LINEAR-STABILITY AND TRANSIENT GROWTH IN DRIVEN CONTACT LINES

Fluid flowing down an inclined plane commonly exhibits a fingering ins tability in which the. contact line corrugates. We show that below a c ritical inclination angle the base state before the instability is lin early stable. Several recent experiments explore inclination angles be low this critical angle, yet all clearly show the fingering instabilit y. We explain this paradox by showing that regardless of the long time linear stability of the front, microscopic scale perturbations at the contact Line grow on a transient time scale to a size comparable with the macroscopic structure of the front. This amplification is suffici ent to excite nonlinearities and thus initiate finger formation. The a mplification is a result of the well-known singular dependence of the macroscopic profiles on the microscopic length scale near the contact line. Implications for other types of Forced contact lines are discuss ed. (C) 1997 American Institute of Physics.