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

Abstract

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.

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

“…The dependence Ω L ∝ sin ψ stated in equation (28) that the generation of eddy currents is a nonlinear second order effect, which was proved experimentally in papers [4,5,10], and that the vortices' centers (where the vorticity is maximized) are located in the nodes of the wave pattern, which was also demonstrated experimentally in papers [4][5][6]. Indeed, averaging over time of product of two monochromatic phase-shifted functions must be proportional to sin(ψ + α), where ψ is the phase shift and α is some possible correction, and therefore Ω L ∝ sin(ψ + α).…”

“…For this reason, we first analyse how thin compressible liquid film modifies the wave motion in the linear approximation with respect to the wave steepness and how one can infer the film properties based on the experimental observations. Then we proceed to the secondorder approximation and establish the intensity and the spatial structure of eddy currents (the slow nonlinear motion of passive tracers).We expect that the obtained results can find applications as a particle manipulation technique, see also [6,10] and in geophysics, since the uppermost layer of the ocean is sometimes covered by a monomolecular surface film formed by surfactant [14,15]. Note here that the artificial slicks laid by boats are about a thousand times the thickness of a monomolecular layer.…”

“…Furthermore, for the stationary contribution the first term is localized on the scale of the order of γ/k near the surface in the viscous sublayer, while the second term penetrates deeper, on a distance of the order of 1/k. Let us stress that the nonlinear stationary vorticity (15) has a contribution, which penetrates in the bulk much deeper than the linear horizontal vorticity (10).…”

“…It is natural to describe the horizontal eddy currents [4][5][6] in terms of the vertical vorticity ̟ z . However, in the linear approximation, according to expression (10), there is no contribution to this motion. In this section, we go beyond the approximation and take into account the main nonlinear contribution, which is of the second order in the wave steepness |∇h| ≪ 1.…”

“…On the contrary, the particle motion was observed in freely suspended thin smectic film (can be considered as two-dimensional liquid), which undergoes fast transverse oscillations [10].…”