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Effects of couple-stresses on the dispersion of a soluble matter in a pipe flow of blood

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Summary

An analysis of the effects of couple-stresses on the effective Taylor diffusion coefficient has been carried out with the help of two non-dimensional parameters\(\bar \alpha \) based on the concentration of suspensions and\(\bar \eta \), a constant associated with the couple-stresses. It is observed that the concentration distribution increases with increasing\(\bar \alpha \) or\(\bar \eta \) The effective Taylor diffusion coefficient falls rapidly with increasing\(\bar \alpha \) when\(\bar \eta \) is negative.

Zusammenfassung

Der Einfluß der Momentenspannungen auf den effektiven Taylorschen Diffusionskoeffizienten wird untersucht. Dabei treten zwei dimensionslose Parameter\(\bar \alpha \) and\(\bar \eta \) auf: Der erste bezieht sich auf die Suspensionskonzentration, der zweite kennzeichnet die Momentenspannungen. Man findet, daß die Verteilungsgeschwindigkeit mit wachsendem\(\bar \alpha \) oder\(\bar \eta \) zunimmt. Dagegen fällt der Taylorsche Diffusionskoeffizient bei wachsendem\(\bar \alpha \) stark ab, wenn\(\bar \eta \) negativ ist.

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Abbreviations

a :

Tube radius

C :

Concentration

C i :

Body moment vector

C 0 :

Concentration at the axis of the tube

C m :

Mean concentration

D :

Molecular diffusion coefficient

d ij :

Symmetric part of velocity gradient

F :

Function of\(\bar \alpha \) and\(\bar \eta \) characterising effective Taylor diffusion coefficient

f i :

Body force vector

H :

A function of\(\bar \alpha \) and\(\bar \eta \)

K 2 :

Integration constant

K * :

Effective Taylor diffusion coefficient

k :

Radius of gyration of a unit cuboid with its sides normal to the spatial axes

I n :

Modified Bessel's function ofnth order

L :

Length of the tube over which the concentration is spread

M :

Function ofH and\(\bar \alpha \)

M ij :

Couple stress tensor

P :

Function of\(\bar \alpha \)

p :

Fluid pressure

Q :

Volume rate of the transport of the solute across a section of the tube

r :

Radial distance from the axis of the tube

T ij :

Stress tensor

t :

Time coordinate

T A ij :

Antisymmetric part of the stress tensor

u :

Relative fluid velocity

\(\bar v\) :

Average velocity

v i :

Velocity vector

\(\bar v\) :

Fluid velocity at any point of the tube

v n0 :

Velocity of Newtonian fluid at the axis of the tube

ω i :

Vorticity vector

x :

Axial coordinate

x 1 :

Relative axial coordinate

z :

Non-Dimensional radial coordinate

ρ :

Density

τ ij :

Symmetric part of the stress tensor

µ :

Viscosity of the fluid

µ ij :

Deviatoric part ofM ij

η′, η :

Constants associated with couple-stress

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, P.O. IIT Powai, 400076, Bombay, India

    V. M. Soundalgekar & P. Chaturani

Authors
  1. V. M. Soundalgekar
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  2. P. Chaturani
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Soundalgekar, V.M., Chaturani, P. Effects of couple-stresses on the dispersion of a soluble matter in a pipe flow of blood. Rheol Acta 19, 710–715 (1980). https://doi.org/10.1007/BF01521862

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  • DOI: https://doi.org/10.1007/BF01521862

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