Abstract
The basic motive of this model is to understand the dispersion process of a solute in non-Newtonian fluid flow subjected to external body acceleration when taking into account the solute absorption at the tube wall. Generalized dispersion method approach is used and hence the local concentration is assumed as a series in terms of the mean concentration and its derivatives, with coefficients being functions of time. With this approach, the mean concentration is expressed in terms of three transport coefficients, namely the absorption, convection, and dispersion coefficients for the case of solute transfer at the wall. A finite-difference scheme is used to solve the intermediate equations in order to evaluate these transport coefficients. The effects of non-Newtonian rheology, pulsatile pressure gradient, external body acceleration, and the wall absorption on the dispersion coefficient and mean concentration are analysed. It is seen that the dispersion coefficient is affected by the presence of body acceleration as is evidenced by dramatic fluctuations in its magnitude during the course of the flow. We confirm that the peak of the mean concentration is dramatically reduced as the wall absorption coefficient increases, even in the presence of body acceleration. Based on the values of different parameters considered in the problem, the study can be applied to understand the dispersion phenomenon in narrow arteries.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig12_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig13_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig14_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig15_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig16_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig17_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig18_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig19_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig20_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjs%2Fs11734-021-00051-x/MediaObjects/11734_2021_51_Fig21_HTML.png)
Similar content being viewed by others
References
R. Aris, On dispersion of a solute in a pulsating flow through a tube. Proc. R. Soc. Lond. Ser A 259, 370–376 (1960)
J. Aroesty, J.F. Gross, The mathematics of pulsatile flow in small blood vessels, I. Casson theory. Micro Vasc. Res. 4, 1–12 (1972a)
O.A. Bég, O.D. Makinde, Viscoelastic flow and species transfer in a Dacian high-permeable channel. J. Petrol. Sci. Eng. 76, 93–99 (2011)
P. Chaturani, P. Palanisamy, Casson fluid model for pulsatile flow of blood under periodic body acceleration. Biorheology 27, 619–630 (1990)
P. Chaturani, I.A.S.A. Wassf, Blood flow with body acceleration forces. Int. J. Eng. Sci. 33, 1807–1820 (1995)
P.C. Chatwin, On the longitudinal dispersion of passive contaminant in oscillatory flow in tube. J. Fluid Mech. 7, 513–527 (1975)
T. Chinyoka, O.D. Makinde, Analysis of nonlinear dispersion of a pollutant ejected by an external source into a channel flow. Math. Probl. Eng. 827363, 1–17 (2010)
R.K. Dash, G. Jayaraman, K.N. Mehta, Shear augmented dispersion of a solute in a Casson fluid flowing in a conduit. Ann. Biomed. Eng. 28(4), 373–385 (2000)
Y.C. Fung, Biomechanics: Circulation (Springer, New York, 1984).
F. Gentile, P. Decuzzi, Time dependent dispersion of nanoparticles in blood vessels. J. Biomed. Sci. Eng. 3, 517–524 (2010)
W.N. Gill, R. Sankarasubramanian, Exact analysis of unsteady convective diffusion. Proc. R. Soc. Lond. Ser A 316, 341–350 (1970)
H.G. Harris, S.L. Gorren, Axial diffusion in a cylinder with pulsed flow. J. Fluid Mech. 249, 535–555 (1993)
P.E. Hydon, T.J. Pedley, Axial dispersion in a channel with oscillating walls. J. Fluid Mech. 249, 535–555 (1993)
W.Q. Jiang, G.Q. Chen, Solution of Gill’s generalized dispersion model: solute transport in Poiseuille flow with wall absorption. Int. J. Heat Mass Transf. 127, 34–43 (2018)
Y. Jiang, J.B. Grotberg, Bolus contaminant dispersion in oscillatory tube flow with conductive walls. J. Biomed. Eng. Trans. ASME 115(4A), 424–431 (1993)
S. Kumar, G. Jayaraman, Method of moments for laminar dispersion in an oscillatory flow through curved channels with absorbing walls. Heat Mass Transf. 44(11), 1323–1336 (2008)
M.J. Lighthill, Initial development of diffusion in Poiseuille flow. IMA J. Appl. Math. 2(1), 97–108 (1966)
M.J. Lighthill, Physiological fluid dynamics: a survey. J. Fluid Mech. 52, 475–497 (1972)
O.D. Makinde, T. Chinyoka, Transient analysis of pollutant dispersion in a cylindrical pipe with a nonlinear waste discharge concentration. Comput. Math. Appl. 60, 642–652 (2010)
B.S. Mazumder, S.K. Das, Effect of boundary reaction on solute dispersion in pulsatile flow through a tube. J. Fluid Mech. 239, 523–549 (1992)
K.K. Mondal, B.S. Mazumder, On solute dispersion in pulsatile flow through a channel with absorbing walls. Int. J. Non-linear Mech. 40, 69–81 (2005)
P. Nagarani, G. Sarojamma, G. Jayaraman, Effect of boundary absorption in dispersion in Casson fluid flow in a tube. Ann. Biomed. Eng. 32(5), 706–719 (2004)
J. Rana, P.V.S.N. Murthy, Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption. Proc. R. Soc. 472, 20160294 (2017)
A. Sarkar, G. Jayaraman, The effect of wall absorption on dispersion in oscillatory flow in an annulus: application to catheterized artery. Acta Mech. 172, 151–167 (2004)
R. Sankarasubramanian, W.N. Gill, Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. Lond. Ser A 333, 115–132 (1973)
B.T. Sebastian, P. Nagarani, On convection-diffusion in non-Newtonian fluid flow in an annulus with wall oscillations. Eur. Phys. J. Spec. Top. 228, 2729–2752 (2019)
K.M. Sharp, Shear augmented dispersion in non-Newtonian fluids. Ann. Biomed. Eng. 21, 407–415 (1993)
V.K. Sud, G.S. Sekhon, Arterial flow under periodic body acceleration. Bull. Math. Biol. 47, 35–52 (1985)
G. Taylor, Dispersion of a soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. Ser A. 219(1137), 186–203 (1953)
A. Tiwari, P.D. Shah, S.S. Chauhan, Solute dispersion in two-fluid flowing through tubes with a porous layer near absorbing wall: model for dispersion in microvessels. Int. J. Multiph. Flow 131, 103380 (2020)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ausaru, A., Nagarani, P. & Sebastian, B.T. Dispersion with wall absorption in non-Newtonian fluid flow subjected to external body acceleration. Eur. Phys. J. Spec. Top. 230, 1399–1414 (2021). https://doi.org/10.1140/epjs/s11734-021-00051-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjs/s11734-021-00051-x