Dispersion of a solute in pulsatile nonNewtonian fluid flow through a tube
 P. Nagarani,
 B. T. Sebastian
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Abstract
The unsteady dispersion of a solute by an imposed pulsatile pressure gradient in a tube is studied by modeling the flowing fluid as a Casson fluid. The generalized dispersion model is applied to study the dispersion process, and according to this process, the entire dispersion process is expressed in terms of two coefficients, the convection and the dispersion coefficients. This model mainly brings out the effects of yield stress and flow pulsatility on the dispersion process. It is observed that the dispersion phenomenon in the pulsatile flow inherently differs from the steady flow, which is due to a change in the plug flow radius during a cycle of oscillation. Also, it was found that the dispersion coefficient fluctuates due to the oscillatory nature of the velocity. It is seen that the dispersion coefficient changes cyclically, and the amplitude and magnitude of the dispersion coefficient increases initially with time and reaches a nontransient state after a certain critical time. It is also seen that this critical time varies with Womersley frequency parameter and Schmidt number and is independent of yield stress and fluctuating pressure component. It is observed that the yield stress and Womersley frequency parameter inhibit the dispersion of a solute. It is also observed that the dispersion coefficient decreased approximately 4 times as the Womersley frequency parameter increases from 0.5 to 1. The study can be used in the understanding of the dispersion process in the cardiovascular system and blood oxygenators.
 Taylor G.I.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. A 219, 186–203 (1953) CrossRef
 Aris R.: On dispersion of solute in a fluid flowing through a tube. Proc. R. Soc. Lond. Ser. A 235, 67–77 (1956) CrossRef
 Gill W.N., Sankarasubramanian R.: Exact analysis of unsteady convective diffusion. Proc. Roy. Soc. Lond. A 316, 341–350 (1970) CrossRef
 Aris R.: On dispersion of solute in a pulsating flow through a tube. Proc. R. Soc. Lond. A 259, 370–376 (1960) CrossRef
 Chatwin P.C.: On the longitudinal dispersion of passive contaminant in oscillatory flow in tube. J. Fluid Mech. 7, 513–527 (1975) CrossRef
 Purtel L.P.: Molecular diffusion in oscillating laminar flow in a pipe. Phys. Fluids 24, 789–793 (1981) CrossRef
 Smith R.: Contaminant dispersion in oscillating flows. J. Fluid Mech. 114, 379–398 (1982) CrossRef
 Bandyopadhyay S., Mazumder B.S.: Unsteady convective diffusion in a pulsatile flow through a channel. Acta Mech. 134, 1–16 (1999) CrossRef
 Mazumder B.S, Mandal K.K.: On the solute transport in oscillatory flow through an annular pipe with a reactive wall and its application to a catheterized artery. Q. J. Mech. Appl. Math. 58, 349–365 (2005) CrossRef
 Sarkar A., Jayaraman G.: The effect of wall absorption on dispersion in oscillatory flow in an annulus. Acta Mech. 172, 151–167 (2004) CrossRef
 Ng C.O.: Dispersion in steady and oscillatory flows through a tube with reversible and irreversible wall reactions. Proc. R. Soc. A 462, 481–515 (2006) CrossRef
 Kumar S., Jayaraman G.: Method of moments for laminar dispersion in an oscillatory flow through curved channels with absorbing walls. Heat Mass Transf. 44, 1323–1336 (2008) CrossRef
 Paul S.: Axial dispersion in pressure perturbed flow through an annular pipe oscillating around its axis. ZAMP 60, 899–920 (2009) CrossRef
