An Acousto–Gravitational Balance in Climbing Films of liquid*

A balance between acoustical, capillary, and gravitational stresses determines the extent in which a liquid film may climb over a vertical substrate, when it is excited by a MHz-frequency acoustic wave. Moreover, the rise level of the film against gravity serves as a simple tool for the measurement of the acoustic forcing in the film. The experimental system is made from a 20 MHz SAW (surface acoustic wave) actuator. The actuator is mounted on a vertical stage, so that its edge comes in contact with a reservoir of liquid. Partially wetting films of water and surfactant solutions, which satisfy finite three phase contact angles between the liquid, vapor, and the solid substrate, appear to reach a steady state height above the level of liquid in the reservoir. The theory predicts that the steady state height is a product of the balance between acoustical, capillary, and gravitational stresses in the film. In contrast, fully wetting films of oil are found to continuously wet and climb over the SAW device, ignoring gravity. The theory shows that the acoustical stress balances gravitational stress in the nearly flat oil film. The balance stabilises the thickness of the oil film, supporting its continuous rise.