Long bubbles in tubes filled with viscoplastic fluid

Jalaal, Maziyar; Balmforth, N. J.

doi:10.1016/j.jnnfm.2016.06.006

Cited by 23 publications

(22 citation statements)

References 28 publications

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“…We also note that, while the work of Zamankhan et al (2012) consider a parallel plate geometry, it is in good agreement with the work of Jalaal & Balmforth (2016), and the present analytic expression, which are both derived for axisymmetric geometries. This may come from the approximation of an almost two dimensional flow in the matching region under conditions of sufficiently small values of Ca (Bretherton 1961;Jalaal & Balmforth 2016). Using the same values α = 0.33 and β = 2.4, we compare equation 4.7 with our experimental data in Figure 3a).…”

Section: Model and Discussionsupporting

confidence: 85%

“…However, the thickness deposited behind a Herschel-Bulkley with τ y = 0 and n < 1 or behind a newtonian fluid τ y = 0 and n = 1 is less straightforward to compare. Equation 4.4 suggests that the yield stress will balance the shear-thinning effects when τ y ∼ k Using lubrication theory, they calculate and compute h/R up to value of Ca in the order of 1 by retaining the full surface curvature of the interface, which induces non-linear effects (Jalaal & Balmforth 2016). In figure 3b, we fit the numerical data of Zamankhan et al (2012) and Jalaal & Balmforth (2016) (chosen for their wide range of Ca) using equation 4.7.…”

Section: Model and Discussionmentioning

confidence: 99%

“…Equation 4.4 suggests that the yield stress will balance the shear-thinning effects when τ y ∼ k Using lubrication theory, they calculate and compute h/R up to value of Ca in the order of 1 by retaining the full surface curvature of the interface, which induces non-linear effects (Jalaal & Balmforth 2016). In figure 3b, we fit the numerical data of Zamankhan et al (2012) and Jalaal & Balmforth (2016) (chosen for their wide range of Ca) using equation 4.7. By adjusting the fitting parameters of equation 4.7 to their data, which gives α = 0.33 and β = 2.4, we obtain an excellent agreement as long as Ca < 0.01.…”

Section: Model and Discussionmentioning

confidence: 99%

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Yield-stress fluid deposition in circular channels

et al. 2017

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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 ∼ RCa 2/3 ), where R is the radius of the circular tube and the Capillary number, Ca, comparing the viscous and capillary effects. This law, known as Bretherton law, is only valid 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 HerschelBulkley fluid in the limit where the yield-stress is of similar order of magnitude as the capillary pressure and for 0.1 < Ca < 1. To understand our observation, we use scaling arguments to extend the analytical expression of Bretherton's law to YSF 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 fluid, 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 fluid. 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 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, non-linear effects must be taken into account.

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Section: Model and Discussionsupporting

confidence: 85%

Section: Model and Discussionmentioning

confidence: 99%

Section: Model and Discussionmentioning

confidence: 99%

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Yield-stress fluid deposition in circular channels

et al. 2017

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“…Moreover, his theory was extended later on to a larger range of flow parameters, e.g. larger capillary and Reynolds numbers [15,16], more complex tube geometry [17][18][19], or non-Newtonian embedding liquids [20,21].…”

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confidence: 99%

Motion of Long Levitating Drops in Tubes in an Anti-Bretherton Configuration

Favreau

Duchesne²,

Zoueshtiagh³

et al. 2020

Phys. Rev. Lett.

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“…They attributed this to inadequate values of the regularization parameter used in those computations. Jalaal and Balmforth [48] through lubrication theory computed the shape of the front and rear menisci of a long bubble travelling in 2D channel and axisymmetric tubes filled by a viscoplastic fluid. For the film thickness, they have proposed an expression covering larger Ca values.…”

Section: -Introductionmentioning

confidence: 99%

Steady displacement of long gas bubbles in channels and tubes filled by a Bingham fluid

2018

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Bingham fluids behave like solids below a von Mises stress threshold, the yield stress, while above it they behave like Newtonian fluids. They are characterized by a dimensionless parameter, Bingham number (Bn), which is the ratio of the yield stress to a characteristic viscous stress. In this study, the non-inertial steady motion of a finite size gas bubble in both a plane 2D channel and an axi-symmetric tube filled by a Bingham fluid has been studied numerically. The Bingham number, Bn, is in the range 0 ≤ Bn ≤ 3, where Bn=0 is the Newtonian case, while the Capillary number which is the ratio of a characteristic viscous force to the surface tension has values Ca=0.05, 0.10, and 0.25. The volume of all axi-symmetric and 2D bubbles has been chosen to be identical for all parameter choices and large enough for the bubbles to be long compared to the channel/tube width/diameter. The Bingham fluid constitutive equation is approximated by a regularized equation. During the motion, the bubble interface is separated from the wall by a static liquid film. The film thickness scaled by the tube radius (axi-symmetric)/half of the channel height (2D) is the dimensionless film thickness, h. The results show that increasing Bn initially leads to an increase in h, however, the profile h versus Bn can be monotonic or non-monotonic depending on Ca values and 2D/axi-symmetric configurations. The yield stress also alters the shape of the front and rear of the bubble and suppresses the capillary waves at the rear of the bubble. The yield stress increases the magnitude of the wall shear stress and its gradient and therefore increases the potential for epithelial cell injuries in applications to lung airway mucus plugs. The topology of the yield surfaces as well the flow pattern in the bubble frame of reference varies significantly by Ca and Bn.

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Long bubbles in tubes filled with viscoplastic fluid

Cited by 23 publications

References 28 publications

Yield-stress fluid deposition in circular channels

Yield-stress fluid deposition in circular channels

Motion of Long Levitating Drops in Tubes in an Anti-Bretherton Configuration

Steady displacement of long gas bubbles in channels and tubes filled by a Bingham fluid

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