Dynamics of a liquid film of arbitrary thickness perturbed by a nano-object

We provide a theoretical description of the dynamics of a liquid film perturbed by a nano-object. Our analysis is based on the general dispersion relation for surface perturbations which is valid for films of arbitrary thickness. In the case of thin liquid films the lubrication approximation is retrieved. The relevant time scales are derived and related to the characteristic length scales present in the system. We show that the multi length-scale character of the interfacial deformation is reflected in a wide range of the time scales describing the dynamics of the liquid film. In the case of relaxation under the action of a time-independent perturbation the analytical approximations to the interface evolution are obtained in several time regimes. The case of a general time-dependent perturbation is studied within the point-force approximation which allows determination of the universal aspects of liquid film dynamics. This method is also used to describe the response of the liquid film to a periodic perturbation which simulates the dynamic mode of the tip of an atomic force microscope. It is shown that proper consideration of the thickness of the film leads to results which significantly differ from those obtained within the lubrication approximation even for relatively thin films.