Abstract
The present study investigates the combined effects of non-Newtonian rheology and unsteady nature of the fluid on dispersion of a soluble substance between two coaxial cylinders having wall permeability at the outer wall with the flowing fluid is modelled as Casson fluid. Generalized dispersion method in combination with a finite difference scheme is used to study the dispersion phenomenon. Using the generalized dispersion model, the entire process of dispersion is expressed in terms of three transport coefficients viz., absorption, convection, and dispersion (effective diffusion) coefficients. These transport coefficients are evaluated numerically using Crank-Nicolson finite difference method. The mean concentration is expressed in terms of these transport coefficients. Effects of annular gap, yield stress, Womersley frequency parameter, amplitude of the pressure pulsation, and the absorption parameter on the transport coefficients and mean concentration are studied. Flow unsteadiness is observed influencing the dispersion coefficient both quantitatively and qualitatively. It is observed that, as Womersley number increases the fluctuation of the dispersion coefficient increases and the magnitude of dispersion coefficient decreases for small values of time (< 0.5) and increases for later values of time.
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Ananthakrishnan V., W.N. Gill, and A.J. Barduhn, 1965, Laminar dispersion in capillaries: Part I. mathematical analysis, AICHE J. 11, 1063–1072.
Aris R., 1956, On dispersion of a solute in a fluid flowing through a tube, Proc. R. Soc. Lond. A 235, 67–77.
Aroesty J. and J.F. Gross, 1972, The mathematics of pulsatile flow in small vessels I. Casson theory, Microvasc. Res. 4,1–12.
Caro C.G., T.J. Pedley, R.C. Schroter, and W.A. Seed, 1978, The Mechanics of the Circulation, Oxford University Press, New York.
Dash R.K., G. Jayaraman, and K.N. Mehta, 1996, Estimation of increased flow resistance in a narrow catheterized artery–A theoretical model, J. Biomech. 29, 917–930.
Gill W.N., 1967, A note on the solution of transient dispersion problems, Proc. R. Soc. Lond. A 298, 335–339.
Gill W.N. and R. Sankarasubramanian, 1970, Exact analysis of unsteady convective diffusion, Proc. R. Soc. Lond. A 316, 341–350.
Kaye S.R., P. Kavafyan, and R.C. Schroter, 1993, Dispersion and uptake in a coiled tube, J. Biomech. Eng.–Trans. ASME 115, 125–126.
Mazumder B.S. and K.K. Mondal, 2005, On solute transport in oscillatory flow through an annular pipe with a reactive wall and its application to a catheterized artery, Q. J. Mech. Appl. Math. 58, 349–365.
McDonald D.A., 1974, Blood Flow in Arteries, Edward Arnold, London.
Nagarani, P. and B.T. Sebastian, 2017, Effect of flow unsteadiness on dispersion in non–Newtonian fluid in an annulus, J. Appl. Math. & Inform. 35, 241–260.
Nagarani P., G. Sarojamma, and G. Jayaraman, 2006, Exact analysis of unsteady convective diffusion in Casson fluid flow in an annulus–Application to catheterized artery, Acta Mech. 187, 189–202.
Nagarani P., G. Sarojamma, and G. Jayaraman, 2009, Effect of boundary absorption on dispersion in Casson fluid flow in an annulus: Application to catheterized artery, Acta Mech. 202, 47–63.
Palma M. and R. Giudici, 2003, Analysis of axial dispersion in an oscillatory–flow continuous reactor, Chem. Eng. J. 94,189–198.
Pedley T.J. and R.D. Kamm, 1988, The effect of secondary motion on axial transport in oscillatory tube flow, J. Fluid Mech. 193, 347–367.
Ramana B. and G. Sarojamma, 2012, Effect of wall absorption on dispersion of a solute in a Herschel–Bulkley fluid through an annulus, Adv. Appl. Sci. Res. 3, 3878–3889.
Rao A.R. and K.S. Deshikachar, 1987, An exact analysis of unsteady convective diffusion in an annular pipe, ZAMM–Z. Angew. Math. Mech. 67, 189–195.
Sankarasubramanian R. and W.N. Gill, 1973, Unsteady convective diffusion with interphase mass transfer, Proc. R. Soc. Lond. A 333, 115–132.
Sarkar A. and G. Jayaraman, 2002, The effect of wall absorption on dispersion in annular flows, Acta Mech. 158, 105–119.
Sarkar A. and G. Jayaraman, 2004, The effect of wall absorption on dispersion in oscillatory flow in an annulus: Application to a catheterized artery, Acta Mech. 172, 151–167.
Taylor G.I., 1953, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. Lond. A 219, 186–203.
Truskey G.A., F. Yuan, and D.F. Katz, 2009, Transport Phenomena in Biological Systems, Pearson Prentice Hall, New Jersey.
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Sebastian, B.T., Nagarani, P. Convection-diffusion in unsteady non-Newtonian fluid flow in an annulus with wall absorption. Korea-Aust. Rheol. J. 30, 261–271 (2018). https://doi.org/10.1007/s13367-018-0025-7
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DOI: https://doi.org/10.1007/s13367-018-0025-7