A moving front kinetic Monte Carlo approach to model sessile droplet spreading on superhydrophobic surfaces

Abstract

This study reports the development of a Moving Front kinetic Monte Carlo (MFkMC) algorithm to capture the behaviour of sessile droplets on pillared superhydrophobic surfaces (SHSs). This model depicts the stochastic evolution a droplet on an SHS as a state-by-state process based on the balance of forces acting locally along the droplet interface length. The proposed SHS-based MFkMC (SHS-MFkMC) model was adapted based on a previously-established MFkMC model that captured droplet spreading on an ideally-smooth surface, and it was developed to accommodate for both Cassie mode wetting and to capture Cassie-to-Wenzel (C2W) transitions of the droplet on the SHS. Furthermore, the SHS-MFkMC model incorporates several novel features needed to accommodate for the geometry and the physics of SHS-based droplet spreading. In particular, the proposed approach incorporates the Periodic Unit (PU) method, which was developed to efficiently map a periodic array of SHS pillars for use in models such as MFkMC. Furthermore, the SHS-MFkMC model accommodates for the additional physics necessary to capture the droplet spreading behaviour across the gaps between the pillars of an SHS (i.e., Cassie mode wetting), as well as to incorporate spontaneous and inertia-driven C2W droplet transitions on the solid surface. The capabilities of the full SHS-MFkMC model to capture both radial sessile droplet spread and C2W transitions are compared to experimental results from within the literature. Furthermore, the developed model’s predictive capabilities are further examined via sensitivity analysis to assess the effects of the various system parameters on the model performance and compare them with the expected system results. Overall, these results demonstrate the SHS-MFkMC model’s ability to predict the droplet spreading behaviour of a given SHS design and to assess its likelihood to undergo C2W transitions.