A couple stress model of blood flow in the microcirculation
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.
- Bugliarello, G., C. Kapur and G. Hsiao. 1965. “The Profile Viscosity and other Characteristics of Blood Flow in a Non-uniform Shear Field”. Symposium on Biorheology, Proc. 4th Int. Cong. Rheology, New York: Interscience.
- — and J. Sevilla. 1970. “Velocity Distribution and other Characteristics of Steady and Pulsatile Blood Flow in Fine Glass Tubes”.Biorheology 7, 85–107.
- Cokelet, G. R. 1972.Biomechanics: Its Foundations and Objectives, Y. G. Fung (Ed.), p. 63. Englewood Cliffs: Prentice Hall.
- Goldsmith, H. L. and R. Skalak. 1975.Annual Review of Fluid Dynamics, p. 231. California: Annual Review Inc. Palo Alto.
- Lighthill, M. J. 1969. “Motion in Narrow Capillaries from the Stand Point of Lubrication Theory”. InCirculatory and Respiratory Mass Transport, G. E. N. Wolstenholme and J. Knight (Eds.), pp. 85–96. London: Churchill.
- Oka, S. and T. Murata. 1970. “A Theoretical Study of the Flow of Blood in a Capillary with Permeable Wall”.Jap. J. Appl. Phys. 9, 345–352. CrossRef
- — 1981.Cardiovascular Hemotheology, p. 90. Cambridge: Cambridge University Press.
- Popel, A. S., S. A. Regirer and P. I. Usick. 1974. “A Continuum Model of Blood Flow”.Biorheology 11, 427–437.
- Skalak, R. 1972.Biomechanics: Its Foundations and Objectives, Y. C. Fung (Ed.), p. 457. Englewood Cliffs: Prentice-Hall.
- Stokes, V. K. 1966. “Couple Stress in Fluids”.Phys. Fluids 9, 1709–1715. CrossRef
- Valanis, K. C. and C. T. Sun. 1969. “Poiseuille Flow of Fluid with Couple Stress with Applications to Blood Flow”.Biorheology 6, 85–97.
- A couple stress model of blood flow in the microcirculation
Bulletin of Mathematical Biology
Volume 50, Issue 4 , pp 329-344
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links