Particle-Scale Modeling to Understand Liquid Distribution in Twin-Screw Wet Granulation
<p>Representation of normal and tangential contact forces using a spring, dash-pot and slider approach.</p> "> Figure 2
<p>Shear box initial condition, front and side views. The red coloured particles indicate the liquid addition region (i.e., the wetting zone).</p> "> Figure 3
<p>The 3D STL mesh for the kneading discs and barrel used for TSG mixing zone simulation.</p> "> Figure 4
<p>Transfer of liquid from particle surface (<b>top left</b>) to other particles by convective transport (<b>top right</b>) and transfer of liquid from particle surface to liquid bridges between particles by conductive transport before (<b>bottom left</b>) and after shearing (<b>bottom right</b>).</p> "> Figure 5
<p>Changes in (<b>a</b>) average number of liquid bridges per particle <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>Z</mi> <mo stretchy="false">¯</mo> </mover> <mi>b</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) the volume fraction of liquid in bridges <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> </mrow> </semantics></math> when the particle volume fraction <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> was increased from 0.3 to 0.5 for liquid loading of 7.5 × 10<sup>−4</sup>.</p> "> Figure 6
<p>Changes in (<b>a</b>) average number of liquid bridges per particle <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>Z</mi> <mo stretchy="false">¯</mo> </mover> <mi>b</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) volume fraction of liquid in bridges <span class="html-italic">V</span><sub><span class="html-italic">bf</span></sub> when the liquid loading on particles <span class="html-italic">Q<sub>lod</sub></span> was increased at particle volume fraction <span class="html-italic">ϕ</span> of 0.4.</p> "> Figure 7
<p>Changes in (<b>a</b>) average number of liquid bridges per particle <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>Z</mi> <mo stretchy="false">¯</mo> </mover> <mi>b</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) volume fraction of liquid in bridges <span class="html-italic">V<sub>bf</sub></span> when the wetting zone width <span class="html-italic">WZ<sub>width</sub></span> was increased, keeping the flux of liquid addition constant and particle volume fraction <span class="html-italic">ϕ</span> of 0.4.</p> "> Figure 8
<p>Changes in volume of liquid on particle surface (left side snapshot in each sub-plot) and liquid in bridges (right side snapshot in each sub-plot) when two kneading discs were co-rotating at 100 rpm. The plots below every snapshot indicate the volume of liquid on particle and volume of liquid in bridge for each particle in the system.</p> "> Figure 9
<p>Changes in (<b>a</b>) volume of liquid on particle surface and (<b>b</b>) liquid in bridges when two kneading discs were co-rotating at 100 rpm.</p> ">
Abstract
:1. Introduction
2. Particle Scale Modeling Approach
2.1. Particle Flow Model
2.2. Liquid Bridge Model
Liquid Loading, Bridge Volume Fraction & Liquid Bridge Coordination Number
2.3. Simulation Set-Up and Input Parameters
2.3.1. Simple Periodic Simulation Box
2.3.2. Mixing Zone of a TSG
3. Results and Discussion
3.1. Solid-Liquid Mixing in the Simple Periodic Simulation Box
3.1.1. Effect of Change in Volume Fraction of Particles
3.1.2. Effect of Change in Liquid Loading on Particles
3.1.3. Effect of Change in Liquid Addition Zone Width
3.2. Solid-Liquid Mixing in the Mixing Zone of a TSG
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Abbreviations
List of Acronyms | |
DEM | discrete element method. |
HSWG | high shear wet granulation. |
PBE | population balance equation. |
PBM | population balance model. |
TSG | twin-screw granulator. |
List of Symbols | |
Characteristic contact time . | |
Dimensionless filling rate coefficient . | |
Normal overlap between particles i and j [m]. | |
Particle diameter . | |
Dimensionless reference film thickness . | |
Normal damping coefficient . | |
Normal coefficient of restitution . | |
Tangential damping coefficient . | |
body force of a particle i . | |
Cohesion force between particle i and j . | |
Contact force between particle i and j . | |
Normal component of force acting on particle i . | |
Tangential component of force acting on particle i . | |
Shear rate . | |
Scaled shear rate . | |
Dimensional reference film thickness [m]. | |
Normal spring stiffness . | |
Tangential spring stiffness . | |
Volume of liquid present on the particle . | |
Reference liquid content on the particles . | |
Effective mass of the particle [kg]. | |
Dynamic viscosity of liquid . | |
Number of liquid bridge connected to particle i . | |
Number of particles . | |
Number of particles in the liquid addition region . | |
Unit normal vector . | |
Eigen frequency of damped harmonic oscillator . | |
Volume fraction of particles . | |
Fraction of liquid on the surface that is transferred into the bridge . | |
Liquid addition rate to particle i in the liquid addition region . | |
Dimensionless liquid load per particle . | |
Liquid transfer rate for particle . | |
r | Radius of the particle . |
Position vector of the particle . | |
Effective radius of the particle . | |
Density of the particles . | |
Surface tension of liquid . | |
Liquid addition time . | |
Reference liquid bridge filling time [s]. | |
Tangential overlap between particles i and j . | |
Liquid bridge volume . | |
Liquid bridge fraction . | |
Normal relative particle velocity components . | |
Tangential relative particle velocity components . | |
Average number of liquid bridges per particle . |
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Quantity | Symbol | Value | Unit |
---|---|---|---|
Particle diameter | 1.00E-03 | [m] | |
Young’s modulus | G | 3.45E+9 | [N/m2] |
Initial particle velocity | , | 1, 0.1 | [m/s] |
Coefficient of restitution | 0.9 | [–] | |
Coefficient of friction | µ | 0.1 | [–] |
Poisson ratio | 0.33 | [–] | |
Film thickness | / | 1.00E-02 | [–] |
Dimensionless filling rate coefficient | 1 | [–] |
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Kumar, A.; Radl, S.; Gernaey, K.V.; De Beer, T.; Nopens, I. Particle-Scale Modeling to Understand Liquid Distribution in Twin-Screw Wet Granulation. Pharmaceutics 2021, 13, 928. https://doi.org/10.3390/pharmaceutics13070928
Kumar A, Radl S, Gernaey KV, De Beer T, Nopens I. Particle-Scale Modeling to Understand Liquid Distribution in Twin-Screw Wet Granulation. Pharmaceutics. 2021; 13(7):928. https://doi.org/10.3390/pharmaceutics13070928
Chicago/Turabian StyleKumar, Ashish, Stefan Radl, Krist V. Gernaey, Thomas De Beer, and Ingmar Nopens. 2021. "Particle-Scale Modeling to Understand Liquid Distribution in Twin-Screw Wet Granulation" Pharmaceutics 13, no. 7: 928. https://doi.org/10.3390/pharmaceutics13070928
APA StyleKumar, A., Radl, S., Gernaey, K. V., De Beer, T., & Nopens, I. (2021). Particle-Scale Modeling to Understand Liquid Distribution in Twin-Screw Wet Granulation. Pharmaceutics, 13(7), 928. https://doi.org/10.3390/pharmaceutics13070928