The electrified pressure-driven instability of thin liquid films, also called electrohydrodynamic (EHD) lithography, is a pattern transfer method, which has gained much attention due to its ability in the fast and inexpensive creation of novel micro- and nano-sized features. In this chapter, the mathematical model describing the dynamics and spatiotemporal evolution of thin liquid film is presented. The governing hydrodynamic equations, intermolecular interactions, and electrostatic force applied to the film interface and assumptions used to derive the thin film equation are discussed. The electrostatic conjoining/disjoining pressure is derived based on the long-wave limit approximation since the film thickness is much smaller than the characteristic wavelength for the growth of instabilities. An electrostatic model, called an ionic liquid (IL) model, is developed which considers a finite diffuse electric layer with a comparable thickness to the film. This model overcomes the lack of assuming very large and small electrical diffuse layer, as essential elements in the perfect dielectric (PD) and the leaky dielectric (LD) models, respectively. The ion distribution within the IL film is considered using the Poisson-Nernst-Planck (PNP) model. The resulting patterns formed on the film for three cases of PD-PD, PD-IL, and IL-PD double layer system are presented and compared.
Part of the book: Electric Field