Resonance Coherence Optimization of Structure Formation in Nanofilms Undergoing Thermocapillary Instability

External temporal modulation of time periodic phenomena is a well-known method for inducing resonant behavior in mechanical or electrical systems. While temporal modulation has been used as an effective control mechanism for decades, there have been far fewer studies of external spatial modulation to enforce pattern uniformity and growth in the presence of noise. One such example involves a liquid film undergoing a spinodal instability subject to an externally imposed wavenumber close to the stability threshold of the unforced homogeneous system, which has been shown to induce resonance leading to a bifurcation in equilibrium film shapes. In this talk, we examine a linear instability in molten nanofilms undergoing thermocapillary growth leading to structure formation resembling 3D microlens arrays. Noisy initial conditions, however, are found to generate non-uniform peak heights which accelerate at different rates and significantly compromise pattern fidelity. Using a combination of weakly nonlinear analysis and numerical simulations, we demonstrate the existence of a resonant regime with high spatial coherence leading to microarrays with uniform pitch and height. This regime should provide optimal conditions for fabrication of micro-optical arrays.