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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 slip on the growth rate.The inset shows the dimensionless growth rate 1/τ* normalized by the no-slip case β, as a function of α/(βa), see equation (6) and equations (7a,b), . The slip length b is obtained from a best linear fit (dash-dotted) to the slip data. The error bars are calculated from the error in the geometry and the inaccuracy given by the growth rate measurement. The main curve shows the dimensionless growth rate of the fastest growing mode on no-slip (glass) and slip (AF2400) fibres, as a function of the dimensionless initial total radius H0=1+e0/a (see Fig. 1a). Open symbols represent growth rates calculated from equation (6) using b=4.0±0.4 μm and the respective experimental geometries. Also shown is the theoretical curve for no slip (equation (6), with B=0). Furthermore, the theoretical curve for slip (equation (6), with B=0.3) is plotted as a guide to the eye.
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f4: Influence of slip on the growth rate.The inset shows the dimensionless growth rate 1/τ* normalized by the no-slip case β, as a function of α/(βa), see equation (6) and equations (7a,b), . The slip length b is obtained from a best linear fit (dash-dotted) to the slip data. The error bars are calculated from the error in the geometry and the inaccuracy given by the growth rate measurement. The main curve shows the dimensionless growth rate of the fastest growing mode on no-slip (glass) and slip (AF2400) fibres, as a function of the dimensionless initial total radius H0=1+e0/a (see Fig. 1a). Open symbols represent growth rates calculated from equation (6) using b=4.0±0.4 μm and the respective experimental geometries. Also shown is the theoretical curve for no slip (equation (6), with B=0). Furthermore, the theoretical curve for slip (equation (6), with B=0.3) is plotted as a guide to the eye.

Mentions: The dimensionless growth rates 1/τ* are shown in Fig. 4 for both slip and no-slip fibres as a function of the dimensionless initial total radius H0. We see that for both the slip and no-slip boundary conditions, the growth rates show a similar geometry dependence. The maxima for the slip and no-slip data can be easily understood: a decreasing growth rate as H0 converges to 1 is due to the diminishing thickness of the liquid film, and thus to the reduced mobility, whereas the decreasing growth rate for large H0 is due to smaller curvatures and thus a smaller driving force of the instability.


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 slip on the growth rate.The inset shows the dimensionless growth rate 1/τ* normalized by the no-slip case β, as a function of α/(βa), see equation (6) and equations (7a,b), . The slip length b is obtained from a best linear fit (dash-dotted) to the slip data. The error bars are calculated from the error in the geometry and the inaccuracy given by the growth rate measurement. The main curve shows the dimensionless growth rate of the fastest growing mode on no-slip (glass) and slip (AF2400) fibres, as a function of the dimensionless initial total radius H0=1+e0/a (see Fig. 1a). Open symbols represent growth rates calculated from equation (6) using b=4.0±0.4 μm and the respective experimental geometries. Also shown is the theoretical curve for no slip (equation (6), with B=0). Furthermore, the theoretical curve for slip (equation (6), with B=0.3) is plotted as a guide to the eye.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Influence of slip on the growth rate.The inset shows the dimensionless growth rate 1/τ* normalized by the no-slip case β, as a function of α/(βa), see equation (6) and equations (7a,b), . The slip length b is obtained from a best linear fit (dash-dotted) to the slip data. The error bars are calculated from the error in the geometry and the inaccuracy given by the growth rate measurement. The main curve shows the dimensionless growth rate of the fastest growing mode on no-slip (glass) and slip (AF2400) fibres, as a function of the dimensionless initial total radius H0=1+e0/a (see Fig. 1a). Open symbols represent growth rates calculated from equation (6) using b=4.0±0.4 μm and the respective experimental geometries. Also shown is the theoretical curve for no slip (equation (6), with B=0). Furthermore, the theoretical curve for slip (equation (6), with B=0.3) is plotted as a guide to the eye.
Mentions: The dimensionless growth rates 1/τ* are shown in Fig. 4 for both slip and no-slip fibres as a function of the dimensionless initial total radius H0. We see that for both the slip and no-slip boundary conditions, the growth rates show a similar geometry dependence. The maxima for the slip and no-slip data can be easily understood: a decreasing growth rate as H0 converges to 1 is due to the diminishing thickness of the liquid film, and thus to the reduced mobility, whereas the decreasing growth rate for large H0 is due to smaller curvatures and thus a smaller driving force of the instability.

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.