Enslaved phase-separation fronts in one-dimensional binary mixtures

Foard, Eric; Wagner, A. James

doi:10.1103/physreve.79.056710

Cited by 23 publications

(54 citation statements)

References 21 publications

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“…Within this reduced model the SMC effect is incorporated via a spatially varying free energy and the moving substrate is modeled by an advective transport term. Similar problems have been investigated by Krekhov [25] as well as Foard and Wagner [26]. Both consider the pattern formation behind a propagating quench front which results, within certain parameter ranges, in similar structures to those observed here.…”

Section: Introductionsupporting

confidence: 77%

“…A further promising task would be the application of the techniques we have employed here to a similar problem of pattern formation in the wake of a quench front as studied by Krekhov [25] and Foard and Wagner [26]. This would allow one to investigate the structure of the stationary solutions as well as the bifurcations leading to the formation of the various patterns observed by these authors.…”

Section: Discussionmentioning

confidence: 97%

“…and periodic in the Y -direction. Although closely related to the problem considered here, the models investigated by Krekhov [25] as well as Foard and Wagner [26] differ from our approach as they use symmetric free energies that switch the sign of the c 2 term at the location of the moving front; that is, the free energies change from a single-well to a double-well potential. Furthermore, in the here considered monolayer transfer with SMC, the inflow of the surfactant is controlled by the transfer velocity V and is not an independent parameter.…”

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confidence: 99%

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Substrate-mediated pattern formation in monolayer transfer: a reduced model

et al. 2012

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The formation of regular stripe patterns during the transfer of surfactant monolayers from water surfaces onto moving solid substrates can be understood as a phase decomposition process under the influence of the effective molecular interaction between the substrate and the monolayer, also called substrate-mediated condensation (SMC). To describe this phenomenon, we propose a reduced model based on an amended Cahn-Hilliard equation. A combination of numerical simulations and continuation methods is employed to investigate stationary and time-periodic solutions of the model and to determine the resulting bifurcation diagram. The onset of spatiotemporal pattern formation is found to result from a homoclinic and a Hopf bifurcation at small and large substrate speeds, respectively. The critical velocity corresponding to the Hopf bifurcation can be calculated by means of the marginal stability criterion for pattern formation behind propagating fronts. In the regime of low transfer velocities, the stationary solutions exhibit snaking behavior.

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Section: Introductionsupporting

confidence: 77%

Section: Discussionmentioning

confidence: 97%

mentioning

confidence: 99%

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Substrate-mediated pattern formation in monolayer transfer: a reduced model

et al. 2012

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“…Not only phase separation starts close to the walls and is not homogeneous, but domains grow along preferential directions and isotropy symmetry is broken. Our results agree with Furukawa (1992), Foard andWagner (2009) andKrekov (2009), with the main Figure 4. From left to right, concentration patterns for composition 50/50 at times t ¼ 32:5 £ 10 5 , t ¼ 37:5 £ 10 5 , t ¼ 300 £ 10 5 with w ¼ 1, w ¼ 5 £ 10 21 , w ¼ 10 24 , respectively Note: The simulations are performed on a lattice of size L = 512 at very high viscosity Thermal phase separation difference that in our case the thermodynamics of the mixture is fully consistently treated and the temperature fronts have no sharp imposed profile.…”

Section: Numerical Resultssupporting

confidence: 94%

Pattern study of thermal phase separation for binary fluid mixtures

Tiribocchi

Piscitelli

Gonnella

et al. 2011

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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PurposeThe purpose of this paper is to present numerical results about phase separation of binary fluid mixtures quenched by contact with cold walls.Design/methodology/approachThe thermal phase separation is simulated by using a hybrid lattice Boltzmann method that solves the continuity and the Navier‐Stokes equations. The equations for energy and concentration are solved by using a finite‐difference scheme. This approach provides a complete description of the thermo‐hydrodynamic effects in the mixture.FindingsA rich variety of domain patterns are found depending on the viscosity and on the heat conductivity of the mixture. Ordered lamellar structures are observed at high viscosity while domains rounded in shape dominate the phase separation at low viscosity, where two scales characterize the growth of domains.Research limitations/implicationsThe present approach provides a numerical method that can be extended to other systems such as liquid‐vapor or lamellar systems. Moreover, a three‐dimensional study can give a complete picture of thermo‐hydrodynamic effects.Originality/valueThis paper provides a consistent thermodynamic theoretical framework for a binary fluid mixture and a numerically stable method to simulate them.

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“…The velocity of phase separation fronts was determined analytically and/or numerically in [11][12][13] for diffusive dynamics governed by gradient-flow dynamics; however, gradient-flow is much simpler than the situation considered here that includes the momentum of the phases. Rather than a front of polymerization, we are focusing on situations that involve mass redistribution and momentum cannot be neglected.…”

Section: Introductionmentioning

confidence: 99%

Marginal stability and traveling fronts in two-phase mixtures

Cogan

Donahue²,

Whidden³

2012

Phys. Rev. E

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Mixtures of materials that move relative to each other arise in a variety of applications, especially in biophysical problems where the mixture consists of materials with different material properties. The variety of applications leads to a bewildering array of multiphase models, each with slightly different behaviors and interpretations, depending on the application. Some of the behaviors include phase separation, traveling waves and linear instabilities. Because of the variability of the predicted behaviors, there has been considerable attention payed to minimal models to determine the fundamental solutions, bifurcations and instabilities. In this manuscript, we describe a new solution for the simplest two-phase system where both phases are dominated by viscous forces, one phase response to osmotic forces and the phases interact through a drag term. The system develops a traveling front separating an unstable, uniform solution from a patterned, phase separated solution. We seek the velocity of the traveling front and show that, for large diffusion, marginal stability gives a simple and accurate prediction for the velocity. For smaller diffusion constants, the front is 'pushed', and the linear prediction fails.

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Enslaved phase-separation fronts in one-dimensional binary mixtures

Cited by 23 publications

References 21 publications

Substrate-mediated pattern formation in monolayer transfer: a reduced model

Substrate-mediated pattern formation in monolayer transfer: a reduced model

Pattern study of thermal phase separation for binary fluid mixtures

Marginal stability and traveling fronts in two-phase mixtures

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