# Mass Transfer in Time Dependent Blood Flow

## Abstract

The particulate nature of blood is usually ignored in the analysis of mass transfer in the cardiovascular system ; see for example, reviews by Middleman (1972), Lightfoot (1974) and Fletcher (1978). However, both the flow field and mass transfer rates may be modified significantly by micro-rotation of the red blood cells responsible for the facilitated oxygen transport to the tissue. The exact analysis of mass transfer in the cardiovascular system, taking into account the particulate nature of the blood, is obviously very difficult because of the complex geometry of the red blood cells and the complexity of flow conditions. One promising approach in describing the particulate nature of blood is the microcontinuum approach in which blood is treated as a suspension containing spherical non-deformable particles (red blood cells) whose rotational motion is described through a dynamic kinematical variable, called spin vector. The exact solution of the time dependent uniaxial laminar flows of micropolar fluids are given in a series of papers by Arlman and his colleagues, see for example, Arlman et al.(1974). However, in these studies, a spin boundary condition has to be assumed in order to be able to solve the necessary equations. The axial velocity profile is strongly dependent on this spin boundary condition, but the lack of any definite spin boundary condition, places limitations on the application of polar fluids as a model for the flow of suspensions.

## Keywords

Couple Stress Mass Transfer Rate Micropolar Fluid Particulate Nature Axial Velocity Profile## Preview

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## References

- Akay,G.,1977, Numerical solutions of some unsteady laminar flows of viscoelastic fluids in concentric annuli with axially moving bo-undaries, Rheol. Acta, 16: 589.CrossRefGoogle Scholar
- Akay,G.,1979, Non-steady two-phase stratified laminar flow of polymeric liquids in pipes, Rheol. Acta, 18: 256.MATHCrossRefGoogle Scholar
- Akay,G.,1980, Numerical solution of unsteady convective diffusionwith chemical reaction in time dependent flows, Chem. Eng. Comm. 4(1)CrossRefGoogle Scholar
- Akay,G.,1980-b, Mechanochemical degradation of macromolecules during laminar flow, presented in the VIII th Int. Congress on Rheology.Google Scholar
- Ariman,T., Turk,M.A., and Sylvester,N.D.,1974, On steady and pulsatile flow of blood, J. Appl. Mech., 41: 1.Google Scholar
- Chaturani,P., and Upadhya,V.S.,1979, A two-fluid model for blood flow through small diameter tubes, Biorheol., 16: 109.Google Scholar
- Ellison,B.T., and Cornet,I., 1971, Mass transfer to rotating disk, J. Electrochem. Soc., 118: 68.CrossRefGoogle Scholar
- Eringen,A.C., 1966, Theory of micropolar fluids, J.Math.Mech., 16:1.MathSciNetGoogle Scholar
- Fletcher,J.E.,1978, Mathematical modeling of the microcirculation, Math. Biosci., 38: 159.MathSciNetMATHCrossRefGoogle Scholar
- Lightfoot,E.N.,1974, “Transport Phenomena and Living Systems”,Wiley Interscience, New York.Google Scholar
- Middleman,S.,1972, “Transport Phenomena in the Cardiovascular System” Wiley Interscience, New York.Google Scholar
- Tirrell,M., and Malone,M.F.,1977, Stress-induced diffusion in macromolecules, J. Polym. Sci., Polymer Physics Edition, 15: 1569.ADSCrossRefGoogle Scholar
- Townsend,P.,1973, Numerical solutions of some unsteady flows of elastico-viscous liquids, Rheol. Acta, 12: 13.MATHCrossRefGoogle Scholar