Abstract
In the present work, a brief survey has been made on the Newtonian and non-Newtonian approach of blood flow in a step like stenosed artery. A comprehensive theoretical study on the relation between the shear rate and the viscosity of the fluid has been carried out in the case of each non-Newtonian model (e.g. Maxwell fluid model, Casson fluid model, Carreau model, etc.). In this paper, we have considered a backward-facing step for simulation of the blood flow by employing a few of the above-mentioned models. The simulation is performed by using the available CFD package.
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Abbreviations
- \(\dot{\gamma _e}\) :
-
Total strain experienced by the spring
- \(\dot{\gamma _v}\) :
-
Total strain experienced by the dashpot
- \(\dot{\gamma }\) :
-
Strain rate
- \(\lambda \) :
-
Relaxation time
- \(\lambda _r\) :
-
Retardation time
- \(\mu \) :
-
Viscosity of the fluid
- \(\mu _0\) :
-
Zero shear viscosity
- \(\mu _\infty \) :
-
Infinite shear viscosity
- \(\mu _p\) :
-
Polymer viscosity
- \(\mu _s\) :
-
Solvent viscosity
- \(\nabla \) :
-
Vector differential operator
- \(\overset{\nabla }{\tau }\) :
-
Upper convected time derivative of \(\tau \)
- \(\rho \) :
-
Density of the fluid
- \(\tau \) :
-
Stress
- \(\tau _0\) :
-
Yield stress
- \(\tau _e\) :
-
Stress in the spring
- \(\tau _v\) :
-
Stress in the dashpot
- f :
-
Body force of the fluid
- G :
-
Shear modulus
- H :
-
Hematocrit count
- K :
-
Flow consistency index
- n :
-
Flow behaviour index
- P :
-
Pressure
- t :
-
Time of flow
- u :
-
Velocity of the fluid
References
Bessonov N, Sequeira A, Simakov S, Vassilevskii Y, Volpert V (2016) Methods of blood flow modelling. EDP sciences. Math Model Nat Phenom 11(1):1–25. https://doi.org/10.1051/mmnp/201611101
Blair GWS (1959) An equation for the flow of blood, plasma and serum through glass capillaries. Nature 183(4661):613–614. https://doi.org/10.1038/183613a0
Blair GWS, Spanner DC (1974) An introduction to biorheology. Elsevier, Amsterdam, The Netherlands
Chakravarty S, Mandal P (2000) Two-dimensional blood flow through tapered arteries under stenotic conditions. In J Nonlinear Mech 35:779–793. https://doi.org/10.1016/S0020-7462(99)00059-1
Chaturani P, Samy VRP (1985) A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases. Biorheology 22(6):521–531
Cho YI, Kensey KR (1991) Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: steady flows. Biorheology 28:241
Copley AL (1960) Apparent viscosity and wall adherence of blood systems. In: Copley AL, Stainsly G (eds) Flow properties of blood and other biological systems. Pergamon Press, Oxford
Haghighi AR, Asl MS, Kiyasatfar M (2015) Mathematical modelling of unsteady blood flow through elastic tapered artery with overlapping stenosis. J Braz Soc Mech Sci Engg 37(2):571–578
Irgens F (2004) Rheology and Non-Newtonian fluids. Springer
Johnston BM, Johnson PR, Corney S, Kilpatrick D (2004) Non-Newtonian blood flow in human right coronary arteries: steady state simulations. J Biomech 37:709–720
Johnston BM, Johnson PR, Corney S, Kilpatrick D (2006) Non-Newtonian blood flow in human right coronary arteries: transient simulations. J Biomech 39:1116–1128
Mandal PK (2005) An unsteady analysis of non-newtonian blood flow through tapered arteries with a stenosis. Int J Non-linear Mech 40(1):151–164
Macosko CW (1993) Rheology, principles, measurements and applications. VCH Publisher. ISBN 1-56081-579-5
Merrill EW, Benis AM, Gilliland ER, Sherwood TK, Salzman EW (1965) Pressure-flow relations of human blood in hollow fibers at low flow rates. J Appl Physiol 20(5):954–967
Misra JC, Shit GC (2006) Blood flow through arteries in a pathological state: a theoretical study. Int J Eng Sci 44(10):662–671
Sacks AH, Raman KR, Burnell JA, Tickner EG (1963) Auscultatory versus direct pressure measurements for Newtonian fluids and for blood in simulated arteries. VIDYA Report 119
Siebert MW, Fodor PS (2009) Newtonian and non-Newtonian blood flow over a backward-facing step- a case study. Proceedings of the COMSOL Conference, Boston
Zaman A, Ali N, Sajid M, Hayat T (2015) Effects of unsteadiness and non-Newtonian rheology on blood flow through a tapered time-variant stenotic artery. AIP Adv 5:037129 (2015). https://doi.org/10.1063/1.4916043
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Udupa, M., Shankar Narayan, S., Saha, S. (2021). A Study of the Blood Flow Using Newtonian and Non-Newtonian Approach in a Stenosed Artery. In: Singh, P., Gupta, R.K., Ray, K., Bandyopadhyay, A. (eds) Proceedings of International Conference on Trends in Computational and Cognitive Engineering. Advances in Intelligent Systems and Computing, vol 1169. Springer, Singapore. https://doi.org/10.1007/978-981-15-5414-8_21
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