Korea-Australia Rheology Journal, Vol.28, No.3, 217-227, August, 2016
Particulate suspension Jeffrey fluid flow in a stenosed artery with a particle-free plasma layer near the wall
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The present article concerns the problem of blood flow through an artery with an axially asymmetric stenosis (constriction). The two-layered macroscopic model consisting of a cell-rich core of suspension of all the erythrocytes described as a particle-fluid suspension (Jeffrey fluid) and a peripheral zone of cell-free plasma (Newtonian fluid). The analytical expressions for flow characteristics such as fluid phase and particle phase velocities, flow rate, wall shear stress, and resistive force are obtained. It is of interest to mention that the magnitudes of wall shear stress and flow resistance increase with red cell concentration but the flow resistance decreases with increasing shape parameter. One of the important observations is that when blood behaves like a Jeffrey fluid, the flowing blood experiences lesser wall shear stress and flow resistance than in the case of blood being characterized as a Newtonian fluid in both the particle-fluid suspension and particle-free flow studies. The rheology of blood as Jeffrey fluid and the introduction of plasma layer thickness cause significant reduction in the magnitudes of the flow characteristics.
Keywords:blood flow;Jeffrey fluid;erythrocytes;suspension;plasma layer;stenosis or constriction;resistive force
- Abd-Alla AM, Abo-Dahab SM, Kilicman A, J. Magn. Magn. Mater., 384, 79 (2015)
- Ademiloye AS, Zhang LW, Liew KM, Appl. Math. Comput., 268, 334 (2015)
- Akbar NS, Nadeem S, Commun. Theor. Phys., 57, 133 (2012)
- Akbar NS, Nadeem S, Lee C, Results Phys., 3, 152 (2013)
- Allan FM, Hamdan MH, Appl. Math. Comput., 183, 1208 (2006)
- Baskurt OK, Meiselman HJ, Semin. Thromb. Haemost., 29, 435 (2003)
- Boyd W, 1963, Text Book of Pathology: Structure and Functions in Diseases, Lea and Fibiger, Philadelphia.
- Bugliarello G, Sevilla J, Biorheology, 7, 85 (1970)
- Bugliarello G, Hayden JW, Trans. Soc. Rheol., 7, 209 (1963)
- Caro CG, Pedley TJ, Schroter RC, Seed WA, 1978, The Mechanics of the Circulation, Oxford Medical, New York.
- Caro CG, Recent Adv. In Cardiov Diseases, 2, 6 (1981)
- Chakraborty US, Biswas D, Paul M, Korea-Aust. Rheol. J., 23, 25 (2011)
- Charm SE, Kurland GS, 1974, Blood Flow and Microcirculation, John Wiley, New York.
- Chaturani P, Kaloni PN, Biorheology, 13, 243 (1976)
- Chaturani P, Ponalagusamy R, 1982, A two-layered model for blood flow through stenosed arteries, 11th National Conference on fluid mechanics and fluid power, B.H.E.L(R & D), Hydrabad, India, 16-22.
- Chaturani P, Ponalagusamy R, Biorheology, 22, 521 (1985)
- Chaturani P, Ponalagusamy R, 1986a, “Dilatancy effects of blood on flow through arterial stenosis”, 28th Congress of The Indian Society of Theoretical and Applied Mechanics, Waltair, India, 87-96.
- Chaturani P, Ponalagusamy R, Biorheology, 23, 499 (1986)
- Cokelet GR, 1972, The Rheology of Human Blood: In Biomechanies, Prentice-Hall, Englewood Cliffs, New Jersey.
- Deshpande MD, Giddens DP, Mabon RF, J. Biomech. Eng. -Trans. ASME, 9, 65 (1979)
- Distenfass L, Cardiovasc. Med., 2, 337 (1971)
- Drew DA, Arch. Ration. Mech. Anal., 62, 149 (1976)
- Drew DA, Phys. Fluids, 19, 2081 (1979)
- Forrester JH, Young DF, J. Biomech. Eng. -Trans. ASME, 3, 297 (1970)
- Fry DL, Circ. Res., 22, 165 (1968)
- Gad NS, Appl. Math. Comput., 217, 4313 (2011)
- Haynes RH, Am. J. Physiol., 198, 1193 (1960)
- Jyothi KL, Devaki P, Sreenadh S, Int. J. Math. Arch., 4, 75 (2013)
- Macdonald DA, J. Biomech., 12, 13 (1979)
- Mann FG, Herrick JF, Essex H, Blades BJ, Surgery, 4, 249 (1938)
- Mekheimer KS, El Kot MA, Chem. Eng. Commun., 197(9), 1195 (2010)
- Ponalagusamy R, 1986, Blood Flow Through Stenosed Tube. Ph.D. Thesis, IIT, Bombay, India.
- Ponalagusamy R, J. Appl. Sci., 7, 1071 (2007)
- Ponalagusamy R, J. Frankl. Inst-Eng. Appl. Math., 349, 2861 (2012)
- Ponalagusamy R, 2013, Pulsatile flow of Herschel-Bulkley fluid in tapered blood vessels, Proc. of the 2013 International Conference on Scientific Computing (CSC 2013), WorldComp’13, Lasvegas, USA, 67-73.
- Ponalagusamy R, Selvi RT, J. Frankl. Inst-Eng. Appl. Math., 348, 2308 (2011)
- Ponalagusamy R, Selvi RT, Meccanica, 48, 2427 (2013)
- Ponalagusamy R, Selvi RT, Meccanica, 50, 927 (2015)
- Rao KS, Rao RK, Int. J. Math. Arch., 3, 4692 (2012)
- Santhosh N, Radhakrishnamacharya G, Int. J. Eng. Math., 2014, 713 (2014)
- Shukla JB, Parihar RS, Gupta SP, Biorheology, 17, 403 (1980)
- Shukla JB, Parihar RS, Gupta SP, Bull. Math. Biol., 42, 797 (1980)
- Skalak R, 1972, Mechanics of Microcirculation, In: Fung YC, ed., Biomechanics, Its Foundation and Objectives, Prentice Hall, Englewood Cliffs, New Jersey.
- Srivastava LM, Indian J. Pure Appl. Math., 33, 1353 (2002)
- Srivastava VP, Saxena M, J. Biomech. Eng. -Trans. ASME, 27, 921 (1994)
- Srivastava VP, Saxena M, Math. Biosci., 139, 79 (1997)
- Srivastava VP, Rastogi R, Comput. Math. Appl., 59, 1377 (2010)
- Srivastava VP, Rastogi R, Vishnoi R, Comput. Mater. Appl., 60, 432 (2010)
- Srivastava LM, Srivastava VP, Biorheology, 20, 761 (1983)
- Srivastava VP, Srivastava R, Comput. Math. Appl., 58, 227 (2009)
- Tam CKW, J. Fluid Mech., 38, 537 (1969)
- Vajravelu K, Sreenadh S, Lakshminarayana P, Commun. Nonlinear Sci. Numer. Simul., 16, 3107 (2011)
- Young DF, J. Eng. Ind. Trans. AMSE, 90, 248 (1968)
- Young DF, J. Biomech. Eng. -Trans. ASME, 101, 157 (1979)
- Young DF, Tsai FY, J. Biomech. Eng. -Trans. ASME, 6, 395 (1973)