Probing of thin slipping films by persistent external disturbances

Abstract

This paper investigates the propagation of thickness disturbances on the free surface of a thin viscous liquid film on a solid substrate. On the free surface of the film the disturbances are induced by moving local external pressure perturbations acting on the surface. The analysis is performed by the Fourier-Laplace transform applied to the linearized perturbation equations for small amplitudes. The amplitude of the interface deflection caused by the disturbance, is reconstructed by the inverse Fourier-Laplace transform and numerically evaluated in the long time limit in long wave approximation. The proposed technique appears promising for probing the slip length of a thin film by recording its free surface response to a moving perturbation.