Study of Transport of Nanoparticles with Power Law fluid Model for Blood Rheology in Capillaries

Rekha Bali; Nivedita Gupta; Swati Mishra

Rekha Bali Department of Mathematics, HBTI, Kanpur, India
Nivedita Gupta Department of Mathematics, HBTI, Kanpur, India
Swati Mishra Department of Mathematics, HBTI, Kanpur, India

Keywords: Nanoparticles, power law fluid, erythrocytes, concentration, longitudinal transport, peripheral layer, slip velocity.

Abstract

The present paper deals with a mathematical model for blood flow through an axially symmetric blood capillary with peripheral layer and slip at the wall. The longitudinal transport of nanoparticles in blood vessels has been analyzed with blood as a power law fluid in a central core region of suspension of all the erythrocytes and a Newtonian fluid in a peripheral layer of plasma. In present analysis, the capillary walls are impermeable and not absorbent for the nanoparticles. The expressions for velocity profile, flow rate, mean velocity and concentration of the solute have been obtained and results have been discussed through graphs.

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References

Basu Mallik et al., A non-Newtonian fluid model for blood flow using power-law through an atherosclerotic arterial segment having slip velocity. Int. Jour. of Pharm. Chem. and Bio. Scien., 3(3), 752-760, 2013.

Caro, C.G., Fitz-Gerald J.M., and Schroter R.C., Atheroma and arterial wall shear observation, Correlation and Proposal of a shear dependent mass transfer mechanism for Atherogenesis. Proc. R. Soc. 177: 109-159, 1971.

Charm S. and Kurland G., Viscometry of human blood for shear rates of 0-100,000 sec-1,” Nature. 206: 4984, 617-618, 1965.

Ellahi, R., Rahman S.U., Nadeem, S., Akbar, N.S., Blood flow of nanofluid through an artery with composite stenosis and permeable walls. Appl. Nanosci. 4: 919-926, 2014.

Gentile F., Ferrari M., Decuzzi P. The transport of nanoparticles in blood vessels: the effect of vessel permeability and blood rheology. Ann Boimed. Eng. 36 (2), 254-261, 2008.

Gentile, F., Decuzzi P., Time dependent dispersion of nanoparticles in blood vessels. J. Biomed. Sci. and Eng. 3, 517-524, 2010.

Hershey, D., Byrnes, R.E., Deddens R.L. and Rao, A.M., Blood rheology: Temperature dependence of the power law model. Paper presented at A.I.Ch.E., Bostan, 1964.

Lee, L.S., On the coupling and detection of motion between an artery with a localized lesion and its surrounding tissue. Biomech. 7: 403, 1974.

May, A.G., Deweese, J.A. and Rob, C.B., Hemodynamic effects of arterial stenosis. 53: 513-524, 1963.

Mekheimer Kh. S., and El kot M.A., Mathematical modeling of unsteady flow of a Sisko fluid through an isotropically tapered elastic arteries with time-variant overlapping stenosis, App. Math. Model. 36, 5393, 2012.

Misra, J.C. and Shit, G.C., Role of slip velocity in blood flow through stenosed arteries: A Non- Newtonian model. Jour. of mech. in medic. and biology,7: 337-353, 2007.

Mostafa A.A. Mahmoud, Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Math. and Compu. Modell., 54, 1228-1237, 2011.

Richard, L.K., Young, D.F. and Chalvi, N.R., Wall vibrations induced by flow through simulated stenosed arteries. Biomech. 10: 431, 1977.

Shukla, J.B., Parihar, R.S., Gupta, S.P., Biorheological aspects of blood flow through artery with mild stenosis: Effects of peripheral layer. Biorhe. 17: 403-410, 1990.

Srivastava V.P., A theoretical model for blood flow in small vessels. Appl. and Appl. Math., 2(1), 51-65, 2007.

Texon, M., A homodynamic concept of atherosclerosis with particular reference to coronary occlusion. 99.418, 1957.

Verma, N., Parihar, R.S., Mathematical model of blood flow through a tapered artery with mild stenosis and hematocrit. Jour. of modern Math. and Stati. 4(1): 38-43, 2011.

Verma S.R. and Srivastava A., Analytical study of a two-phase model for steady flow of blood in a circular tube. Int. Jour. of Engg. Res. and Appli., 4(12), 01-10, 2014.