Capillary instabilities of liquid films inside a wedge

We consider a liquid meniscus inside a wedge of included angle 2 beta that wets the solid walls with a contact angle theta. The meniscus has a convex interface that satisfies pi/2 < theta+beta < pi. The capillary pressure gradient due to a small disturbance of the location of the contact line moves fluid from a neck region to a bulge region, causing instabilities. A dynamic contact-line condition is considered in which the contact angle varies linearly with the slipping speed of the contact line with a slope of G:G=0 representing perfect slip and a fixed contact angle. A nonlinear thin film equation is derived and numerically solved for the shape of the contact line as a function of parameters. The result for G=0 shows that the evolution process consists of a successive formation of bulges and necks in decreasing length and time scales, eventually resulting in a cascade structure of primary, secondary, and tertiary droplets. When G > 0, there is a similar but slower nonlinear evolution process. The numerical results agree qualitatively with very recent experimental results. (c) 2007 American Inst of Phys.