Decomposition driven interface evolution for layers of binary mixtures. I. Model derivation and stratified base states

Thiele, Uwe; Madruga, Santiago; Fraštia, Ľubor

doi:10.1063/1.2824404

Cited by 61 publications

(74 citation statements)

References 113 publications

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“…For binary fluids, several variants of model H have been proposed to study thermocapillary flows [50], two-phase flows with a density contrast [51], and influence of convection on phase segregation [52]. The translation between several interrelated models was also discussed [53]. For one-component fluids, phase field models have been developed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Droplet motion in one-component fluids on solid substrates with wettability gradients

Qian

2012

Phys. Rev. E

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CitationDroplet motion in one-component fluids on solid substrates with wettability gradients 2012, 85 (5) Physical Review E Droplet motion on solid substrates has been widely studied not only because of its importance in fundamental research but also because of its promising potentials in droplet-based devices developed for various applications in chemistry, biology, and industry. In this paper, we investigate the motion of an evaporating droplet in onecomponent fluids on a solid substrate with a wettability gradient. As is well known, there are two major difficulties in the continuum description of fluid flows and heat fluxes near the contact line of droplets on solid substrates, namely, the hydrodynamic (stress) singularity and thermal singularity. To model the droplet motion, we use the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] for the hydrodynamic equations in the bulk region, supplemented with the boundary conditions at the fluid-solid interface. In this continuum hydrodynamic model, various physical processes involved in the droplet motion can be taken into account simultaneously, e.g., phase transitions (evaporation or condensation), capillary flows, fluid velocity slip, and substrate cooling or heating. Due to the use of the phase field method (diffuse interface method), the hydrodynamic and thermal singularities are resolved automatically. Furthermore, in the dynamic van der Waals theory, the evaporation or condensation rate at the liquid-gas interface is an outcome of the calculation rather than a prerequisite as in most of the other models proposed for evaporating droplets. Numerical results show that the droplet migrates in the direction of increasing wettability on the solid substrates. The migration velocity of the droplet is found to be proportional to the wettability gradients as predicted by Brochard [Langmuir 5, 432 (1989)]. The proportionality coefficient is found to be linearly dependent on the ratio of slip length to initial droplet radius. These results indicate that the steady migration of the droplets results from the balance between the (conservative) driving force due to the wettability gradient and the (dissipative) viscous drag force. In addition, we study the motion of droplets on cooled or heated solid substrates with wettability gradients. The fast temperature variations from the solid to the fluid can be accurately described in the present approach. It is observed that accompanying the droplet migration, the contact lines move through phase transition and boundary velocity slip with their relative contributions mostly determined by the slip length. The results presented in this paper may lead to a more complete understanding of the droplet motion driven by wettability gradients with a detailed picture of the fluid flows and phase transitions in the vicinity of the moving contact line.

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Section: Introductionmentioning

confidence: 99%

Droplet motion in one-component fluids on solid substrates with wettability gradients

Qian

2012

Phys. Rev. E

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“…(v) Leidenfrost hydrodynamics in binary fluid mixtures is an interesting topic to pursue [18,22,57,58]. In these systems, the Marangoni effects may decisively govern the droplet dynamics even at small solute concentrations [59].…”

Section: Discussionmentioning

confidence: 99%

Hydrodynamics of Leidenfrost droplets in one-component fluids

Qian

2013

Phys. Rev. E

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Using the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], we numerically investigate the hydrodynamics of Leidenfrost droplets under gravity in two dimensions. Some recent theoretical predictions and experimental observations are confirmed in our simulations. A Leidenfrost droplet larger than a critical size is shown to be unstable and break up into smaller droplets due to the Rayleigh-Taylor instability of the bottom surface of the droplet. Our simulations demonstrate that an evaporating Leidenfrost droplet changes continuously from a puddle to a circular droplet, with the droplet shape controlled by its size in comparison with a few characteristic length scales. The geometry of the vapor layer under the droplet is found to mainly depend on the droplet size and is nearly independent of the substrate temperature, as reported in a recent experimental study [Phys. Rev. Lett. 109, 074301 (2012)]. Finally, our simulations demonstrate that a Leidenfrost droplet smaller than a characteristic size takes off from the hot substrate because the levitating force due to evaporation can no longer be balanced by the weight of the droplet, as observed in a recent experimental study [Phys. Rev. Lett. 109, 034501 (2012)].

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“…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%

“…Several groups use model-H to study the dynamics of fluids in the bulk or in a fixed confined geometry [1,35,19,2,41,28,42]. 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].…”

Section: Introductionmentioning

confidence: 99%

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

Fraštia

Thiele

Pismen

2010

Math. Model. Nat. Phenom.

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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.

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Decomposition driven interface evolution for layers of binary mixtures. I. Model derivation and stratified base states

Cited by 61 publications

References 113 publications

Droplet motion in one-component fluids on solid substrates with wettability gradients

Droplet motion in one-component fluids on solid substrates with wettability gradients

Hydrodynamics of Leidenfrost droplets in one-component fluids

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

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