Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows
Abstract
:1. Introduction
2. Numerical Methods
2.1. Computational Models
2.2. Governing Equation for Fluid Part
2.3. Governing Equation for Particles
2.4. Virtual Flux Method
2.5. Lift Coefficient
2.6. Relative Viscosity
3. Results and Discussion
3.1. Periodic Length and Grid Resolution
3.2. Effects of Aspect Ratio of Elliptical Particle on the Equilibrium Position Due to Inertial Migration
3.3. Effects of Aspect Ratio of Elliptical Particle on the Effective Viscosity
3.4. Spatial and Temporal Changes in the Effective Viscosity
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
AR | aspect ratio |
a | semi-major axis |
b | semi-minor axis |
C (C1, C2, C3) | confinement |
cs | sound speed |
c | lattice speed |
D | channel width (characteristic length) |
Dp | diameter of sphere |
eα | discrete velocity vector |
fα | distribution function |
equilibrium distribution function | |
non-equilibrium distribution function | |
virtual distribution function | |
virtual equilibrium distribution function | |
Fp | total force vector acting on the particle |
I | moment of inertia |
L | channel length |
m | mass of the suspended particle |
n | normal unit vector |
p0 | reference pressure |
pp | pressure on the solid particle surface |
Δp0 | pressure drop for particle-free flow |
Δp | pressure drop |
pα | pressure distribution function |
Re | Reynolds number |
Rep | particle Reynolds number |
r | radius of circular particle |
t | time |
Tp | torque for particle |
Tw | stress tensor |
U | characteristic velocity |
u | fluid velocity vector |
Δx, Δy | grid resolution |
xp | position vector for particle |
yeq | equilibrium position of inertial migration |
y0 | initial position of a particle in y-coordinate |
wα | weight coefficients |
ε | ellipticity |
effective viscosity | |
viscosity of solvent | |
[η] | intrinsic viscosity |
θp | particle angle |
non-equilibrium stress tensor | |
ρ | fluid density |
τ | single relaxation time |
τw | shear stress tensor |
τ0 | wall shear stress for particle-free flow |
area fraction |
Abbreviations
eq | equilibrium |
neq | non-equilibrium |
eff | effective |
Appendix A
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L/D [-] | yeq/D [-] |
---|---|
1 | 0.248 |
2 | 0.256 |
4 | 0.258 |
6 | 0.258 |
Number of Cells for D [Cells] | Number of Cells for 2r [Cells] | yeq/D [-] |
---|---|---|
400 | 20 | 0.255 |
600 | 30 | 0.258 |
800 | 40 | 0.258 |
AR [-] | yeq/D [-] | ||
---|---|---|---|
C3 = 0.05 | C3 = 0.1 | C3 = 0.2 | |
1 | 0.258 | 0.263 | 0.277 |
2 | 0.260 | 0.267 | 0.284 |
4 | 0.260 | 0.282 | 0.314 |
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Kawaguchi, M.; Fukui, T.; Morinishi, K. Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows. Appl. Sci. 2021, 11, 6727. https://doi.org/10.3390/app11156727
Kawaguchi M, Fukui T, Morinishi K. Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows. Applied Sciences. 2021; 11(15):6727. https://doi.org/10.3390/app11156727
Chicago/Turabian StyleKawaguchi, Misa, Tomohiro Fukui, and Koji Morinishi. 2021. "Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows" Applied Sciences 11, no. 15: 6727. https://doi.org/10.3390/app11156727
APA StyleKawaguchi, M., Fukui, T., & Morinishi, K. (2021). Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows. Applied Sciences, 11(15), 6727. https://doi.org/10.3390/app11156727