Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption

The theory of miscible dispersion in a straight circular pipe with interphase mass transfer that was investigated by Sankarasubramanian & Gill (1973Proc. R. Soc. Lond. A333, 115–132. (doi:10.1098/rspa.1973.0051); 1974Proc. R. Soc. Lond. A341, 407–408. (doi:10.1098/rspa.1974.0195)) in Newtonian fluid flow is extended by considering various non-Newtonian fluid models, such as the Casson (Rana & Murthy 2016J. Fluid Mech.793, 877–914. (doi:10.1017/jfm.2016.155)), Carreau and Carreau–Yasuda models. These models are useful to investigate the solute dispersion in blood flow. The three effective transport coefficients, i.e. exchange, convection and dispersion coefficients, are evaluated to analyse the dispersion process of solute. The convection and dispersion coefficients are determined asymptotically at large time which is sufficient to understand the nature of the solute dispersion process in a tube. The axial mean concentration is analysed, using the asymptotic expressions for these three coefficients. The effect of the wall absorption parameter, Weissenberg number, power-law index, Yasuda parameter and Peclet number on the dispersion process is discussed clearly in this study. A comparative study of the solute dispersion among the Newtonian and all other non-Newtonian models is presented. At low shear rate, it is observed that Carreau fluid behaves like Newtonian fluid, whereas the other fluids exhibit significant differences during the solute dispersion. This study may be applicable to understand the dispersion process of drugs in the blood stream.

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Mathematical Analysis of Unsteady Solute Dispersion with Chemical Reaction Through a Stenosed Artery

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences ◽

10.37934/arfmts.86.2.5673 ◽

2021 ◽

Vol 86 (2) ◽

pp. 56-73

Author(s):

Nurul Aini Jaafar ◽

Siti NurulAifa Mohd ZainulAbidin ◽

Zuhaila Ismail ◽

Ahmad Qushairi Mohamad

Keyword(s):

Blood Flow ◽

Chemical Reaction ◽

Power Law ◽

Plug Flow ◽

Arterial Disease ◽

Arterial Stenosis ◽

Dispersion Function ◽

Dispersion Process ◽

Solute Dispersion ◽

Power Law Index

One major kind of arterial disease in blood flow that attracted many researchers is arterial stenosis. Arterial stenosis occurs when a lumen of artery is narrowed by the accumulation of fats, cholesterols and lipids plaques at the inner layer of the wall of an artery. To treat this arterial disease, the drug (solute) is injected into the blood vessels. Injection of the drug into the blood vessel cause the occurrence of chemical reaction between the drug and blood proteins and it affects the effectiveness of the solute transportation in blood flow. Hence, this study examines the unsteady dispersion of solute with the influence of chemical reaction and stenosis height through a very narrow artery with a cosine-curved stenosis. The blood is treating as Herschel-Bulkley (H-B) fluid. The momentum and constitutive equations are solved analytically to gain velocity of H-B blood flow. The convective-diffusion equation is solved by applying the generalized dispersion model to gain the dispersion function of solute. The influence of chemical reaction, power-law index, plug flow radius and stenosis height on the solute dispersion process is investigated. The results are validated with the previous solution without the effect of chemical reaction and stenosis. The results showed a good conformity between the two solutions. An increase in the chemical reaction coefficient, stenosis height, power-law index and plug flow radius reduces the dispersion function. It is observed that the solute dispersion in blood flow is affected by chemical reaction and stenosis height. H-B fluid is an appropriate fluid to investigate the blood velocity and transportation of the drug in blood flow to the targeted stenosed region through a very narrow artery for the treatment of arterial diseases. The results of the present study can potentially be used to predict the changes of blood flow behavior and dispersion process in blood flow.

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Influence of Viscoelasticity on Turbulent Flow Over a Backward-Facing Step

Volume 1A: Symposia, Part 2 ◽

10.1115/ajkfluids2015-25251 ◽

2015 ◽

Author(s):

Akito Ikegami ◽

Takahiro Tsukahara ◽

Yasuo Kawaguchi

Keyword(s):

