A Model of Synovial Fluid with a Hyaluronic Acid Source: A Numerical Challenge
Abstract
:1. Introduction
2. Model
2.1. Equations
2.2. Viscosity Model
2.3. Analysis of the Model: Steady State
2.4. Stability Consideration
3. Results
4. Discussion about Numerics
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
c | concentration | |
dimensionless concentration | - | |
D | diffusion coefficient | |
h | half distance between the plates | m |
K | stress | |
dimensionless stress | - | |
n | flow behavior index | - |
r | strength of the source term | 1/s |
dimensionless strength of the source term | - | |
t | time | s |
dimensionless time | - | |
u | velocity | m/s |
dimensionless velocity | - | |
wall velocity | m/s | |
viscosity | kg/m/s | |
zero-shear viscosity | kg/m/s | |
dimensionless viscosity | - | |
Cross time constant | s | |
density |
Abbreviations
SF | Synovial fluid |
HA | Hyaluronic acid |
CSC | Chebyshev spectral collocation |
Re | Reynolds number |
Pe | Péclet number |
Appendix A. Numerical Treatment of the Problem
Appendix A.1. Spatial Discretization
Appendix A.2. Temporal Discretization
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Ozan, S.C.; Labrosse, G.; Uguz, A.K. A Model of Synovial Fluid with a Hyaluronic Acid Source: A Numerical Challenge. Fluids 2021, 6, 152. https://doi.org/10.3390/fluids6040152
Ozan SC, Labrosse G, Uguz AK. A Model of Synovial Fluid with a Hyaluronic Acid Source: A Numerical Challenge. Fluids. 2021; 6(4):152. https://doi.org/10.3390/fluids6040152
Chicago/Turabian StyleOzan, S. Canberk, Gérard Labrosse, and A. Kerem Uguz. 2021. "A Model of Synovial Fluid with a Hyaluronic Acid Source: A Numerical Challenge" Fluids 6, no. 4: 152. https://doi.org/10.3390/fluids6040152