Dynamics of a thin liquid film interacting with an oscillating nano-probe
The dynamic interaction between a local probe and a viscous liquid film, which provokes the deformation of the latter, has been studied. The pressure difference across the air–liquid interface is calculated with a modified Young–Laplace equation, which takes into account the effects of gravity, surface tension, and liquid film–substrate and probe–liquid attractive interaction potentials. This pressure difference is injected into the lubrication approximation equation, in order to depict the evolution of a viscous thin-film. Additionally, a simple periodic function is added to an average separation distance, in order to define the probe motion. The aforementioned coupled equations, which describe the liquid film dynamics, were analysed and numerically solved. The liquid surface undergoes a periodic motion: the approaching probe provides an input energy to the film, which is stored by the latter by increasing its surface deformation; afterwards, when the probe moves away, an energy dissipation process occurs as the surface attempts to recover its original flat shape. Asymptotic regimes of the film surface oscillation are discerned, for extreme probe oscillation frequencies, and several length, wavenumber and time scales are yielded from our analysis, which is based on the Hankel transform. For a given probe–liquid–substrate system, with well-known physical and geometric parameters, a periodic stationary regime and instantaneous and delayed probe wetting events are discerned from the numerical results, depending on the combination of oscillation parameters. Our results provide an interpretation of the probe–liquid film coupling phenomenon, which occurs whenever an AFM test is performed over a liquid sample.