Particulate suspension Jeffrey fluid flow in a stenosed artery with a particle-free plasma layer near the wall

다국어 초록 (Multilingual Abstract)

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.

참고문헌 (Reference)

1 Distenfass, L., "Viscosity factors in hypertensive and cardiovascular diseases" 2 : 337-349, 1971

2 Bugliarello, G., "Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes" 7 : 85-107, 1970

3 Drew, D.A., "Two-phase flow: Constitutive equations for lift and brownian motion and some basic flows" 62 : 149-158, 1976

4 Chaturani, P., "Two-layered poiseuille flow model for blood flow through arteries of small diameter and arterioles" 13 : 243-250, 1976

5 Srivastava, V.P., "Two-layered model of Casson fluid flow through stenotic blood vessels: Applications to cardiovascular system" 27 : 921-928, 1994

6 Vajravelu, K., "The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum" 16 : 3107-3125, 2011

7 Tam, C.K.W., "The drag on a cloud of spherical particles in low Reynolds number flows" 38 : 537-546, 1969

8 Cokelet, G.R., "The Rheology of Human Blood: In Biomechanies" Prentice-Hall 1972

9 Caro, C.G., "The Mechanics of the Circulation" Oxford Medical 1978

10 Boyd, W., "Text Book of Pathology: Structure and Functions in Diseases" Lea and Fibiger 1963

11 Srivastava, V.P., "Suspension model for blood flow through stenotic arteries with a cell-free plasma layer" 139 : 79-102, 1997

12 Mekheimer, Kh.S., "Suspension model for blood flow through arterial catheterization" 197 : 1195-1214, 2010

13 Uday Shankar Chakraborty, "Suspension model blood flow through an inclined tube withan axially non-symmetrical stenosis" 한국유변학회 23 (23): 25-32, 2011

14 Deshpande, M.D., "Steady laminar flow through modeled vascular stenosis" 9 : 65-174, 1979

15 Drew, D.A., "Stability of stokes layer of a dusty gas" 19 : 2081-2084, 1979

16 Akbar, N.S., "Simulation of variable viscosity and Jeffrey fluid model for blood flow through a tapered artery with a stenosis" 57 : 133-140, 2012

17 Jyothi, K.L., "Pulsatile flow of a Jeffrey fluid in a circular tube having internal porous lining" 4 : 75-82, 2013

18 Ponalagusamy, R., "Pulsatile flow of Herschel-Bulkley fluid in tapered blood vessels" 67-73, 2013

19 Chaturani, P., "Pulsatile flow of Casson’s fluid through stenosed arteries with applications to blood flow" 23 : 499-511, 1986

20 Haynes, R.H., "Physical basis on dependence of blood viscosity on tube radius" 198 : 1193-1205, 1960

21 Abd-Alla, A.M., "Peristaltic flow of a Jeffrey fluid under the effect of radially varying magnetic field in a tube with an endoscope" 384 : 79-86, 2015

22 Srivastava, L.M., "Particulate suspension blood flow through stenotic arteries: Effects of hematocrit and stenosis height" 33 : 1353-1360, 2002

23 Srivastava, V.P., "Particulate suspension blood flow through a narrow catheterized artery" 58 : 227-238, 2009

24 Srivastava, L.M., "On two-phase model of pulsatile blood flow with entrance effects" 20 : 761-777, 1983

25 Macdonald, D.A, "On steady flow through modeled vascular stenosis" 12 : 13-20, 1979

26 Ademiloye, A.S., "Numerical computation of the elastic and mechanical properties of red blood cell membrane using the higher-order Cauchy-Bornrule" 268 : 334-353, 2015

27 Ponalagusamy, R., "Mathematical analysis on effect of non-Newtonian behavior of blood on optimal geometry of microvascular bifurcation system" 349 : 2861-2874, 2012

28 Santhosh, N., "Jeffrey fluid flow through porous medium in the presence of magnetic field in narrow tubes" 2014 : 713-831, 2014

29 Ponalagusamy, "Influence of magnetic field and heat transfer on two-phase fluid model for oscillatory blood flow in an arterial stenosis" 50 : 927-943, 2015

30 Allan, F.M., "Fluid-particle model of flow through porous media: The case of uniform particle distribution and parallel velocity fields" 183 : 1208-1213, 2006

31 Young, D.F., "Fluid mechanics of arterial stenoses" 101 : 157-175, 1979

32 Forrester, J.H., "Flow through a converging-diverging tube and its implications in occlusive vascular diseases" 3 : 297-305, 1970

33 Young, D.F., "Flow characteristic in models of arterial stenosis-I, steady flow" 6 : 395-410, 1973

34 Shukla, J.B., "Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis" 42 : 797-805, 1980

35 Mann, F.G., "Effects of blood flow on decreasing the lumen of a blood vessel" 4 : 249-252, 1938

36 Young, D.F., "Effects of a time-dependent stenosis on flow through a tube" 90 : 248-254, 1968

37 Rao, K.S., "Effect of heat transfer on MHD oscillatory flow of Jeffrey fluid through a porous medium in a tube" 3 : 4692-4699, 2012

38 Gad, N.S., "Effect of Hall currents on interaction of pulsatile and peristaltic transport induced flows of a particle-fluid suspension" 217 : 4313-4320, 2011

39 Chaturani, P., "Dilatancy effects of blood on flow through arterial stenosis" 87-96, 1986

40 Bugliarello, G., "Detailed characteristics of the flow of blood in Vitro" 7 : 209-230, 1963

41 Akbar, N.S., "Characteristics of Jeffrey fluid model for peristaltic flow of chime" 3 : 152-160, 2013

42 Baskurt, O.K., "Blood rheology and hemodynamics" 29 : 435-450, 2003

43 Ponalagusamy, R., "Blood flow through an artery with mild stenosis: A two-layered model, different shapes of stenoses and slip velocity at the wall" 7 : 1071-1077, 2007

44 Srivastava, V.P., "Blood flow through a stenosed catheterized artery: Effects of hematocrit and stenosis shape" 59 : 1377-1385, 2010

45 Ponalagusamy, R., "Blood flow in stenosed arteries with radially variable viscosity, peripheral plasma layer thickness and magnetic field" 48 : 2427-2438, 2013

46 Charm, S.E., "Blood Flow and Microcirculation" John Wiley 1974

47 Ponalagusamy, R., "Blood Flow Through Stenosed Tube" IIT 1986

48 Shukla, J.B., "Biorhelogical aspects of blood flow through artery with mild stenosis: Effects of peripheral layer" 17 : 403-410, 1980

49 Skalak, R., "Biomechanics, Its Foundation and Objectives" Prentice Hall 1972

50 Caro, C.G., "Arterial fluid mechanics and atherogenesis" 2 : 6-11, 1981

51 Fry, D.L., "Acute vascular endothelial changes associated with increased blood velocity gradients" 22 : 165-197, 1968

52 Srivastava, V.P., "A two-layered suspension blood flow through an overlapping stenosis" 60 : 432-441, 2010

53 Chaturani, P., "A two-layered model for blood flow through stenosed arteries" B.H.E.L(R & D) 16-22, 1982

54 Ponalagusamy, R., "A study on two-fluid model (Casson-Newtonian) for blood flow through an arterial stenosis: Axially variable slip velocity at the wall" 348 : 2308-2321, 2011

55 Chaturani, P., "A Study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases" 22 : 521-531, 1985