Unsteady solute dispersion in blood rheology with reversible phase exchange at the artery wall

  • Authors

    • D S Sankar School of Applied Sciences and MathematicsUniversiti Teknologi Brunei
    • Nurul Aini Jaafar School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
    • Yazariah Yatim School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
    2018-05-17
    https://doi.org/10.14419/ijet.v7i2.11527
  • Blood Flow, Narrow Artery, Casson Fluid, Unsteady Solute Dispersion, Reversible Phase Exchange.

  • The effect of reversible phase exchange between the flowing fluid and wall tissues of arteries in the unsteady dispersion of solute in blood flow through a narrow artery is analysed mathematically, modelling the blood as Casson fluid. The resulting convective diffusion equation along with the initial and boundary conditions is solved analytically using the derivative series expansion method. The expressions for the negative asymptotic phase exchange, negative asymptotic convection, longitudinal diffusion coefficient and mean concentration are obtained. It is noted that when the solute disperses in blood flow through a narrow artery, the negative exchange coefficient, the negative convection coefficient increase and the longitudinal diffusion coefficient decreases with the increase of the Damköhler number and partition coefficient.

  • References

    1. [1] Taylor G. (1953). “Dispersion of soluble matter in solvent flowing slowly through a tubeâ€, Proc. R. Soc. A Math. Phys. Eng. Sci. 219 (1137): 186–203. https://doi.org/10.1098/rspa.1953.0139.

      [2] Aris R. (1956). “On the dispersion of a solute in a fluid flowing through a tubâ€, Proc. R. Soc. A Math. Phys. Eng. Sci. 235 (1200): 66–77. https://doi.org/10.1098/rspa.1956.0065.

      [3] Bailey H. R. and Gogarty W. B. (1962). “Numerical and experimental results on the dispersion of a solute in a fluid in laminar flow through a tubeâ€, Proc. R. Soc. A Math. Phys. Eng. Sci. 333 (1592): 99–114. https://doi.org/10.1098/rspa.1962.0182.

      [4] Ananthakrishnan V., Gill W. N. and Barduhn A. J. (1965). “Laminar dispersion in capillariesâ€, A.I.Ch. E. J. 11(6): 1063–1072. https://doi.org/10.1002/aic.690110620.

      [5] Sankarasubramanian R. and Gill W. N. (1973). “Unsteady convective diffusion with interphase mass transferâ€, Proc. R. Soc. A Math. Phys. Eng. Sci. 333(1592): 115–132. https://doi.org/10.1098/rspa.1973.0051.

      [6] Ng C. O. (2006). “Dispersion in open-channel flow subject to the processes of sorptive exchange on the bottom and air-water exchange on the free surfaceâ€. J. Hydrodyn. 18 (3): 57–64. https://doi.org/10.1016/S1001-6058(06)60031-0.

      [7] Zhang D., Lu Z., Liu Y. and Ng C. (2009). “Numerical simulation of the dispersion in oscillating flows with reversible and irreversible wall reactionsâ€, J. Hydrodyn. 21(4): 482–490. https://doi.org/10.1016/S1001-6058(08)60174-2.

      [8] Chiu N. G. and YIP T. L. (2001). “Effects of kinetic absorptive exchange on solute transport in open channel flowâ€, J. Fluid Mech. 446: 321-345.

      [9] Scott Blair G. W. (1966). “The success of Casson’s equationâ€, Rheol. Acta 5(3): 184–187. https://doi.org/10.1007/BF01982424.

      [10] Gill W. N. and Sankarasubramanian R. (1971). “Dispersion of a non-uniform slug in time-dependent flowâ€, Proc. R. Soc. London A, 322: 101–117. https://doi.org/10.1098/rspa.1971.0057.

  • Downloads

  • How to Cite

    Sankar, D. S., Jaafar, N. A., & Yatim, Y. (2018). Unsteady solute dispersion in blood rheology with reversible phase exchange at the artery wall. International Journal of Engineering & Technology, 7(2), 750-754. https://doi.org/10.14419/ijet.v7i2.11527