Inverse Solution for High Fidelity Shaping of Slender Liquid Films by Electrohydrodynamic Patterning

Electrohydrodynamic patterning describes a technique whereby a slender liquid film is deformed into complex shapes by application of a strong transverse electric field pattern and then solidified in-situ. Most studies have focused on the forward problem in which the evolution equation for the liquid interface, which is subject to an applied field pattern, is propagated in time. Since the governing equation is 4th order and highly nonlinear, field patterns based on an intuitive approach typically fail to yield high fidelity shapes required for stringent micro-optical applications. In this study, we tackle the inverse problem and identify the optimal field patterns required to achieve specific shapes in a given time interval by posing the problem as a PDE-constrained optimization problem. We illustrate this methodology, which can efficiently handle both static and time-dependent field distributions, by deforming a flat film into a lens or waveguide. This ttalk shall conclude with discussion of optimal parameter sets and limitations of this approach.