014) | DoE | 3 | Non-Newtonian | Schlick 970, 0/4 | Laboratory, production | 34 | Phase-Doppler, volume-based | Pharmacy, film coating |
|
Mueller and Kleinebudde (2007) | DoE | 4 | Newtonian | 970/7-1 S75 ABC, 930/7-1 S35 ABC | Laboratory, production | 27 | Phase-Doppler particle analyzer, volume-based | Pharmacy, film coating |
|
Gauno et al. (2013) | ANOVA + PCA | 3 | Newtonian | Glatt 1-050-00190 X171 | Laboratory | 48 | Malvern laser diffraction, volume-based | Pharmacy, film coating (Wurster) |
|
Dennison et al. (2016) | DoE | 3 | Newtonian | 1/8 JJAU-SS | Laboratory | 17 | Real time laser diffraction, volume-based | Pharmacy, film coating |
|
Schoefer and Worts (1977) | Not used, single experiments compared | 4 | Newtonian * | 941-943/7 | Pilot | 160 | Photo-micrographs of droplets collected on oil-covered slides | Pharmacy, fluid bed granulation |
|
Viscosity [mPas] | Surface Tension (1) [mN/m] | Density (1) [kg/m3] | |
---|---|---|---|
Acetone | 0.306 | 24.5 ± 0.11 | 790 ± 0 |
Water | 0.894 | 72.0 | 1000 |
9.3 w/w% hypromellose in ethanol and water (9:1) | 225 | 26.9 ± 0.17 | 880 ± 20 |
6.5 w/w% hypromellose in ethanol | 75.2 | 25.8 ± 0.13 | 830 ± 0 |
10.0 w/w% copolymer of acrylic and methacrylic acid in ethanol | 16 | 24.0 ± 0.06 | 840 ± 0 |
1.8 w/w% copolymer of acrylic and methacrylic acid in ethanol | 2.2 | 23.7 ± 0.02 | 810 ± 10 |
4.0 w/w% ethylcellulose in ethanol | 10.6 | 24.3 ± 0.04 | 830 ± 20 |
6.5 w/w% hypromellose in water | 50.4 | 47.0 ± 0.44 | 1030 ± 0 |
Exp. Name | [kg/m3] | η [Ns/m2] | λ [N/m] | M [g/min] | pa [bar] | pm [bar] | lnα | lnβ | lnγ | lnδ | d [µm] | E[ln(d10/D)] | SD[ln(d10/D)] |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N1 | 880 | 0.225 | 0.0269 | 20 | 2.6 | 0.2 | −4.18 | −0.579 | −2.55 | −9.36 | 6.99 | −5.37 | 0.658 |
N10 | 880 | 0.225 | 0.0269 | 113 | 1.3 | 0.1 | −2.10 | −0.579 | −2.54 | −8.67 | 11.0 | −4.87 | 0.626 |
N11 | 790 | 0.000306 | 0.0245 | 12 | 1.1 | 0.2 | −4.21 | 12.4 | −1.72 | −8.61 | 7.17 | −5.25 | 0.509 |
N12 | 790 | 0.000306 | 0.0245 | 100 | 1.1 | 0.1 | −2.09 | 12.4 | −2.48 | −8.61 | 13.5 | −4.93 | 0.822 |
N13 | 880 | 0.225 | 0.0269 | 14 | 1.3 | 1.3 | −4.19 | −0.579 | −0.0038 | −8.67 | 5.96 | −5.40 | 0.449 |
N14 | 880 | 0.225 | 0.0269 | 113 | 1.3 | 1.3 | −2.11 | −0.579 | −0.0123 | −8.67 | 8.87 | −5.05 | 0.543 |
N15 | 790 | 0.000306 | 0.0245 | 12 | 1.1 | 1.1 | −4.21 | 12.42 | −0.00274 | −8.59 | 12.9 | −4.85 | 0.838 |
N17 | 830 | 0.0752 | 0.0258 | 70 | 3.1 | 0.9 | −2.99 | 1.51 | −1.24 | −9.58 | 9.32 | −4.267 | 0.305 |
N18 | 830 | 0.0752 | 0.0258 | 70 | 3.1 | 0.9 | −2.99 | 1.51 | −1.24 | −9.58 | 8.25 | −4.44 | 0.261 |
N19 | 830 | 0.0686 | 0.026 | 70 | 3.1 | 0.9 | −2.99 | 1.71 | −1.23 | −9.57 | 18.0 | −4.26 | 0.335 |
N2 | 880 | 0.225 | 0.0269 | 160 | 2.6 | 0.2 | −2.10 | −0.579 | −2.56 | −9.36 | 9.65 | −5.00 | 0.592 |
N20 | 1000 | 0.000894 | 0.0720 | 113 | 1.3 | 0.1 | −2.17 | 11.6 | −2.58 | −7.68 | 24.8 | −4.12 | 0.701 |
N3 | 790 | 0.000306 | 0.0245 | 18 | 2.2 | 0.2 | −4.15 | 12.4 | −2.57 | −9.29 | 7.11 | −5.28 | 0.540 |
N4 | 790 | 0.000306 | 0.0245 | 141 | 2.2 | 0.2 | −2.10 | 12.4 | −2.55 | −9.30 | 12.2 | −4.77 | 0.611 |
N5 | 880 | 0.225 | 0.0269 | 20 | 2.6 | 2.6 | −4.18 | −0.579 | −0.00653 | −9.36 | 6.29 | −5.36 | 0.469 |
N6 | 880 | 0.225 | 0.0269 | 160 | 2.6 | 2.6 | −2.10 | −0.579 | −0.00769 | −9.36 | 10.9 | −4.92 | 0.613 |
