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Influence of slip on the Plateau-Rayleigh instability on a fibre.

Haefner S, Benzaquen M, Bäumchen O, Salez T, Peters R, McGraw JD, Jacobs K, Raphaël E, Dalnoki-Veress K - Nat Commun (2015)

Bottom Line: In contrast to the case of a free liquid cylinder, describing the evolution of a liquid layer on a solid fibre requires consideration of the solid-liquid interface.Here we revisit the Plateau-Rayleigh instability of a liquid coating a fibre by varying the hydrodynamic boundary condition at the fibre-liquid interface, from no slip to slip.Although the wavelength is not sensitive to the solid-liquid interface, we find that the growth rate of the undulations strongly depends on the hydrodynamic boundary condition.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Experimental Physics, Saarland University, D-66041 Saarbrücken, Germany [2] Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada, L8S 4M1.

ABSTRACT
The Plateau-Rayleigh instability of a liquid column underlies a variety of fascinating phenomena that can be observed in everyday life. In contrast to the case of a free liquid cylinder, describing the evolution of a liquid layer on a solid fibre requires consideration of the solid-liquid interface. Here we revisit the Plateau-Rayleigh instability of a liquid coating a fibre by varying the hydrodynamic boundary condition at the fibre-liquid interface, from no slip to slip. Although the wavelength is not sensitive to the solid-liquid interface, we find that the growth rate of the undulations strongly depends on the hydrodynamic boundary condition. The experiments are in excellent agreement with a new thin-film theory incorporating slip, thus providing an original, quantitative and robust tool to measure slip lengths.

No MeSH data available.


Influence of the geometry on the wavelength of the instability.Wavelength of the fastest growing mode as a function of the total initial radius (see Fig. 1a). The black dashed line represents equation (5). The error bars are calculated from the error in the geometry and the inaccuracy given by the wavelength measurement.
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f2: Influence of the geometry on the wavelength of the instability.Wavelength of the fastest growing mode as a function of the total initial radius (see Fig. 1a). The black dashed line represents equation (5). The error bars are calculated from the error in the geometry and the inaccuracy given by the wavelength measurement.

Mentions: Figure 2 displays the wavelength λ* of the fastest growing modes, measured on no-slip and slip fibres, as a function of the initial total radius h0. As expected from equation (5), the wavelength λ* grows linearly with increasing radius of the fibre–polymer system and is identical on slip and no-slip fibres. This is consistent with experiments and a theoretical framework for retracting liquid ridges on planar substrates26. The spatial morphology of the instability at short times is thus unaffected by the solid–liquid boundary condition. Although it is clear from Fig. 2 that the wavelength is the same on slip and no-slip fibres, there is a small systematic deviation from the theory. This slight deviation could perhaps be related to the lowest lubrication order of the present model9, but could also be attributed to the experimental contribution of several modes and the asymmetry of the rate function (see equation (4)) in the vicinity of the fastest growing mode.


Influence of slip on the Plateau-Rayleigh instability on a fibre.

Haefner S, Benzaquen M, Bäumchen O, Salez T, Peters R, McGraw JD, Jacobs K, Raphaël E, Dalnoki-Veress K - Nat Commun (2015)

Influence of the geometry on the wavelength of the instability.Wavelength of the fastest growing mode as a function of the total initial radius (see Fig. 1a). The black dashed line represents equation (5). The error bars are calculated from the error in the geometry and the inaccuracy given by the wavelength measurement.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4490368&req=5

f2: Influence of the geometry on the wavelength of the instability.Wavelength of the fastest growing mode as a function of the total initial radius (see Fig. 1a). The black dashed line represents equation (5). The error bars are calculated from the error in the geometry and the inaccuracy given by the wavelength measurement.
Mentions: Figure 2 displays the wavelength λ* of the fastest growing modes, measured on no-slip and slip fibres, as a function of the initial total radius h0. As expected from equation (5), the wavelength λ* grows linearly with increasing radius of the fibre–polymer system and is identical on slip and no-slip fibres. This is consistent with experiments and a theoretical framework for retracting liquid ridges on planar substrates26. The spatial morphology of the instability at short times is thus unaffected by the solid–liquid boundary condition. Although it is clear from Fig. 2 that the wavelength is the same on slip and no-slip fibres, there is a small systematic deviation from the theory. This slight deviation could perhaps be related to the lowest lubrication order of the present model9, but could also be attributed to the experimental contribution of several modes and the asymmetry of the rate function (see equation (4)) in the vicinity of the fastest growing mode.

Bottom Line: In contrast to the case of a free liquid cylinder, describing the evolution of a liquid layer on a solid fibre requires consideration of the solid-liquid interface.Here we revisit the Plateau-Rayleigh instability of a liquid coating a fibre by varying the hydrodynamic boundary condition at the fibre-liquid interface, from no slip to slip.Although the wavelength is not sensitive to the solid-liquid interface, we find that the growth rate of the undulations strongly depends on the hydrodynamic boundary condition.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Experimental Physics, Saarland University, D-66041 Saarbrücken, Germany [2] Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada, L8S 4M1.

ABSTRACT
The Plateau-Rayleigh instability of a liquid column underlies a variety of fascinating phenomena that can be observed in everyday life. In contrast to the case of a free liquid cylinder, describing the evolution of a liquid layer on a solid fibre requires consideration of the solid-liquid interface. Here we revisit the Plateau-Rayleigh instability of a liquid coating a fibre by varying the hydrodynamic boundary condition at the fibre-liquid interface, from no slip to slip. Although the wavelength is not sensitive to the solid-liquid interface, we find that the growth rate of the undulations strongly depends on the hydrodynamic boundary condition. The experiments are in excellent agreement with a new thin-film theory incorporating slip, thus providing an original, quantitative and robust tool to measure slip lengths.

No MeSH data available.