Numerical characterization of electrohydrodynamic micro- or nanopatterning processes based on a phase-field formulation of liquid dielectrophoresis.

The electrohydrodynamic patterning of polymer is a unique technique for micro- and nanostructuring where an electric voltage is applied to an electrode pair consisting of a patterned template and a polymer-coated substrate either in contact or separated by an air gap to actuate the deformation of the rheological polymer. Depending on the template composition, three processes were proposed for implementing the EHDP technique and have received a great amount of attention (i.e., electrostatic force-assisted nanoimprint, dielectrophoresis-electrocapillary force-driven imprint, and electrically induced structure formation). A numerical approach, which is versatile for visualizing the full evolution of micro- or nanostructures in these patterning processes or their variants, is a desirable critical tool for optimizing the process variables in industrial applications of this structuring technique. Considering the fact that all of these processes use a dielectric and viscous polymer (behaving mechanically as a liquid) and are carried out in ambient air, this Article presents a generalized formulation for the numerical characterization of the EHDP processes by coupling liquid dielectrophoresis (L-DEP) and the phase field of the air-liquid dual phase. More importantly, some major scale effects, such as the surface tension, contact angle, liquid-solid interface slip, and non-Newtonian viscosity law are introduced, which can impact the accuracy of the numerical results, as shown experimentally by our electrical actuation of a dielectric microdroplet as a test problem. The numerical results are in good agreement with or are well explained by experimental observations published for the three EHDP processes.