Linear stability analysis of constant volume thin film flows

J. M. GOMBA; J. DIEZ; R. GRATTON; A. G. GONZÁLEZ

Mendoza (Argentina)

Conferencia; IX Reunión sobre Recientes Avances en Física de Fluidos y sus Aplicaciones; 2006

División Fluidos y Plasmas, Asociación Física Argentina

We numerically study the linear stability of a constant volume of fluid spreading down a plate. The base flow does not admit a traveling wave solution, as it is the case when a constant flow is applied far from the advancing front. Consequently, we simultaneously solve the 1D nonlinear evolution of the base flow and the linear equation for the normal modes. We found that the eigenfunctions adopt a well define shape after a short transient stage and travel with the same velocity as the leading contact line.  The spectral analysis indicates the existence of a unique mode with a constant growth rate whose sign of this mode depends on the thickness of the precursor film. The study of the modes amplitude evolution reveals that the wavelength of the dominant mode rapidly decreases with time and reaches an asymptotic value. For vertical spreading, this value is in good agreement with the experimental results. We explore the dependences of the most dominant wavelength with the cross sectional area, A, and the inclination angle of the substrate.