Instabilities and pattern formation in thin liquid films: from micrometric to nanometric scales

J. A. DIEZ; A. G. GONZÁLEZ

Maceió

Workshop; 9th Ibero-American Workshop on Complex Fluids; 2013

We present a series of theoretical and experimental results regardingthe instability of thin liquid films on solid substrates. We considerdifferent shapes, such as long filaments, rings or simply flat layers,and study their free surface instability due to the effect of surfacetension, solid-liquid intermolecular interaction, and gravity. Theflows are modelled within the long wave approximation, which leads to anon-linear fourth order differential equation for the fluid thickness.This model equation also includes the partial wetting condition betweenthe liquid and the solid. In the theoretical models, we analyze thelinear stability of the equilibrium configurations. In the case of filaments on inclined planes and rings, the problem requires consideringthe presence of fronts with different contact angles, whosedynamics is treated by using a slip model. The linear stability analyses lead to eigenvalue problems that are solved using pseudo spectral methods. The ring problem has additional curvature effects that are taken intoaccount in the calculations. The full non-linear equation is also numerically solved. Whenever possible, the theoretical results arecompared with experiments performed on a submillimetric scale (siliconoils on glass), as well as on nanometric scale (copper films melted bylaser irradiation on SiO2 substrates). The problem of extended flat thin films (layers) in the nanometric scale is strongly influenced by van derWaals forces (vdW). We use the predictions of our stability theory andexperimental evidence to obtain relevant information about theunderlying vdW potentials which describe the interaction between liquidmetals and the silicon substrate.