Stability of a two-layer binary-fluid system with a diffuse interface

Abstract

The phase separation of a binary fluid can lead to the creation of two horizontal fluid layers with different concentrations resting on a solid substrate and divided by a diffuse interface. In the framework of the Cahn-Hilliard equation, it is shown analytically and numerically that such a layered system is subject to a transverse instability that generates a slowly coarsening multidomain structure. The influence of gravity, solutocapillary effect at the free boundary, and Korteweg stresses inside the diffuse interface on the stability of the layers is studied using the coupled system of the hydrodynamic equations and the nonlinear equation for the concentration ͑H model͒. The parameter regions of long-wave instabilities are found.

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

“…The dynamics of a fluid binary mixture is often described by the so called model-H, which couples transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) 26,27 . It has been extensively studied for various isothermal and non-isothermal settings [27][28][29][30][31][32][33][34] . None, however, involves beside the diffuse internal interface a free liquid-gas interface, i.e., a free surface.…”

Fundamentals of Phase Separation in Polymer Blend Thin Films

“…However, the film composition has no vertical dependence in these models, which means that a meaningful preferential surface attraction of blend components cannot be included. A vertical dependence has been included by way of two-layer models, including models with immiscible fluid layers [79,80] and layers with a diffuse boundary for films with no preferential surface attraction [81]. A schematic of a two-layer model is given in figure 5.2.…”

“…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.…”

Pattern Formation in Polymer Blend Thin Films: Surface Roughening Couples to Phase Separation

“…However, the film composition has no vertical dependence in these models, so a meaningful preferential surface attraction of blend components cannot be included. Two-layer models exist, including models with immiscible fluid layers [15,16] and layers with a diffuse boundary for films with no preferential surface attraction [17]. However, a general vertical composition dependence, which could allow vertical phase separation to occur during a simulation, is typically not included [9], though such a case has been studied with regards to stability but not simulated [18].…”

“…This bilayer then breaks up via the mechanism given in Ref. [27], which describes how the order parameter at the film surfaces divides as the film becomes laterally segregated (bilayer instability is also studied in [17] and [18]). When the film is in the bilayer state (Figs.…”