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.
We demonstrate that the Einstein relation for the diffusion of a particle in the random-energy landscape with the Gaussian density of states is an exclusive one-dimensional property and does not hold in higher dimensions. We also consider the analytical properties of the particle velocity and diffusivity for the limit of weak driving force and establish a connection between these properties and dimensionality and spatial correlation of the random-energy landscape.