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

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.

Figure 1

(a) The horizontal vorticity ${\varpi }_{\alpha }$, which arises due to the air viscosity, is slightly rotated by the surface tilt. As a result, this nonlinear interaction produces the vertical vorticity ${\varpi }_z$—vortices in the film plane; (b) vortices in the film plane visualized by disk-shaped islands. This vortex flow corresponds to the excitation of $(3,1)$ and $(1,3)$ bending modes slightly time-shifted relative to each other.

Figure 2

(a) Experimental setup for the study of vibration and vortex motion in the liquid crystal membrane: 1, guide rails; 2, mobile barriers; 3, liquid crystal membrane; 4, digital camera; 5, condenser microphone connected to the acoustic power meter; 6, laser; 7, screen; 8, loudspeaker; 9, low-frequency generator based on the PC sound card; 10, computer. (b) Acoustic excitation by the waveguide: 1, sound waveguide; 2, frame with the membrane; 3, sound generator.

Figure 3

Horizontal streaming at a high acoustic pressure: (a) Vortex visualized by disk-shaped islands. The dotted line shows the trajectory of islands. (b) Four vortices visualized by an excess number of islands.

Figure 4

Experimental results of the acoustic streaming study for a slightly rectangular film: $a=16.5$ mm, $b=17$ mm. (a) The size of the laser-beam projection on a screen after reflection from a surface of the film vs the frequency of the acoustic excitation. (b) Angular velocity of islands depending on the acoustic frequency; $\mathrm{\Delta }p=0.2$ Pa. (c) Trajectory of the solidlike island. Point C is the membrane center; $\mathrm{\Delta }p=0.2$ Pa, $\nu =350$ Hz. (d) The velocity of the island on the trajectory depending on time point C corresponds to the passage of the island near the membrane center; $\mathrm{\Delta }p=0.2$ Pa, $\nu =350$ Hz. (e) Island angular velocity depending on the squared amplitude of the acoustic pressure; $\nu =350$ Hz.