Simulation of polymer rheology in an electrically induced micro- or nano-structuring process based on electrohydrodynamics and conservative level set method
An electrically induced structuring process, such as an electrohydrodynamic (EHD) approach for fabricating polymeric micro-/nano-structures in various micro-/nano-devices, was performed by applying a voltage to an electrode pair consisting of a planar or structured template and a polymer-coated substrate sandwiching an air gap, resulting in either periodic columns or template-modulated structures. Analytical approaches were explored to characterize this micro-/nano-structuring process, based on a linear thermodynamic instability of the polymer film combining capillary waves and electrostatic forces, leading to a definition of “most unstable wavelength” in relation to various process variables such as external voltage, polymer film thickness, and so on. For mathematical simplicity, the linear stability analysis was only carried out to demonstrate an initiation of the polymer structuring under electrical induction by an infinite planar template, and cannot numerically visualize the evolution of the polymer structure which grows from an initially flat film upwards to the template underside. Therefore, a numerical modelling of such a process, which is capable of demonstrating a full-cycle evolution of the polymer structuring, is desirable to provide an in-depth insight into this electrically induced structuring technique. This paper presents a detailed numerical formulation for simulating the rheological behaviour for this structuring process based on EHD equations and a conservative level set approach. Firstly, a numerical simulation is performed to demonstrate the dynamic evolution of periodic structures for a planar (non-structured) template and compared with the linear instability analysis to validate the effectiveness of the proposed numerical modelling. Then simulations are performed to numerically visualize the evolution of a polymer structure induced by a structured template, with a subsequent discussion about the influences of some critical process variables, such as voltage, air gap, polymer thickness, depth of template patterns, and so on, on the electrohydrodynamic rheology of the polymer.