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… Show more
“…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.…”
Section: Discussionmentioning
confidence: 99%
“…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].…”
Section: Computational Procedures and Parametersmentioning
confidence: 99%
“…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.…”
Abstract. We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem is numerically solved employing a Finite Element Method on an adaptive grid. The developed numerical scheme allows us to obtain the coupled steady-state film thickness profile and the concentration profile inside the film. As an example we determine steady state profiles for a reflection-symmetric twodimensional droplet for various surface tensions of the film and various preferential attraction strength of one component to the substrate. We discuss the relation of the results of the present diffuse interface theory to the sharp interface limit and determine the effective interface tension of the diffuse interface by several means.
“…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.…”
Section: Discussionmentioning
confidence: 99%
“…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].…”
Section: Computational Procedures and Parametersmentioning
confidence: 99%
“…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.…”
Abstract. We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem is numerically solved employing a Finite Element Method on an adaptive grid. The developed numerical scheme allows us to obtain the coupled steady-state film thickness profile and the concentration profile inside the film. As an example we determine steady state profiles for a reflection-symmetric twodimensional droplet for various surface tensions of the film and various preferential attraction strength of one component to the substrate. We discuss the relation of the results of the present diffuse interface theory to the sharp interface limit and determine the effective interface tension of the diffuse interface by several means.
“…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].…”
Section: Models Of Deformable Fluid Filmsmentioning
confidence: 99%
“…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.…”
Section: Antisymmetric Films and Asymmetric Filmsmentioning
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.