Growth saturation of unstable thin films on transverse-striped hydrophilic-hydrophobic micropatterns

Abstract

Using three-dimensional numerical simulations, we demonstrate the growth saturation of an unstable thin liquid film on micropatterned hydrophilic–hydrophobic substrates. We consider different transverse-striped micropatterns, characterized by the total fraction of hydrophilic coverage and the width of the hydrophilic stripes. We compare the growth of the film on the micropatterns to the steady states observed on homogeneous substrates, which correspond to saturated sawtooth and growing finger configurations for hydrophilic and hydrophobic substrates, respectively. The proposed micropatterns trigger an alternating fingering–spreading dynamics of the film, which leads to a complete suppression of the contact line growth above a critical fraction of hydrophilic stripes. Furthermore, we find that increasing the width of the hydrophilic stripes slows down the advancing front, giving smaller critical fractions the wider the hydrophilic stripes are. Using analytical approximations, we quantitatively predict the growth rate of the contact line as a function of the covering fraction, and predict the threshold fraction for saturation as a function of the stripe width.