Flow of a Newtonian fluid and a yield stress fluid around a plate inclined at 45° in interaction with a wall

AIChE Journal ◽  
2019 ◽  
Vol 65 (5) ◽  
pp. e16562
Author(s):  
Ziemihori Ouattara ◽  
Pascal Jay ◽  
Albert Magnin
Keyword(s):  
Yield Stress ◽  
Newtonian Fluid ◽  
Yield Stress Fluid

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

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
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.

Removal of a yield stress fluid by a heavier Newtonian fluid in a vertical pipe

2019 ◽  
Vol 268 ◽  
pp. 81-100 ◽  
Author(s):  
A. Amiri ◽  
A. Eslami ◽  
R. Mollaabbasi ◽  
F. Larachi ◽  
S.M. Taghavi
Keyword(s):  
Yield Stress ◽  
Newtonian Fluid ◽  
Vertical Pipe ◽  
Yield Stress Fluid

scholarly journals Yield-stress fluid deposition in circular channels

2017 ◽  
Vol 818 ◽  
pp. 838-851 ◽  
Author(s):  
Benoît Laborie ◽  
Florence Rouyer ◽  
Dan E. Angelescu ◽  
Elise Lorenceau
Keyword(s):  
Yield Stress ◽  
Newtonian Fluid ◽  
Capillary Number ◽  
Pure Shear ◽  
Scaling Law ◽  
Classical Problem ◽  
Nonlinear Effects ◽  
Shear Thinning ◽  
Quantitative Agreement ◽  
Yield Stress Fluid

Since the pioneering works of Taylor and Bretherton, the thickness $h$ of the film deposited behind a long bubble invading a Newtonian fluid is known to increase with the capillary number power $2/3$ ($h\sim RCa^{2/3}$), where $R$ is the radius of the circular tube and $Ca$ is the capillary number, comparing the viscous and capillary effects. This law, known as Bretherton’s law, is valid only in the limit of $Ca<0.01$ and negligible inertia and gravity. We revisit this classical problem when the fluid is a yield-stress fluid (YSF) exhibiting both a yield stress and a shear-thinning behaviour. First, we provide quantitative measurement of the thickness of the deposited layer for Carbopol, a Herschel–Bulkley fluid, in the limit where the yield stress is of a similar order of magnitude to the capillary pressure and for $0.1<Ca<1$. To understand our observations, we use scaling arguments to extend the analytical expression of Bretherton’s law to YSFs in circular tubes. In the limit of $Ca<0.1$, our scaling law, in which the adjustable parameters are set using previous results concerning non-Newtonian fluids, successfully retrieves several features of the literature. First, it shows that (i) the thickness deposited behind a Bingham YSF (exhibiting a yield stress only) is larger than for a Newtonian fluid and (ii) the deposited layer increases with the amplitude of the yield stress. This is in quantitative agreement with previous numerical results concerning Bingham fluids. It also agrees with results concerning pure shear-thinning fluids in the absence of yield stress: the shear-thinning behaviour of the fluid reduces the deposited thickness as previously observed. Last, in the limit of vanishing velocity, our scaling law predicts that the thickness of the deposited YSF converges towards a finite value, which presumably depends on the microstructure of the YSF, in agreement with previous research on the topic performed in different geometries. For $0.1<Ca<1$, the scaling law fails to describe the data. In this limit, nonlinear effects must be taken into account.

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