The Multi-layer Rayleigh-Taylor Instability

Abstract

Complex, textured surfaces are ubiquitous throughout nature and industry where they serve as hydrophobic, self-cleaning, adhesive, and abrasive materials. This work details a passive experimental methodology for fabricating materials with periodic arrays of spike surface structures through the Rayleigh-Taylor instability (RTI). Inspired, by the growth of natural formations such as stalactites and icicles, this methodology involved repeatedly coating layers of liquid-curing polymer on to acrylic substrates, inducing the RTI, and allowing the polymer to cure in order to produce a solid elastomer material. The layer-by-layer (discrete) growth rate of the surface structures was found to be linear, on average, and was quantified across a variety of length scales. Two distinct growth phases were identified and discrete growth rates for each phase were determined. The curvature of the spikes was characterized by mapping their shape to a piece-wise function composed of a thin film region and a pendant drop region; this model was confirmed numerically using a shooting methodology. Lastly, the 2-D spatial arrangement of the surface structures was explored and the area density of spikes was found to increase with the number of layers. Looking forward, these materials may be modified for promising applications in omniphobic materials, packaging, or soft robotics.