The process of dispersion of soluble matter in blood flow has been investigated in the present study. The constitutive equation of blood obeys the law of K-L fluid model. The first order homogeneous chemical reaction is taken in the analysis which has been studied by Taylor’s dispersion method in a circular tube. The influences of the reaction rate constant, the yield stress and K-L parameters on the equivalent dispersion coefficient are discussed. A decrease in the value of dispersion coefficient has been observed in Newtonian as well as non-Newtonian fluids with increase in the rate of chemical reaction. The dispersion coefficient is further decreased with the enhancement of yield stress. It is pertinent to point out that one of K-L parameters tends to decrease the equivalent dispersion coefficient while another K-L parameter enhances the equivalent dispersion coefficient. From the present investigation, many rheological models for blood such as Newtonian, Bingham plastic and Casson can be obtained by giving appropriate values to yield stress and parameters of K-L fluid. The present analytical study provides useful information to the bio-chemical processing and physiological process in the cardiovascular system.
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Griffth, A.: On the movement of a coloured index along a capillary tube, and its application to the measurement of the circulation of water in a closed circuit. Proc. Phys. Soc. Lond. 23, 190 (1911)
Taylor, G.I.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 219, 186–203 (1953)
Taylor, G.I.: The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 223(1155), 446–468 (1954). https://doi.org/10.1098/rspa.1954.013
Aris, R.: On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 235, 67–77 (1956)
Welstenholme, G.E.W., Knight, J.W.: Circulatory and Respiratory Mass Transfer. Churchill London (1969)
Fan, L.T., Hwang, W.S.: Dispersion of Ostwald-de Waele fluid in laminar flow through a cylindrical tube. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 283, 576–582 (1965). https://doi.org/10.1098/rspa.1965.0046
Fan, L.T., Wang, C.B.: Dispersion of matter in non-Newtonian laminar flow through a circular tube. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 292, 203–208 (1966). https://doi.org/10.1098/rspa.1966.0129
Ghoshal, S.: Dispersion of solutes in non-Newtonian flows through a circular tube. Chem. Eng. Sci. 26, 185–188 (1971). https://doi.org/10.1016/0009-2509(71)80002-7
Shah, S.H., Cox, K.E.: Dispersion of solutes in non-Newtonian laminar flow through a circular tube-Eyring model fluid. Chem. Eng. Sci. 29, 1282–1286 (1974). https://doi.org/10.1016/0009-2509(74)80129-6
Prenosil, J.E., Jarvis, P.E.: Note on Taylor diffusion for a power Law fluid. Chem. Eng. Sci. 29, 1290 (1974)
Sharp, M.K.: Shear-augmented dispersion in non-Newtonian fluids. Ann. Biomed. Eng. 21(4), 407–415 (1993). https://doi.org/10.1007/BF02368633
Sankar, D.S., Jaafar, N.A.B., Yatim, Y.M.: Nonlinear analysis for shear augmented dispersion of solutes in blood flow through narrow arteries. J. Appl. Math. (2012). https://doi.org/10.1155/2012/812535
Katz, S.: Chemical reactions catalysed on a tube wall. Chem. Eng. Sci. 10, 202–211 (1959). https://doi.org/10.1016/0009-2509(59)80054-3
Walker, R.E.: Chemical reaction and diffusion in a catalytic tubular reactor. Phys. Fluids 4, 1211–1216 (1961). https://doi.org/10.1063/1.1706198
Soloman, R.L., Hudson, J.L.: Homogeneous and heterogeneous reactions in a tubular reactor. Am. Inst. Chem. Eng. J. 13, 545–550 (1967). https://doi.org/10.1002/aic.690130326
Gill, W.N., Shankarasubramaniam, R.: Exact analysis of unsteady convective diffusion. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 316, 341–350 (1970). https://doi.org/10.1098/rspa.1970.0083
