Motion of a confined bubble in a shear-thinning liquid

Picchi, Davide; Ullmann, Amos; Brauner, Neima; Poesio, Pietro

doi:10.1017/jfm.2021.321

Cited by 21 publications

(58 citation statements)

References 81 publications

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“…It has been proved by other authors that power-law can model the viscosity of aqueous xanthan solutions with high accuracy [36,37]. It is worth mentioning that although the power-law model may not be applicable at low-shear rates [38,39], in confined flows the shear rate is relatively large due to the no-slip boundary condition of the walls and small dimensions. Thus, the power-law can accurately model fluid behaviour.…”

Section: Fluid Propertiesmentioning

confidence: 99%

Non-Newtonian Droplet Generation in a Cross-Junction Microfluidic Channel

2021

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A two-dimensional CFD model based on volume-of-fluid (VOF) is introduced to examine droplet generation in a cross-junction microfluidic using an open-source software, OpenFOAM together with an interFoam solver. Non-Newtonian power-law droplets in Newtonian liquid is numerically studied and its effect on droplet size and detachment time in three different regimes, i.e., squeezing, dripping and jetting, are investigated. To understand the droplet formation mechanism, the shear-thinning behaviour was enhanced by increasing the polymer concentrations in the dispersed phase. It is observed that by choosing a shear-dependent fluid, droplet size decreases compared to Newtonian fluids while detachment time increases due to higher apparent viscosity. Moreover, the rheological parameters—n and K in the power-law model—impose a considerable effect on the droplet size and detachment time, especially in the dripping and jetting regimes. Those parameters also have the potential to change the formation regime if the capillary number (Ca) is high enough. This work extends the understanding of non-Newtonian droplet formation in microfluidics to control the droplet characteristics in applications involving shear-thinning polymeric solutions.

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Section: Fluid Propertiesmentioning

confidence: 99%

Non-Newtonian Droplet Generation in a Cross-Junction Microfluidic Channel

2021

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“…the film thickness, the bubble speed) can be expressed as a function of the capillary number and that the film profile can be described with a similarity solution typical of Landau-Levich-Derjaguin-Bretherton problems (see de Gennes, Brochard-Wyart & Quéré 2003;Stone 2010). The theory is supported by several experimental measurements (Fairbrother & Stubbs 1935;Taylor 1961;Schwartz, Princen & Kiss 1986;Aussillous & Quéré 2000) and, in the last decades, it has been extended to include the effect of viscous forces and weak inertia (Cox 1962;Reinelt & Saffman 1985;Aussillous & Quéré 2000;Heil 2001;de Ryck 2002;Khodaparast et al 2015;Magnini et al 2017), unsteady flow, (Yu et al 2018), buoyancy, (Leung et al 2012;Atasi et al 2017;Lamstaes & Eggers 2017), bubble viscosity and non-Newtonian effects (Chen 1986;Hodges, Jensen & Rallinson 2004;Balestra, Zhu & Gallaire 2018;Shukla et al 2019;Picchi et al 2021).…”

Section: Introductionmentioning

confidence: 94%

“…The code used in this work for this purpose has been developed in a previous publication (Picchi et al. 2021), where all the details concerning the boundary conditions are discussed.…”

Section: Theoretical Derivationmentioning

confidence: 99%

Dispersion of a passive scalar around a Taylor bubble

Picchi

Poesio

2022

J. Fluid Mech.

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The motion of Taylor bubbles in capillaries is typical of many engineering and biological systems, ranging from subsurface flows to small-scale reactors. Although the hydrodynamics of elongated bubbles has been the object of several studies, the case where a solute is transported in the surrounding liquid and surface mass-transfer mechanisms act on the solid wall or the bubble–fluid interface is much less understood. To fill this gap, we investigate the transport problem around a confined Taylor bubble to access the competition between advection, diffusion and surface mass transfer in the different regions of the bubble. With this aim, we derive a one-dimensional advection–diffusion–mass-transfer equation where the transport mechanisms are described through an effective velocity, an effective diffusion coefficient and an effective Sherwood number. Our model generalises the Aris–Taylor dispersion to the case of a Taylor bubble and clarifies the impact of surface mass transfer in the advection and diffusion dominated regimes for both the front and rear menisci. The model recovers the typical Pèclet square relationship of the effective diffusion coefficient, which also depends on the film thickness. Also, when the Pèclet number balances with the Sherwood number, there exist conditions that lead to the formation of hot spots of concentration. We show that the typical shape oscillations of the bubble rear locally enhance superficial mass transfer. Finally, we study the transport problem in the uniform film region where the concentration field can be found analytically.

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“…2021; Picchi et al. 2021). The Ellis model relates the apparent viscosity to the stress tensor as where is the shear stress corresponding to an apparent viscosity and for a shear-thinning fluid is an indicial parameter.…”

Section: The Ellis Model For the Inner Ascending Currentmentioning

confidence: 99%

“…Myers 2005). In order to eliminate this inconsistency and to adapt the rheological model to the effective experimental behaviour of shear-thinning fluids, we adopt the three-parameter Ellis model, which has been extensively and successfully applied to describe the flow in complex geometries (Al-Behadili et al 2019;Ali et al 2019;Celli, Barletta & Brandão 2021;Ciriello et al 2021;Picchi et al 2021). The Ellis model relates the apparent viscosity to the stress tensor as…”

Section: The Ellis Model For the Inner Ascending Currentmentioning

confidence: 99%

Ascending non-Newtonian long drops in vertical tubes

et al. 2022

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We report on theoretical and experimental studies describing the buoyancy-driven ascent of a Taylor long drop in a circular vertical pipe where the descending fluid is Newtonian, and the ascending fluid is non-Newtonian yield shear thinning and described by the three-parameter Herschel–Bulkley model, including the Ostwald–de Waele model as a special case for zero yield. Results for the Ellis model are included to provide a more realistic description of purely shear-thinning behaviour. In all cases, lubrication theory allows us to obtain the velocity profiles and the corresponding integral variables in closed form, for lock-exchange flow with a zero net flow rate. The energy balance allows us to derive the asymptotic radius of the inner current, corresponding to a stable node of the differential equation describing the time evolution of the core radius. We carried out a series of experiments measuring the rheological properties of the fluids, the speed and the radius of the ascending long drop. For some tests, we measured the velocity profile with the ultrasound velocimetry technique. The measured radius of the ascending current compares fairly well with the asymptotic radius as derived through the energy balance, and the measured ascent speed shows a good agreement with the theoretical model. The measured velocity profiles also agree with their theoretical counterparts. We have also developed dynamic similarity conditions to establish whether laboratory physical models, limited by the availability of real fluids with defined rheological characteristics, can be representative of real phenomena on a large scale, such as exchanges in volcanic conduits. Appendix B contains scaling rules for the approximated dynamic similarity of the physical process analysed; these rules serve as a guide for the design of experiments reproducing real phenomena.

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Motion of a confined bubble in a shear-thinning liquid

Abstract: Abstract

Cited by 21 publications

References 81 publications

Non-Newtonian Droplet Generation in a Cross-Junction Microfluidic Channel

Non-Newtonian Droplet Generation in a Cross-Junction Microfluidic Channel

Dispersion of a passive scalar around a Taylor bubble

Ascending non-Newtonian long drops in vertical tubes

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