2.Non-Newtonian flows
Synovial fluid is a chemically-reacting non-Newtonian fluid, which is responsible for the viscous, elastic and lubricant properties in the joints. Variations in these properties of the synovial fluid may result into joint diseases such as osteoarthritis and rheumatoid arthritis. The response of synovial fluid to instantaneous external stimuli is non-Newtonian when it is healthy, whereas the response is Newtonian when it is inflamed. Presence of hyaluronic acid is the main reason behind that behavior and the response is affected by the concentration of hyaluronic acid in joints. Governing equations are derived using Couette flow. Cross model is used to model the viscosity that depends on shear and concentration. To solve the system numerically spectral method is used.
References
- Massoudi, M. and Uguz, A.K 2012 Chemically-reacting fluids with variable transport properties Applied Mathematics and Computation 219, 1761-1775 (DOI: 10.1016/j.amc.2012.08.015)
- Uguz, A.K. and Massoudi, M. 2010 Heat transfer and Couette flow of a chemically-reacting non-linear fluid Mathematical Methods in the Applied Sciences 33 (11), 1331-1341 (DOI: 10.1002/mma.1250)
General references
- L. Johns and R. Narayanan, Interfacial Instability (Springer-Verlag, New York, 2002).
- S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1981)
- W. Guo, G. Labrosse, and R. Narayanan, The Application of the Chebyshev-Spectral Method in Transport Phenomena: Lecture Notes in Applied and Computational Mechanics (Springer-Verlag, Berlin/Heidelberg, 2013), Vol. 68.
- G. Labrosse, Méthodes Spectrales(Ellipses, Paris, 2011).
- ImageJ : http://imagej.nih.gov/ij/
