Modelling of the dewetting of ultra-thin liquid films on chemically patterned substrates: linear spectrum and deposition patterns

Liquid films of nanometric thickness are prone to spinodal dewetting driven by disjoining pressure, meaning that a non-wetting liquid film of homogeneous thickness in the range of tens of nanometers will spontaneously break into droplets. The surface energy of the underlying solid substrate heavily influences the dynamics and resulting droplet configurations. Here, we study the dewetting of thin liquid films on physically flat but chemically heterogeneous substrates using the thin film equation. We use linear stability analysis (LSA) to describe and predict the system's behavior until the film ruptures and compare it to numerical simulations. The good agreement between the numerical solutions and the LSA allows us to propose a method for measuring surface energy patterns from early time-step film height profiles with good precision. Furthermore, we study the non-linear dynamics and the eventually formed droplet pattern by numerical simulations. This offers insights into the dependency of the resultant droplet arrays on shape, feature size, and magnitude of the chemical patterning of the underlying substrate.