Decomposition driven interface evolution for layers of binary mixtures. II. Influence of convective transport on linear stability

Abstract

We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces, corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the Surface tension number and the ratio of the typical velocities of convective and diffusive transport.

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

“…This should, however, be seen as an example as the present computational approach can be directly adapted to various different physical settings. For instance, one may (i) employ expressions for the bulk free energy density that are adapted to particular polymer blends, (ii) incorporate a concentration-dependent surface tension at the free surface as in [40,29] to model situations where solutal Marangoni forces are present, (iii) apply the approach to films of liquid crystals by replacing the used scalar order parameter (concentration) by a vectorial or tensorial one (director orientation), (iv) incorporate wetting interactions of the mixture with the substrate. That would allow to investigate coupled dewetting of the film and decomposition inside the film.…”

“…For two polymers one would normally expect γ ≈ 10, i.e., their interfacial tension is about one order of magnitude smaller than their polymer-air surface tension. A further discussion of typical parameter values can be found in [29].…”

“…Recently, model-H was re-derived employing phenomenological non-equilibrium thermodynamics to consolidate a number of slightly differing formulations in the literature [40]. The model is supplemented by boundary conditions for velocity and concentration fields at the free surface and the solid substrate and is used to investigate steady stratified layers [40] and their linear stability with respect to lateral perturbations in the film thickness and concentration profiles [29]. A similar approach employing a simpler model was taken in Ref.…”

Fundamentals of Phase Separation in Polymer Blend Thin Films

“…A general vertical dependence of the film composition, which could allow vertical phase separation to occur during a simulation, is typically not included [74]. Films with a vertical dependence of the composition have been studied with regards to stability, but not simulated [82]. An exception is a model of surface roughening of polymer blend films, although this model is not based upon a dewetting film [83].…”

“…This bilayer then breaks up via the surface bifurcation mechanism ( [67] and chapter 4) in which the single value of the order parameter at the film surfaces divides as laterally coexisting phases appear (c), and the film becomes laterally segregated (d). Hence the films undergo lateral phase separation via a transient wetting layer (the instability of the bilayer is studied in [81] and [82], although due to non-diffusive transport mechanisms). When the film is in the bilayer state as in figures 5.5(a) and 5.7(a) there is no significant roughening of the film surface.…”