Fluid Flow ◽

Turbulent Flow ◽

Newtonian Fluid ◽

Expansion Ratio ◽

Weissenberg Number ◽

Recirculation Region ◽

Viscoelastic Flows ◽

Backward Facing Step ◽

Mean Velocity ◽

Significant Difference

We studied viscoelastic turbulent flow over a backward-facing step of the expansion ratio ER = 1.5 using DNS (direct numerical simulation) at a friction Reynolds number Reτ0 of 100. We chose the Giesekus model as a viscoelastic constitutive equation, and the Weissenberg number is Wiτ0 = 10 and 20. Visualized instantaneous vortices revealing that a few vortices occur only above the recirculation regions in the viscoelastic fluid flow compared to those in the Newtonian flow. This phenomenon might be caused by the fluid viscoelasticity that would suppress the Kelvin-Helmholz vortex emanating from the step edge. The reattachment length from the step is 6.80h for the Newtonian fluid, 7.82h for Wiτ0 = 10, and 8.82h for Wiτ0 = 20, where h is the step height. In the mean velocity distributions normalized by maximum inlet velocity, we have observed no significant difference among the three fluids, except for region near the upper or bottom wall, i.e., the recirculation and recovery regions at the front and behind the reattachment point. The streamwise turbulent intensity u’rms is weaken in the recirculation region of the viscoelastic flows. In terms of v’rms, its magnitude in the recirculation region becomes largest in the case of Wiτ0 = 10, not for the Newtonian fluid flow or more viscoelastic case of Wiτ0 = 20.

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Effect of External Body Acceleration on Solute Dispersion in Unsteady Non-Newtonian Fluid Flow-the Generalized Dispersion Model Approach

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-021-01209-w ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

A. Ausaru ◽

P. Nagarani

Keyword(s):

Fluid Flow ◽

Newtonian Fluid ◽

Dispersion Model ◽

Solute Dispersion ◽

Body Acceleration ◽

Generalized Dispersion Model ◽

Model Approach ◽

External Body

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Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

Open Physics ◽

10.2478/s11534-011-0034-3 ◽

2011 ◽

Vol 9 (5) ◽

Cited By ~ 6

Author(s):

Kuppalapalle Vajravelu ◽

Sreedharamalle Sreenadh ◽

Palluru Devaki ◽

Kerehalli Prasad

Keyword(s):

Shear Stress ◽

Fluid Flow ◽

Wall Shear Stress ◽

Yield Stress ◽

Newtonian Fluid ◽

Power Law ◽

Fluid Model ◽

Elastic Tube ◽

Yield Stress Fluid ◽

Power Law Index

AbstractThe constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t 1 and t 2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

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A general analytical approach to study solute dispersion in non-Newtonian fluid flow

European Journal of Mechanics - B/Fluids ◽

10.1016/j.euromechflu.2019.04.013 ◽

2019 ◽

Vol 77 ◽

pp. 183-200 ◽

Cited By ~ 2

Author(s):

Jyotirmoy Rana ◽

Shijun Liao

Keyword(s):

Fluid Flow ◽

Newtonian Fluid ◽

Analytical Approach ◽

Solute Dispersion

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Optimised multi-stream microfluidic designs for controlled extensional deformation

Microfluidics and Nanofluidics ◽

10.1007/s10404-019-2295-x ◽

2019 ◽

Vol 23 (12) ◽

Cited By ~ 1

Author(s):

Konstantinos Zografos ◽

Simon J. Haward ◽

Mónica S. N. Oliveira

Keyword(s):

Fluid Flow ◽

Newtonian Fluid ◽

Numerical Study ◽

Extensional Flow ◽

Region Of Interest ◽

Weissenberg Number ◽

Creeping Flow ◽

Three Dimensions ◽

Main Stream ◽

Flow Focusing

Abstract In this study, we optimise two types of multi-stream configurations (a T-junction and a flow-focusing design) to generate a homogeneous extensional flow within a well-defined region. The former is used to generate a stagnation point flow allowing molecules to accumulate significant strain, which has been found very useful for performing elongational studies. The latter relies on the presence of opposing lateral streams to shape a main stream and generate a strong region of extension in which the shearing effects of fluid–wall interactions are reduced near the region of interest. The optimisations are performed in two (2D) and three dimensions (3D) under creeping flow conditions for Newtonian fluid flow. It is demonstrated that in contrast with the classical-shaped geometries, the optimised designs are able to generate a well-defined region of homogeneous extension. The operational limits of the obtained 3D optimised configurations are investigated in terms of Weissenberg number for both constant viscosity and shear-thinning viscoelastic fluids. Additionally, for the 3D optimised flow-focusing device, the operational limits are investigated in terms of increasing Reynolds number and for a range of velocity ratios between the opposing lateral streams and the main stream. For all obtained 3D optimised multi-stream configurations, we perform the experimental validation considering a Newtonian fluid flow. Our results show good agreement with the numerical study, reproducing the desired kinematics for which the designs are optimised.

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