Effect of couple stresses on the pulsatile flow through a constricted annulus

D. Srinivasacharya; D. Srikanth

doi:10.1016/j.crme.2008.09.008

Effect of couple stresses on the pulsatile flow through a constricted annulus

Presented by: Évariste Sanchez-Palencia

D. Srinivasacharya ¹ ; D. Srikanth ²

¹ Department of Mathematics, National Institute of Technology, Warangal-506 004, India
² Department of Mathematics, Gokaraju Rangaraju Institute of Engineering & Technology, Hyderabad-500 050, India

Comptes Rendus. Mécanique, Volume 336 (2008) no. 11-12, pp. 820-827.

Abstract (Original language)
Résumé

In this Note, the pulsatile flow of an incompressible couple stress fluid through an annulus with mild constriction at the outer wall is considered. This configuration is intended as a simple model for studying blood flow in a stenosed artery when a catheter is inserted into it. An analytical expression in terms of Bessel functions of the first and second kind is obtained for the velocity component. The impedance (resistance to the flow) and wall shear stress are calculated and their variation with respect to the couple stress fluid parameter, height of the constriction and size of the catheter on the impedance and wall shear stress is studied graphically. It is observed that increase in the catheter size increases the resistance to the flow as well as the wall shear stress while the trend is reversed in case of couple stress fluid parameter.

Dans cette Note on considère le flux pulsatoire d'un fluide incompressible à couple de contrainte à travers d'un tube annulaire dont la paroi externe est légèrement étranglée. Cette configuration sert de modèle simplifié du flux sanguin dans une artère sténosée pendant l'insertion d'un catétère. La composante de vitesse a été obtenue sous la forme d'une expression analytique en termes des fonctions de Bessel de première et seconde espèce. L'impédance de résistance et la tension de cisaillement de la paroi est également évaluée, ainsi que la variation de ces paramètres en fonction du couple de contrainte relatif au fluide. On étudie graphiquement l'influence de la hauteur de la constriction et de la dimension du catétère sur l'impédance et le couple de cisaillement agissant sur la paroi. On observe que l'augmentation des dimensions du catétère fait augmenter la résistance au flux ainsi que la tension de la paroi ; cependant, la tendance est inverse dans le cas du paramètre du couple de cisaillement du fluide.

Received: 2007-04-19
Accepted: 2008-09-08
Published online: 2008-10-14

DOI: 10.1016/j.crme.2008.09.008

Keywords: Fluid mechanics, Pulsatile blood flow, Catheterized artery, Constriction, Annulus, Couple stress fluid
Mots-clés : Mécanique des fluides, Flux sanguin pulsatoire, Artère catérisée, Constriction, Tube annulaire, Fluide à couple de contrainte

Author's affiliations:

D. Srinivasacharya ¹; D. Srikanth ²

¹ Department of Mathematics, National Institute of Technology, Warangal-506 004, India
² Department of Mathematics, Gokaraju Rangaraju Institute of Engineering & Technology, Hyderabad-500 050, India

@article{CRMECA_2008__336_11-12_820_0,
     author = {D. Srinivasacharya and D. Srikanth},
     title = {Effect of couple stresses on the pulsatile flow through a constricted annulus},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {820--827},
     publisher = {Elsevier},
     volume = {336},
     number = {11-12},
     year = {2008},
     doi = {10.1016/j.crme.2008.09.008},
     language = {en},
}

TY  - JOUR
AU  - D. Srinivasacharya
AU  - D. Srikanth
TI  - Effect of couple stresses on the pulsatile flow through a constricted annulus
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 820
EP  - 827
VL  - 336
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crme.2008.09.008
LA  - en
ID  - CRMECA_2008__336_11-12_820_0
ER  -

%0 Journal Article
%A D. Srinivasacharya
%A D. Srikanth
%T Effect of couple stresses on the pulsatile flow through a constricted annulus
%J Comptes Rendus. Mécanique
%D 2008
%P 820-827
%V 336
%N 11-12
%I Elsevier
%R 10.1016/j.crme.2008.09.008
%G en
%F CRMECA_2008__336_11-12_820_0

D. Srinivasacharya; D. Srikanth. Effect of couple stresses on the pulsatile flow through a constricted annulus. Comptes Rendus. Mécanique, Volume 336 (2008) no. 11-12, pp. 820-827. doi : 10.1016/j.crme.2008.09.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.09.008/

References
Cited by

[1] D.F. Young Effect of time dependent stenosis on flow through a tube, J. Engrg. Ind., Trans. ASME, Volume 90 (1968), p. 248

[2] J.S. Lee; Y.C. Fung Flow in locally constricted tubes at low Reynolds numbers, J. Appl. Mech., Trans. ASME, Volume 37 (1970), p. 9

[3] N. Padmanabhan Mathematical model of arterial stenosis, Med. & Biol. Eng. & Comput., Volume 18 (1980), p. 281

[4] V.K. Stokes Couple stresses in fluids, Phys. Fluids, Volume 9 (1966), p. 1710

[5] P. Chaturani; Upadhya Pulsatile flow of a couple stress fluid through circular tubes with applications to blood flow, Biorheology, Volume 15 (1978) no. 3–4, p. 193

[6] P. Sinha; C. Singh Effects of couple stresses on the blood flow through an artery with mild stenosis, Biorheology, Volume 21 (1984) no. 3, p. 303

[7] L.M. Srivastava Flow of couple stress fluid through stenotic blood vessels, J. Biomech., Volume 18 (1985) no. 7, p. 479

[8] D.A. MacDonald Pulsatile flow in a catheterized artery, J. Biomech., Volume 19 (1986), p. 239

[9] G.T. Karahalios Some possible effects of a catheter on the arterial wall, Med. Phys., Volume 17 (1990), p. 922

[10] P. Daripa; R.K. Dash A numerical study of pulsatile blood flow in an eccentric artery using a fast algorithm, J. Engrg. Math., Volume 42 (2002), p. 1

Cited by Sources:

Comments - Policy