Limits...
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.


Temporal growth of the perturbation.Semi-logarithmic plot of the evolution of the perturbation on (a) a no-slip fibre (glass) and (b) a slip fibre (glass coated with AF2400). The radius of the fibre a and initial thickness of the polymer film e0 (see Fig. 1a) are indicated. The solid line is the best linear fit in the initial regime.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4490368&req=5

f3: Temporal growth of the perturbation.Semi-logarithmic plot of the evolution of the perturbation on (a) a no-slip fibre (glass) and (b) a slip fibre (glass coated with AF2400). The radius of the fibre a and initial thickness of the polymer film e0 (see Fig. 1a) are indicated. The solid line is the best linear fit in the initial regime.

Mentions: We now turn from the spatial morphology of the instability to the temporal evolution. From the experimental images (see Fig. 1b), we extract the maximal radius of an individual bulge as it develops, to obtain the amplitude ζ as a function of time. The linear stability analysis presented predicts a perturbation that grows exponentially with a dimensionless growth rate 1/τ* for the fastest growing mode (see equation (6)). Figure 3 displays typical data for the logarithm of the perturbation amplitude normalized by the radius of the fibre, ζ/a, as a function of t, for both no-slip and slip fibres. The data for both boundary conditions are consistent with the expected exponential growth in the early regime. Thus, the initial slopes of these curves provide reliable measurements of the growth rates.


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)

Temporal growth of the perturbation.Semi-logarithmic plot of the evolution of the perturbation on (a) a no-slip fibre (glass) and (b) a slip fibre (glass coated with AF2400). The radius of the fibre a and initial thickness of the polymer film e0 (see Fig. 1a) are indicated. The solid line is the best linear fit in the initial regime.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Temporal growth of the perturbation.Semi-logarithmic plot of the evolution of the perturbation on (a) a no-slip fibre (glass) and (b) a slip fibre (glass coated with AF2400). The radius of the fibre a and initial thickness of the polymer film e0 (see Fig. 1a) are indicated. The solid line is the best linear fit in the initial regime.
Mentions: We now turn from the spatial morphology of the instability to the temporal evolution. From the experimental images (see Fig. 1b), we extract the maximal radius of an individual bulge as it develops, to obtain the amplitude ζ as a function of time. The linear stability analysis presented predicts a perturbation that grows exponentially with a dimensionless growth rate 1/τ* for the fastest growing mode (see equation (6)). Figure 3 displays typical data for the logarithm of the perturbation amplitude normalized by the radius of the fibre, ζ/a, as a function of t, for both no-slip and slip fibres. The data for both boundary conditions are consistent with the expected exponential growth in the early regime. Thus, the initial slopes of these curves provide reliable measurements of the growth rates.

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.