Dynamics of phase separation of sheared inertialess binary mixtures

Bertei, Antonio; Mauri, Roberto

doi:10.1063/1.5144404

Cited by 13 publications

(3 citation statements)

References 89 publications

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“…We assume that the mixture, with composition φ 0 = 0.4, is quenched instantaneously to a temperature well within the unstable region of its phase diagram, with T = − 1 5 (corresponding to a Flory-Huggins parameter, Ψ = 2.5). The reader can refer to Chueh et al [44] for a complete description of model equations.…”

Section: Comparing Mean Field With Full Non-local Modelsmentioning

confidence: 99%

Non-local phase field revisited

Mauri¹,

Bertei²

2021

J. Stat. Mech.

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The phase field model is revisited as an approximation of a full non-local approach. We focus on van der Waals fluids, where the non-local interaction potential consists of short-range repulsion and long-range attraction, characterized by distances d (i.e. a typical molecular size d ≈ 10−9 m) and ℓ ≫ d. The first non-local correction to the thermodynamic limit introduces a density square gradient free energy, expressed in terms of a characteristic length, a. Imposing that the line integral of the non-local free energy functional across an interfacial region must equal the surface tension, we find that a is up to two orders of magnitude larger than the molecular size, in agreement with the local equilibrium assumption. Instead, by finding a directly from the interaction potential, when the attractive force follows a power-law, as in the Lennard-Jones potential, then a ≅ d, which contradicts that a ≈ 10−7 m as from surface tension measurements. Conversely, when the attractive force follows a Debye-like exponentially decaying potential of range ℓ, then a ≈ ℓ ≫ d, in agreement with surface tension measurements and the mean field theory assumption. The other point that we have addressed is determining when the mean field model can be applied. By directly simulating the phase separation of a far-from-critical van der Waals fluid mixture, we find that the growth laws of the mean nuclei size are not modified when higher-order gradient terms are retained. An exponentially decaying attractive potential must be used since the higher-order gradient terms diverge when power-law potentials are considered, confirming that a Lennard-Jones interaction potential is not compatible.

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Section: Comparing Mean Field With Full Non-local Modelsmentioning

confidence: 99%

Non-local phase field revisited

Mauri¹,

Bertei²

2021

J. Stat. Mech.

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“…(2), depends on the concentration gradient and , the capillary width characterizing the thickness of the diffuse interface (interfacial thickness) between the two phases [58][59][60]. It is worth mentioning that the interfacial thickness may range from 10 -9 m up to 10 -7 m for two partially miscible substances [61][62][63]. We need a double-well potential function in order to describe the possible separation of the binary mixture into two distinct phases.…”

Section: Free Energy and Governing Equationsmentioning

confidence: 99%

Influence of evaporation on the morphology of a thin film of a partially miscible binary mixture

Rabani

Sadafi

Machrafi

et al. 2021

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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In this paper, we develop numerical, theoretical and experimental analyses of the different morphologies that can be created by the phase separation phenomena that are induced by solvent evaporation in a thin film of a partially miscible binary mixture. Disregarding hydrodynamic effects, the Cahn-Hilliard-Cook and temperature equations are used to describe the thermodynamics of non-isothermal phase separation in a 2D thin film. Numerical simulations are performed to investigate the interplay between evaporation and phase separation and we examine the effect on the morphology of the film of several parameters such as the initial thickness of the layer, or the initial temperature and concentration of the mixture. Interestingly, the competition between evaporation and phase separation is shown to be the main determinant of the choice between a lamellar or a lateral pattern in the beginning of phase separation. For moderate evaporation rate, the spinodal instability takes place close to the evaporating interface and a lateral structure is formed. For stronger evaporation, the spinodal instability does not occur and a lamellar structure is created. In addition, the mid-or long-term evolution of the system is also considered. The thickness of the film is an important parameter in this analysis and possible modifications of the pattern over time are emphasized. Detailed physical and theoretical interpretations are proposed for the results and experiments in a Hele-Shaw cell that nicely confirm our predictions are presented.

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“…In this way hydrodynamic effects are neglected in the present model so that equation ( 3) is not coupled to the Navier-Stokes equation for the flow field. Very recently the general case, when the capillary number is not large, has been considered in reference [36] for the phase separation of sheared binary mixtures. We also neglect thermal fluctuations.…”

Section: The Modelmentioning

confidence: 99%

Sheared phase-separating binary mixtures with surface diffusion

Gonnella

Lamura

2020

J. Phys. A: Math. Theor.

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The phase-separation process of a binary mixture with order-parameter-dependent mobility under shear flow is numerically studied. The ordering is characterized by an alternate stretching and bursting of domains which produce oscillations in the physical observables. The amplitude of such modulations reduce in time when the mobility vanishes in the bulk phase, disfavoring the growth of bubbles coming from bursted domains. We propose two equations for the typical sizes R x and R y of domains finding the long-time behaviors R x ∼ t 5/4 and R y ∼ t 1/4 in the flow and shear directions, respectively, in the case of surface diffusion. A reduction of the excess viscosity with increasing shear rate is observed in simulations.

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Dynamics of phase separation of sheared inertialess binary mixtures

Cited by 13 publications

References 89 publications

Non-local phase field revisited

Non-local phase field revisited

Influence of evaporation on the morphology of a thin film of a partially miscible binary mixture

Sheared phase-separating binary mixtures with surface diffusion

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