 Paul S.: Effect of wall oscillation on dispersion in axissymmetric flows between two coaxial cylinders. ZAMM 91, 23–37 (2011) CrossRef
 Agarwal S., Jayaraman G.: Numerical simulation of dispersion in the flow of powerlaw fluids in curved tubes. Appl. Math. Model. 18, 504–512 (1994) CrossRef
 Lighthill M.J.: Initial development of diffusion in Poiseuille flow. J. Inst. Math. Appl. 51, 97–108 (1966) CrossRef
 Hazra S.B., Gupta A.S., Niyogi P.: On the dispersion of solute in oscillatory flow of a nonNewtonian fluid in a channel. Heat Mass Transf. 32, 481–487 (1997) CrossRef
 Sharp M.K.: Shear augmented dispersion in nonNewtonian fluids. Ann. Biomed. Eng. 21, 407–415 (1993) CrossRef
 Dash R.K., Jayaraman G., Mehta K.N.: Shear augmented dispersion of a solute in a Casson fluid flowing in a conduit. Ann. Biomed. Eng. 28, 373–385 (2000) CrossRef
 Nagarani P., Sarojamma G., Jayaraman G.: Effect of boundary absorption in dispersion in Casson fluid flow in a tube. Ann. Biomed. Eng. 32, 706–719 (2004) CrossRef
 Aroesty J., Gross J.F.: The mathematics of pulsatile flow in small vessels I. Casson theory. Microvasc. Res. 4, 1–12 (1972) CrossRef
 Aroesty J., Gross J.F.: Pulsatile flow in small blood vessels, I. Casson theory. Biorheology 9, 33–42 (1972)
 Fung Y.C.: Biomechanics: Mechanical Properties of Living Tissues. Springer, New York (1981)
 Cokelet G.R., Merrill E.W., Gilliand E.R., Shin H., Britten A., Wells R.E.: The rheology of human blood measurement near and at zero shear rate. Trans. Soc. Rheol. 7, 303–317 (1963) CrossRef
 Merrill E.W., Benis A.M., Gilland E.R., Shearwood T.K., Salzman E.W.: Pressure flow relations of human blood in hollow fiber at low shear rates. J. Appl. Physiol. 20, 954–967 (1965)
 Dash R.K., Jayaraman G., Mehta K.N.: Estimation of increased flow resistance in a narrow catheterized arterya theoretical model. J. Biomech. 29, 917–930 (1996) CrossRef
 Nagarani P., Sarojamma G.: Effect of body acceleration on pulsatile flow of Casson fluid through a mild stenosed artery. Korea Aust. Rheol. J. 20, 189–196 (2008)
 Boyce W.E., DiPrima R.C.: Elementary Differential Equations and Boundary Value Problems. Wiley, USA (2004)
 Turskey G.A., Yuan F., Katz D.F.: Transport Phenomena in Biological Systems. Pearson Prentice Hall, New Jersey (2004)
 Ananthkrishnan V., Gill W.N., Barduhan A.J.: Laminar dispersion in capillaries: part I. Math. Anal. AICHE J. 11, 1063–1072 (1965) CrossRef
 Reejhsinghani N.S., Gill W.N., Barduhan A.J.: Laminar dispersion in capillaries: part III. Experiments in horizontal tubes including observations on natural convection effects. AICHE J. 12, 916–923 (1966) CrossRef
 Lighthill M.J.: Physiological fluid dynamics: a survey. J. fluid. Mech. 52, 475–497 (1972) CrossRef
 Caro C.G., Pedley T.J., Schroter R.C., Seed W.A.: The Mechanics of Circulation. Oxford University Press, New York (1978)
 Title
 Dispersion of a solute in pulsatile nonNewtonian fluid flow through a tube
 Journal

Acta Mechanica
Volume 224, Issue 3 , pp 571585
 Cover Date
 20130301
 DOI
 10.1007/s0070701207536
 Print ISSN
 00015970
 Online ISSN
 16196937
 Publisher
 Springer Vienna
 Additional Links
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 Industry Sectors
 Authors

 P. Nagarani ^{(1)}
 B. T. Sebastian ^{(1)}
 Author Affiliations

 1. Department of Mathematics, The University of the West Indies, Mona Campus, Kingston 7, Jamaica, West Indies