Dynamics of driven three-dimensional thin films: From hydrophilic to superhydrophobic regimes

Abstract

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

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

“…We use the Lattice-Boltzmann (LB) implementation introduced in detail in Ref. [23,29] in the context of spinodal decomposition of binary fluid mixtures, and which we have used in a previous work [9], where we have focused on the dynamics of unstable thin films in homogeneous solid substrates. In LB, the dynamics are introduced by two sets of velocity distribution functions, f i and g i , which evolve in time according to the discretized Boltzmann equations,…”

“…For hydrophilic substrates, the contact angle of the interface profile is small, making the capillary ridge relatively thin. The instability is thus weakened [9]. Remarkably, if the size of the ridge is sufficiently small, the restoring capillary pressure is strong enough to balance the driving force after the early stages of growth.…”

Thin liquid film flow over substrates with two topographical features

“…In the lubrication approximation it is assumed that the velocity is unidirectional and is a function of the local height h(x) and its derivative. It can be shown that the height of the film in nondimensional form is given by the following fourth-order differential equation [20]: (16) where A = (3Ca 1/3 ) cot(β) is the only controlling parameter. In the expression for A, β stands for the inclination angle of the substrate.…”

“…Recently, the lattice Boltzmann method (LBM) has been increasingly used to study various problems concerning fluids on structured substrates [20][21][22][23][24][25][26][27][28][29][30]. Dupuid and Yeomans [23,24] studied behavior of droplets on topographical substrates.…”

Dynamics of Gravity Driven Three-Dimensional Thin Films on Hydrophilic−Hydrophobic Patterned Substrates

“…As a result, fronts on hydrophilic substrates are stable to longer wavelengths and have smaller growth rates. In a recent work [21], we have validated our numerical method by comparing the linear stability results of the diffuse interface model to those of lubrication theory. A direct comparison is only possible for small dynamic angles and small capillary number, Ca.…”