Inertial and dimensional effects on the instability of a thin film

A. G. GONZÁLEZ; J. A. DIEZ

Tandil

Conferencia; FLUIDOS 2014 - XIII Meeting on Recent Advances in Physics of Fluids and its Applications; 2014

We consider here the effects of inertia on the instability of a flat liquid film, under the effects of capillary and intermolecular forces (van der Waals interaction). Firstly, we peform the linear stability analysis within the lubrication approximation, which shows that the inclusion of inertia does not produce other regions of instability other than the one previously known from the inertialess case. The study shows that the most affected feature of the instability under a decrease of the Ohnesorge number, Oh, is the growth rates of the unstable modes, including that of the maximum growth, $omega_m$. The corresponding wavelength, $lambda_m$, is not practically affected, while the critical (marginal) wavelength does not change at all. In order to put in evidence the effects of the bidimensional aspects of the flow, we also calculate the dispersion relation of the instability from the complete Navier-Stokes equation. Interestingly, within the linear approximation valid for early times, the van der Waals term can be studied as a repulsive gravitational force. This fact allows to perform a linear stability analysis, which is compared with the lubrication prediction and numerical simulations of the N-S equations performed with a Volume of Fluid (VoF) method.