Bifurcation and Nonlinear Analysis of 3D Programmable Formations in Thermocapillary Modulated Nanofilms*

While temporal modulation of a driving field provides an effective means of controlling fluid systems, far less attention has been focused on spatial modulation to enforce high uniformity in pattern and structure growth, especially in phenomena triggered by noise. Here we present a bifurcation and nonlinear analysis of thermocapillary modulated liquid nanofilms prone to an intrinsic 3D instability triggered by noise. In the absence of external modulation, the film develops 3D protrusions separated by tens of microns whose amplitude and spacing are never uniform. External modulation is shown to corral the formations into uniform registry. We examine spatial modulation frequencies both close and far from the frequency of the instrinsic instability to probe early, intermediate and late time behavior as the formations evolve through different stages of development. Frequency analysis coupled with simulations of the governing nonlinear interface equation elucidate the mechanism responsible for bifurcation, influenced strongly by the modulation amplitude. Based on our findings, we provide estimates of various experimental quantities for thermocapillary patterning of microlens arrays.