Viscous and electro-osmotic effects upon motion of an oil droplet through a capillary

Grassia, Paul

doi:10.1017/jfm.2020.458

Cited by 7 publications

(36 citation statements)

References 29 publications

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“…It is only when multiple solution branches occur (the small Γ limit) that we see variation of the viscous contribution to pressure drop which becomes sensitive to the particular solution branch. This comes about because different branches have different shapes for the transition region as seen in [50]. The lower branch exhibits a monotonic increase in the thickness of the transition region but the upper branch exhibits a spatial oscillation with monotonic increase thereafter.…”

Section: Discussionmentioning

confidence: 99%

“…The motivation for considering charged systems in general, and opposite and equal charges in particular is outlined in the next section, namely §2. This next section also identifies the specific novel contribution of the present work over and above what [ 45 , 49 , 50 ] achieved. The main theory that we will use in this work is presented in §3.…”

Section: Introductionmentioning

confidence: 92%

“…When the transition region at the front of the droplet was analysed in the conjoining case with Γ=0.1, there turned out to be multiple solution branches, at least three of them [50]. Physically this means that, at any specified χ, there are multiple possible solutions for film thickness for a droplet advancing at a certain speed (see figure A1 b in the electronic supplementary material, appendix).…”

Section: Background and Motivationmentioning

confidence: 99%

“…This section reviews the important physics of droplets moving through capillary channels, starting with the uncharged case of [ 1 , 2 ] and continuing on to the charged cases considered by [ 45 , 49 ]. This then sets the context for the system to be studied in the present work, in which the droplet itself and the capillary wall carry opposite and equal charges [ 50 ]. Reasons are given why this opposite and equal charge case is of particular interest, thereby leading into the specific novel contribution of the present work, which is itself described in §2i.…”

Section: Background and Motivationmentioning

confidence: 99%

“…Towards this end, the present work analyses the above-mentioned system of a moving non-aqueous droplet surrounded by an aqueous phase and a capillary wall, but allows both the droplet and the capillary wall to carry an electrical charge on their surfaces [ 45 , 49 , 50 ], a common situation for many materials when surface charge adsorption is present. Specifically, a case is considered [ 49 , 50 ] in which these charges are opposite and equal. The motivation for considering charged systems in general, and opposite and equal charges in particular is outlined in the next section, namely §2.…”

Section: Introductionmentioning

confidence: 99%

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Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary

Grassia

2022

Proc. R. Soc. A.

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A charged oil droplet advancing into a charged capillary is considered, assuming the special case in which charges are opposite and equal. The droplet is surrounded by an aqueous phase that wets the capillary wall, such that a thin film adjacent to the wall is laid down as the droplet advances. Electro-osmotic conjoining pressures contrive to make the film even thinner than in an uncharged case. The pressure drop needed to drive the droplet along is examined. The pressure drop is dominated by capillarity but contains electro-osmotic and viscous corrections. The viscous correction is shown to be remarkably insensitive to the presence of electro-osmotic effects. The electro-osmotic pressure correction is negative, reflecting work done by the electro-osmotic conjoining pressure as film is laid down. The negative electro-osmotic correction to pressure drop can far exceed the positive viscous correction. As a result, in the presence of conjoining pressures, a droplet can be driven along a capillary channel with even less pressure drop than is seen for a static uncharged droplet.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 92%

Section: Background and Motivationmentioning

confidence: 99%

Section: Background and Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary

Grassia

2022

Proc. R. Soc. A.

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Movement of oil droplets against salt concentration gradients in thin capillaries

Wang,

Shapiro,

Andersen

2024

Chemical Engineering Science

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Experimental observation of a confined bubble moving in shear-thinning fluids

Yang

Malik

et al. 2022

J. Fluid Mech.

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The motion of a long gas bubble in a confined capillary tube is ubiquitous in a wide range of engineering and biological applications. While the understanding of the deposited thin viscous film near the tube wall in Newtonian fluids is well developed, the deposition dynamics in commonly encountered non-Newtonian fluids remains much less studied. Here, we investigate the dynamics of a confined bubble moving in shear-thinning fluids with systematic experiments, varying the zero-shear-rate capillary number $Ca_0$ in the range of $O(10^{-3}\unicode{x2013}10^2)$ considering the zero-shear-rate viscosity. The thickness of the deposited liquid film, the bubble speed and the bubble front/rear menisci are measured, which are further rationalized with the recent theoretical studies based on appropriate rheological models. Compared with Newtonian fluids, the film thickness decreases for both the carboxymethyl cellulose and Carbopol solutions when the shear-thinning effect dominates. We show that the film thickness follows the scaling law from Aussillous & Quéré (Phys. Fluids, vol. 12, no. 10, 2000, pp. 2367–2371) with an effective capillary number $Ca_e$ , considering the characteristic shear rate in the film as proposed by Picchi et al. (J. Fluid Mech., vol. 918, no. A7, 2021, pp. 1–30). $Ca_e$ is calculated by the Carreau number and the power-law index from the Carreau–Yasuda rheological model. The shear-thinning effect also influences the bubble speed and delays the transition to the parabolic region in the bubble front and rear menisci. In particular, a high degree of undulations on the bubble surface results in an intricate rear viscosity distribution for the rear meniscus and the deviation between the experiments and theory may require a further investigation to resolve the axial velocity field. Our study may advance the fundamental understandings and engineering guidelines for coating processes involving thin-film flows and non-Newtonian fluids.

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Viscous and electro-osmotic effects upon motion of an oil droplet through a capillary

Abstract: Abstract

Cited by 7 publications

References 29 publications

Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary

Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary

Movement of oil droplets against salt concentration gradients in thin capillaries

Experimental observation of a confined bubble moving in shear-thinning fluids

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