Gill, W.N., Shankarasubramaniam, R.: Dispersion of a non-uniform slug in time-dependent flow. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 322, 101–117 (1971). https://doi.org/10.1098/rspa.1971.0057
Gupta, P.S., Gupta, A.S.: Effect of homogeneous and heterogeneous reactions on the dispersion of a solute in the laminar flow between two plates. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 330, 59–63 (1972). https://doi.org/10.1098/rspa.1972.0130
Scherer, P.W., Shendalman, L.H., Greene, N.M.: Simultaneous diffusion and convection in single breath lung washout. Bull. Math. 34, 393–412 (1972). https://doi.org/10.1007/BF02476450
Shukla, J.B., Parihar, R.S., Rao, B.R.P.: Dispersion in non-Newtonian fluids: effects of chemical reaction. Rheol. Acta 18, 740–748 (1979). https://doi.org/10.1007/BF01533349
Singh, S.P., Chadda, G.C., Sinha, A.K.: A study of sectionally related dispersion and chemical reaction effects. Defence Sci. J. 39(3), 305–318 (1989)
Jaafar, N.A.B., Yatim, Y.M., Sankar, D.S.: Effect of chemical reaction in solute dispersion in Herschel–Bulkley fluid flow with applications to blood flow. Adv. Appl. Fluid Mech. 20(2), 279–310 (2017). https://doi.org/10.17654/FM020020279
Chein, S.: Hemorheology in clinical medicine. Recent Adv. Cardiovasc. Dis. 2, 21–26 (1981)
Luo, X.Y., Kuang, Z.B.: A study on the constitutive equation of blood. J. Biomech. 25(8), 929–934 (1992). https://doi.org/10.1016/0021-9290(92)90233-Q
Cokelet, G.R., Merrill, E.W., Gilliland, E.R., Shin, H., Britten, A., Wells, R.E.: Rheology of human blood: measurement near and at zero shear rate. Trans. Sot. Rheol. 7, 303–317 (1963)
Cokelet, G.R.: In: Fung, Y.C., Perrone, N., Anliker, M. (eds.) Bildmeckmics: Its Foundation and Objectives, pp. 63–103. Prentice Hall, Englewood Cliffs (1972)
Bate, H.: Blood viscosity at different shear rates in canillarv tubes. Biorheoloav 14, 267–275 (1977)
Easthope, P.L., Brooks, D.E.: A comparison of rheological constitutive functions for whole human blood. Biorheology 17(3), 235–247 (1980)
Nagarani, P., Sebastian, B.T.: Dispersion of a solute in pulsatile non-Newtonian fluid flow through a tube. Acta Mech. 224, 571–585 (2013). https://doi.org/10.1007/s00707-012-0753-6
Rana, J., Murthy, P.V.S.N.: Unsteady solute dispersion in Herschel–Bulkley fluid in a tube with wall absorption. Phys. Fluids 28(11), 111903 (2016). https://doi.org/10.1063/1.4967210
Bugliarello, G., Sevilla, J.: Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes. Biorheology 7(2), 85–107 (1970). https://doi.org/10.3233/bir-1970-7202
Zhang, J.B., Kuang, Z.B.: Study on blood constitutive parameters in different blood constitutive equations. J. Biomech. 33(3), 355–360 (2000)
Ashrafizaadeh, M., Bakhshaei, H.: A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations. Comput. Math. Appl. 58(5), 1045–1054 (2009)
Sriyab, S.: Mathematical analysis of Non-Newtonian Blood flow in stenosis narrow arteries. Comput. Math. Methods Med. (2014). https://doi.org/10.1155/2014/479152
Bali, Rekha, Gupta, Nivedita: Study of transport of nanoparticles with K-L model through a stenosed microvessels. Appl. Appl. Math. Int. J. (AAM) 13(2), 1157–1170 (2018)
Ponalagusamy, R., Manchi, R.: Mathematical study on two fluid model for flow of K-L fluid in a stenosed artery with porous wall. SN Appl. Sci. 3, 1–21 (2021)
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Ponalagusamy, R., Murugan, D. & Priyadharshini, S. Effects of Rheology of Non-Newtonian Fluid and Chemical Reaction on a Dispersion of a Solute and Implications to Blood Flow. Int. J. Appl. Comput. Math 8, 109 (2022). https://doi.org/10.1007/s40819-022-01312-6
- K-L fluid
- Molecular diffusion
- Non-Newtonian fluid
- Chemical reaction
Mathematics Subject Classification