N7 | 790 | 0.000306 | 0.0245 | 18 | 2.2 | 2.2 | −4.15 | 12.4 | −0.00226 | −9.29 | 8.50 | −5.05 | 0.453 |
N8 | 790 | 0.000306 | 0.0245 | 141 | 2.2 | 2.2 | −2.08 | 12.4 | 0.0128 | −9.28 | 17.1 | −4.35 | 0.438 |
N9 | 880 | 0.225 | 0.0269 | 14 | 1.3 | 0.1 | −4.19 | −0.579 | −2.56 | −8.66 | 6.58 | −5.30 | 0.431 |
C19 | 840 | 0.016 | 0.02395 | 20 | 2.6 | 0.2 | −4.16 | 4.55 | −2.57 | −9.48 | 29.0 | −3.82 | 0.445 |
C20 | 810 | 0.0022 | 0.02366 | 20 | 2.6 | 2.0 | −4.14 | 8.47 | −0.276 | −9.49 | 18.9 | −4.25 | 0.427 |
C21 | 870 | 0.216 | 0.02709 | 113 | 1.3 | 0.2 | −2.10 | −0.50 | −1.88 | −8.67 | 18.7 | −4.21 | 0.295 |
C22 | 790 | 0.000306 | 0.02448 | 113 | 1.3 | 0.6 | −2.05 | 12.42 | −0.868 | −8.77 | 34.2 | −3.73 | 0.571 |
C23 | 840 | 0.016 | 0.02395 | 113 | 1.3 | 1.3 | −2.08 | 4.55 | 0 | −8.79 | 19.5 | −4.23 | 0.489 |
C24 | 1000 | 0.000894 | 0.07197 | 60 | 1.3 | 0.1 | −2.79 | 11.6 | −2.55 | −7.67 | 13.9 | −4.49 | 0.323 |
C25 | 1000 | 0.000894 | 0.07197 | 30 | 1.3 | 1.3 | −3.49 | 11.6 | 0.00766 | −7.68 | 15.3 | −4.39 | 0.318 |
C26 | 830 | 0.0106 | 0.02426 | 40 | 1.3 | 0.4 | −3.11 | 5.37 | −1.18 | −8.77 | 17.3 | −4.28 | 0.283 |
C27 | 830 | 0.0106 | 0.02426 | 40 | 1.3 | 0.4 | −3.11 | 5.37 | −1.18 | −8.77 | 19.2 | −4.17 | 0.260 |
Exp. name | [kg/m3] | η [Ns/m2] | λ [N/m] | M [g/min] | pa [bar] | pm [bar] | Exp. d [µm] | Model Prediction Diameter [µm] | Model Prediction SMD [µm] | Exp. SMD [µm] | Calculation of SMD by N-T [µm] |
---|---|---|---|---|---|---|---|---|---|---|---|
D2 | 870 | 0.216 # | 0.0271 | 70 | 2.49 | 0.4 | 17.8 | 11.8 | 14.6 | 25.3 | 138 |
D5 | 840 | 0.0160 | 0.0240 | 70 | 2.51 | 0.41 | 19.2 | 18.3 | 21.8 | 45.6 | 51.5 |
D10 | 830 | 0.0106 | 0.0243 | 70 | 2.5 | 0.41 | 20.1 | 18.7 | 22.2 | 25.5 | 45.4 |
X2 | 830 | 0.0686 | 0.0260 | 10 | 0.5 | 0.1 | 14.2 | 12.5 | 12.9 | 19.4 | 29.4 |
X7 | 1030 | 0.0504 | 0.0470 | 70 | 2.51 | 0.4 | 16.1 | 15.8 | 18.7 | 19.3 | 54.9 |
X8 | 1030 | 0.0504 | 0.0470 | 140 | 2.49 | 0.4 | 17.4 | 20.6 | 27.6 | 23.5 | 132 |
X9 | 1030 | 0.0504 | 0.0470 | 70 | 3.11 | 0.9 | 16.2 | 17.0 | 19.7 | 19.1 | 54.9 |
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Vidovič, S.; Bizjak, A.; Sitar, A.; Horvat, M.; Janković, B.; Golobič, I. Development of a Semi-Empirical Model for Droplet Size Determination of a Three-Channel Spray Nozzle for Pellet Coating Based on the Optical Method Concept. Processes 2022, 10, 86. https://doi.org/10.3390/pr10010086
Vidovič S, Bizjak A, Sitar A, Horvat M, Janković B, Golobič I. Development of a Semi-Empirical Model for Droplet Size Determination of a Three-Channel Spray Nozzle for Pellet Coating Based on the Optical Method Concept. Processes. 2022; 10(1):86. https://doi.org/10.3390/pr10010086
Chicago/Turabian StyleVidovič, Sara, Alan Bizjak, Anže Sitar, Matej Horvat, Biljana Janković, and Iztok Golobič. 2022. "Development of a Semi-Empirical Model for Droplet Size Determination of a Three-Channel Spray Nozzle for Pellet Coating Based on the Optical Method Concept" Processes 10, no. 1: 86. https://doi.org/10.3390/pr10010086
APA StyleVidovič, S., Bizjak, A., Sitar, A., Horvat, M., Janković, B., & Golobič, I. (2022). Development of a Semi-Empirical Model for Droplet Size Determination of a Three-Channel Spray Nozzle for Pellet Coating Based on the Optical Method Concept. Processes, 10(1), 86. https://doi.org/10.3390/pr10010086