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Unsteady viscous flow with variable viscosity in a vascular tube with an overlapping constriction. (English) Zbl 1213.76265

Summary: Numerical solution of the unsteady viscous flow in the neighborhood of an overlapping constriction is obtained under laminar flow conditions with the motivation for modeling blood flow through a local occlusion of artery formed due to arterial disease. The flowing blood is considered to be incompressible, Newtonian with variable blood viscosity. The functional dependence of blood viscosity on haematocrit (percentage volume of red cells) has been duly accounted for in order to improve resemblance to the real situation. The finite-difference technique with staggered grid distribution is employed to solve the governing equations. The recirculation regions are formed in the downstream of the overlapping constriction. It is noticed that the arterial wall shear stress, pressure distribution and flow rate in particular, in the constricted site, are significantly altered. The peak value of wall shear stress decrease with increasing haematocrit parameter. The flow separation region increases with increasing haematocrit parameter. The results are presented graphically and analyzed in detail to study the effects of variable blood viscosity on the flow field. The motion of the arterial wall and its effects on local flow dynamics are considered. The contribution of deformability of the arterial wall is to reduce the wall shear stress in comparison to the consideration of rigid wall. Arterial wall motion causes to diminish the wall shear stress significantly.

MSC:

76Z05 Physiological flows
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
92C35 Physiological flow
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[1] Anand, M.; Rajagopal, K. R., A mathematical model to describe the change in the constitutive character of blood due to platelet activation, Comptes Rendus Mecanique, 330, 8, 557-562 (2002) · Zbl 1177.76474
[2] Young, D. F.; Tsai, F. Y., Flow characteristics in models of arterial stenoses-I. Steady flow, J. Biomech., 6, 395-410 (1973)
[3] Young, D. F.; Tsai, F. Y., Flow characteristics in models of arterial stenoses-II. Steady flow, J. Biomech., 6, 395-410 (1973)
[4] Despande, M. D.; Giddens, D. P.; Mabon, R. F., Steady laminar flow through modeled vascular stenoses, J. Biomech., 9, 165-174 (1976)
[5] C.G. Caro, T.J. Pedley, R.C. Schroter, W.A. Seed, The Mechanics of the Circulation, Oxford Medical, New York, 1978.; C.G. Caro, T.J. Pedley, R.C. Schroter, W.A. Seed, The Mechanics of the Circulation, Oxford Medical, New York, 1978. · Zbl 1234.93001
[6] Ahmed, A. S.; Giddens, D. P., Velocity measurements in steady flow through axi-symmetric stenosis at moderate Reynolds numbers, J. Biomech., 16, 505-516 (1983)
[7] Ku, D. N., Blood flow in arteries, Ann. Rev. Fluid Mech., 29, 399-434 (1997)
[8] Talukder, N.; Karayannacos, P. E.; Nerem, R. M.; Vasco, J. S., An experimental study of fluid mechanics of arterial stenosis, ASME J. Biomech. Eng., 99, 74 (1977)
[9] Lee, T. S., Numerical studies of fluid flow through tubes with double constrictions, Int. J. Numer. Meth. Fluids, 11, 1113 (1990) · Zbl 0715.76069
[10] Young, D. F., Fluid mechanics of arterial stenosis, J. Biomech. Eng. ASME, 101, 157 (1979)
[11] Layek, G. C.; Mukhopadhyay, S.; Samad, Sk. A., Oscillatory flow in a tube with multiple constrictions, Int. J. Fluid Mech. Res., 32, 402-419 (2005) · Zbl 1189.76787
[12] Pedley, T. J., The Fluid Mechanics of Large Blood Vessels (1980), Cambridge University Press · Zbl 0449.76100
[13] Chakravarty, S.; Mandal, P. K., Mathematical modelling of blood flow through an overlapping arterial stenosis, Math. Comput. Model., 19, 59 (1994) · Zbl 0791.92009
[14] Oka, S., Cardiovascular Hemorheology (1981), Cambridge University Press: Cambridge University Press Cambridge, London, p. 28
[15] Demiray, H., Weakly nonlinear waves in a fluid with variable viscosity contained in a prestressed thin elastic tube, Chaos Soliton Fract., 36, 196-202 (2008) · Zbl 1131.76064
[16] Jesty, J.; Nemerson, Y., The pathways of blood coagulation, (Beutler, E.; Lichtman, M. A.; Coller, B. S.; Kipps, T. J., Williams Hematology (1995), McGraw Hill Inc.), 1222-1238
[17] M.M. Lih, Transport Phenomena in Medicine and Biology, John Wiley, New York, 1975, p. 378.; M.M. Lih, Transport Phenomena in Medicine and Biology, John Wiley, New York, 1975, p. 378.
[18] Mazumdar, H. P.; Ganguly, U. N.; Ghorai, S.; Dalal, D. C., On the distributions of axial velocity and pressure gradient in a pulsatile flow of blood through a constricted artery, Indian J. Pure Appl. Math., 27, 1137 (1996) · Zbl 0863.92004
[19] Harlow, F. H.; Welch, J. E., Numerical calculation of time dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8, 2182 (1965) · Zbl 1180.76043
[20] P.J. Roache, Computational Fluid Dynamics, Hermosa Publishers, New Mexico, 1985.; P.J. Roache, Computational Fluid Dynamics, Hermosa Publishers, New Mexico, 1985. · Zbl 0588.76015
[21] Glagov, S.; Zarins, C.; Giddens, D. P.; Ku, D. N., Hemodynamics atherosclerosis: insights perspectives gained from studies of human arteries, Arch. Pathol. Lab. Med., 112, 1018-1031 (1988)
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