Influence of Plasma layer on Steady Blood flow in micro-vessels

Noriko Iida (1977)

Introduction

• Arterioles are blood vessels with diameter < 200 $\mu m$
• Non-Newtonian behaviour of blood is because of rouleaux formation, aggregation and flexibility of blood cells.
• Volume flow rate in of a non-Newtonian fluid in a pipe is given by

$$Q=\frac{\pi R^4}{8{\eta }_a}\frac{\Delta P}{L}$$

${\eta }_a\to$ apparent viscosity, $R\to$ inner radius, $L\to$ length of pipe, $P\to$ pressure difference across tube

• 80% of the pressure gradient in the circulation systems is caused by arterioles. ¹²
• Mathematical models that give a two fluid description of blood. ³⁴⁵
• This paper describes proposes the Modified Herschel-Bulkley model mathematical model that is a modification of the existing H.B model, which considers blood to have a non-Newtonian core made of RBC’s and a peripheral region of Plasma that behaves as a Newtonian fluid.

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References

Footnotes

1. Burton, A. C. (1972). Physiology and biophysics of the circulation: An introductory text. Chicago: Year Book Medical Publishers. ↩

2. E. U. Renkin and S. Rosell: Acta Physiol. Scandinavica 54 (1962) 381. ↩

3. S. Oka: Advances in Biophysics, ed. M. Kotani (University Park Press, Baltimore, London and Tokyo, 1972) Vol. 3, p. 97. ↩

4. P. Chaturani and P. N. Kaloni: Biorheology 13 (1976) 243. ↩

5. R. N. Das and V. Seshadri: Bull. Math. Biology 37 (1975) 459. ↩