Nonlinear generation of vorticity in thin smectic films

Parfenyev, V. M.; Vergeles, S. S.; Лебедев, В. В.

doi:10.1134/s0021364016030127

Cited by 4 publications

(17 citation statements)

References 13 publications

(26 reference statements)

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“…But the time is small as compared to the setting time of the Eulerian vorticity that is the viscous diffusion time, t ≪ 1/νk 2 . Indeed, the Eulerian vorticity is generated in the viscous sublayer according to equation (13) and then it extends due to the viscosity in the fluid bulk. Thus, one should take into account that the waves were absent before the excitation, h = 0 at t < 0 in expression (27), so the Eulerian part of the vorticity spread only to a depth d ∼ √ νt out of the viscous sublayer at the time of measurements, see equation (13).…”

Section: B Eddy Currents On the Fluid Surface And In The Bulkmentioning

confidence: 99%

“…Indeed, the Eulerian vorticity is generated in the viscous sublayer according to equation (13) and then it extends due to the viscosity in the fluid bulk. Thus, one should take into account that the waves were absent before the excitation, h = 0 at t < 0 in expression (27), so the Eulerian part of the vorticity spread only to a depth d ∼ √ νt out of the viscous sublayer at the time of measurements, see equation (13). Hence, the Reynolds number (18) should be now evaluated as Re ∼ Ω L d 2 /ν ∼ Ω L t (we have used the fact that the nonlinear velocity field is two-dimensional) and it remains of the order or less than unity according to the experimental data.…”

Section: B Eddy Currents On the Fluid Surface And In The Bulkmentioning

confidence: 99%

“…One can also neglect the dilational and shear viscosities of the film for typical experimental conditions. The approximation is justified when ρν ≫ η s k, and here η s stands for the dilational/shear viscosity of the film and k is the characteristic wave number of the flow, see, e.g., [13].…”

Section: Introductionmentioning

confidence: 99%

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Influence of a thin compressible insoluble liquid film on the eddy currents generated by interacting surface waves

Parfenyev

Vergeles

2018

Phys. Rev. Fluids

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Recently the generation of eddy currents by interacting surface waves was observed experimentally. The phenomenon provides the possibility for manipulation of particles which are immersed in the fluid. The analysis shows that the amplitude of the established eddy currents produced by stationary surface waves does not depend on the fluid viscosity in the free surface case. The currents become parametrically larger being inversely proportional to the square root of the fluid viscosity in the case when the fluid surface is covered by an almost incompressible thin liquid (i.e. shear elasticity is zero) film formed by an insoluble agent with negligible internal viscous losses as compared to the dissipation in the fluid bulk. Here we extend the theory for a thin insoluble film with zero shear elasticity and small shear and dilational viscosities on the case of an arbitrary elastic compression modulus. We find both contributions into the Lagrangian motion of passive tracers, which are the advection by the Eulerian vertical vorticity and the Stokes drift. Whereas the Stokes drift contribution preserves its value for the free surface case outside a thin viscous sublayer, the Eulerian vertical vorticity strongly depends on the fluid viscosity at high values of the film compression modulus. The Stokes drift acquires a strong dependence on the fluid viscosity inside the viscous sublayer, however, the change is compensated by an opposite change in the Eulerian vertical vorticity. As a result, the vertical dependence of the intensity of eddy currents is given by a sum of two decaying exponents with both decrements being of the order of the wave number. The decrements are numerically different, so the Eulerian contribution becomes dominant at some depth for the surface film with any compression modulus. *

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Section: B Eddy Currents On the Fluid Surface And In The Bulkmentioning

confidence: 99%

Section: B Eddy Currents On the Fluid Surface And In The Bulkmentioning

confidence: 99%

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Influence of a thin compressible insoluble liquid film on the eddy currents generated by interacting surface waves

Parfenyev

Vergeles

2018

Phys. Rev. Fluids

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“…Thus, the generation mechanism of vertical vorticity is the same as in the clean case [7], except the change in the velocity field, see Eqs. (11) and (12). To find Z-component of the vorticity ̟ z we should solve the equation…”

Section: Nonlinear Mechanismmentioning

confidence: 99%

Effects of thin film and Stokes drift on the generation of vorticity by surface waves

Parfenyev¹,

Vergeles²,

Лебедев³

2016

Phys. Rev. E

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Recently a theoretical scheme explaining the vorticity generation by surface waves in liquids was developed [Phys. Rev. Lett. 116, 054501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.054501]. Here we study how a thin (monomolecular) film presented on the surface of liquid affects the generated vorticity. We demonstrate that the vorticity becomes parametrically larger than for the case of liquid with a free surface, and the parameter is the quality factor of surface waves up to numerical factor. We also discuss the PIV experimental scheme intended to observe the generated vorticity and find that Stokes drift influences the measured velocity field. Explicit expression for the vertical vorticity was obtained.

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“…Results. -Stationary vortex flow is generated due to nonlinear interaction of bending modes excited in the film [11]. Therefore, the acoustic streaming occurs near the frequencies corresponding to the resonance conditions of smectic film transverse oscillations:…”

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confidence: 99%

Acoustic streaming in two-dimensional freely suspended smectic liquid crystal films

2017

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We study horizontal streaming excited by means of a low-frequency and low-intensity acoustic wave in 2D freely suspended films of thermotropic smectic liquid crystals. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of the vortices are measured using a new method, based on tracking solidlike disk-shaped islands. The horizontal motion occurs only when the amplitude of the acoustic pressure exceeds the threshold value, which can be explained by Bingham-like behavior of the smectic film. The measurements above threshold are in good agreement with existing theoretical predictions. We demonstrate experimentally that in-plane flow is well controlled by changing the acoustic pressure, excitation frequency, and geometry of the film. The observations open the way to using the phenomenon in nondisplay applications.

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Nonlinear generation of vorticity in thin smectic films

Cited by 4 publications

References 13 publications

Influence of a thin compressible insoluble liquid film on the eddy currents generated by interacting surface waves

Influence of a thin compressible insoluble liquid film on the eddy currents generated by interacting surface waves

Effects of thin film and Stokes drift on the generation of vorticity by surface waves

Acoustic streaming in two-dimensional freely suspended smectic liquid crystal films

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