Fractal Patterns in the Nanofluidic Sessile Droplet Drying

The two-dimensional lattice-gas kinetic Monte Carlo model is used to simulate the process of a nanofluidic sessile droplet drying with a moving contact line in this study. A new modeling approach is implemented by introducing the two-dimensional circular simulation domain in order to operate with the top view of spherical cap of a drying droplet. The non-uniform effective chemical potential function is applied to the model, taking into account the thickness profile of a droplet. Although our simulation is two-dimensional, this modification mimics to some extent the three-dimensional nature of a mesoscopic sessile droplet. Hence we introduce a new, pseudo-3D modification of Monte Carlo simulation model, i.e., a 2D model with additional dependence of the chemical potential on the local droplet thickness. In result, the evaporation-induced nanoparticle self-assembly led to the formation of a fractal-like structure, which is observed in simulation runs. Interestingly, the fractal-shaped patterns obtained in numerous simulations are comparable to the experimentally recorded images of dried nanoparticle structures. The difference in average fractal dimensions of simulated and experimental images is estimated to be less than 5%. It is suggested that the lattice-gas model provides an easy way to reproduce the formation of branched structures from nanoparticles during the drying of spherical sessile droplets.