Modelling thin-film dewetting on structured substrates and templates: Bifurcation analysis and numerical simulations

Abstract

We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.

Liquid transport generated by a flashing field-induced wettability ratchet

“…1 (d)). This behavior is similar to dewetting on a heterogeneous substrate [15,16]. After a transient it results in the collection of all the liquid in drops situated at the patches of maximal voltage ( Fig.…”

“…(iii) In an ideal situation only one drop remains, corresponding to the equilibrium structure on the heterogeneous wettability pattern produced by the ratchet potential [16]. asymmetry is given by a = L, i.e.j max =hL/2T andv max = L/2T .…”

Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

“…Further studies may also (v) consider substrates with heterogeneities, i.e., with topographical or chemical variations. Although in the latter case experimental results exist for binary mixtures [24,32,13], theoretical results are at present only available for films of simple liquids [22,23,6,39,30].…”

Dry-spot nucleation in thin liquid films on chemically patterned surfaces

“…Sehgal et al (2002) and Zhang et al (2003) performed experiments regarding the dewetting of polystyrene layers on periodically heterogeneous substrates. Thiele et al considered the morphology evolution in a thin liquid film on substrates with one-and two-dimensional sinusoidal surface energy modulation (Brusch et al 2002;Thiele et al 2003;Pototsky et al 2004). Kao et al (2006) investigated the rupture of thin liquid films on substrates with sinusoidal and square-wave resonant surface energy patterning.…”

“…This allows parametrization of arbitrary experimental disjoining pressure isotherms, at least over a finite range of film thicknesses. While several groups have already studied dewetting of thin liquid films on structured surfaces (Kargupta et al 2000;Kargupta and Sharma 2002;Kargupta and Sharma 2003;Sehgal et al 2002;Zhang et al 2003;Brusch et al 2002;Thiele et al 2003;Pototsky et al 2004;Kao et al 2006;Julthongpiput et al 2007;Zhu et al 2010), most of the results have been obtained for small film thicknesses on order of ten times the precursor layer thickness, very specific disjoining pressure isotherms with more than one inflection point or neglecting the influence of gravity. For industrial applications relevant film thicknesses range typically between 1 and 10 lm, which is several orders of magnitude above the precursor layer thickness such that the influence of gravity can be substantial if not decisive.…”