Drop Size Evolution during the Phase Separation of Liquid Mixtures

Califano, Filomena; Mauri, Roberto

doi:10.1021/ie030201m

Cited by 23 publications

(22 citation statements)

References 31 publications

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“…Then, as soon as the nuclei reach a limit size of about 1 mm, which is approximately one-tenth the capillary length in the experiments by Califano and Mauri (2004) , they rapidly sediment, leading to an equilibrium state with two coexisting phases, within a time of about 10 s, in agreement with experimental observations ( Califano and Mauri, 2004;Califano et al, 2005 ).…”

Section: Mixing and Demixingsupporting

confidence: 86%

“…As shown by Santonicola et al (2001) , this process is very slow, as after one hour the interfacial region is only a few millimeters thick. On the other hand, when the mixture is quenched back to 20 °C, the ensuing phase separation process is very rapid and a two-phase equilibrium state is reached within a few seconds ( Califano and Mauri, 2004;Califano et al, 2005 ). To explain this behavior, let us describe first the mixing process, assuming that the mixture is initially quiescent and phase separated (with > 2) along a flat interface at z = 0 , and is then instantaneously heated, so that < 2 at all times t ≥ 0.…”

Section: Mixing and Demixingmentioning

confidence: 99%

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Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

Lamorgese

Mauri

2016

International Journal of Multiphase Flow

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a b s t r a c tA weakly nonlocal phase-field model is used to define the surface tension in liquid binary mixtures in terms of the composition gradient in the interfacial region so that, at equilibrium, it depends linearly on the characteristic length that defines the interfacial width. Contrary to previous works suggesting that the surface tension in a phase-field model is fixed, we define the surface tension for a curved interface and far-from-equilibrium conditions as the integral of the free energy excess (i.e., above the thermodynamic component of the free energy) across the interface profile in a direction parallel to the composition gradient. Consequently, the nonequilibrium surface tension can be widely different from its equilibrium value under dynamic conditions, while it reduces to its thermodynamic value for a flat interface at local equilibrium. In nonequilibrium conditions, the surface tension changes with time: during mixing, it decreases as the inverse square root of time, while in the linear regime of spinodal decomposition, it increases exponentially to its equilibrium value, as nonlinear effects saturate the exponential growth. In addition, since temperature gradients modify the steepness of the concentration profile in the interfacial region, they induce gradients in the nonequilibrium surface tension, leading to the Marangoni thermocapillary migration of an isolated drop. Similarly, Marangoni stresses are induced in a composition gradient, leading to diffusiophoresis. We also review results on the nonequilibrium surface tension for a wall-bound pendant drop near detachment, which help to explain a discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart from a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we present new results from phase-field simulations of the motion of an isolated droplet down an incline in gravity, showing that dynamic contact angle hysteresis can be explained in terms of the nonequilibrium surface tension.

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Section: Mixing and Demixingsupporting

confidence: 86%

Section: Mixing and Demixingmentioning

confidence: 99%

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

Lamorgese

Mauri

2016

International Journal of Multiphase Flow

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“…In previous works we have shown that, for a low-viscosity binary system in a uniform temperature field, this process is driven by the convection induced by phase transition, which is responsible for the enhanced coalescence between single-phase microdomains. [1][2][3][4][5][6] When the temperature field is inhomogeneous, however, another effect becomes relevant, namely, convective heat transport due to phase transition. This effect is well known in vapor-liquid phase transitions, where the density mismatch between the component phases drives a strong, turbulent convection which enhances heat transfer.…”

Section: Introductionmentioning

confidence: 99%

“…2,3,5,6,17 Experimentally, when a nearly isopycnic, low-viscosity binary mixture is quenched deeply and rapidly into the spinodal region of its phase diagram in the presence of a temperature gradient, it develops a unidirectional and large-scale motion of the nucleating droplets along the direction of the temperature gradient 3,14 which, even in the absence of buoyancy, is responsible for a rapid and complete segregation of the mixture. This was initially observed by Califano and Mauri, 3 who used a nearly isopycnic hexadecane-acetone mixture in a temperature-regulated cell for investigating drop size evolution in a phaseseparating system.…”

Section: Introductionmentioning

confidence: 99%

Liquid mixture convection during phase separation in a temperature gradient

Lamorgese

Mauri

2011

Physics of Fluids

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We simulate the phase separation of a low-viscosity binary mixture, assuming that the fluid system is confined between two walls that are cooled down to different temperatures below the critical point of the mixture, corresponding to quenches within the unstable range of its phase diagram. Spinodal decomposition patterns for off-critical mixtures are studied numerically in two dimensions in the creeping flow limit and for a large Lewis number, together with their dependence on the fluidity coefficient. Our numerical results reproduce the large-scale unidirectional migration of phase-separating droplets that was observed experimentally by Califano et al. ͓"Large-scale, unidirectional convection during phase separation of a density-matched liquid mixture," Phys. Fluids 17, 094109 ͑2005͔͒, who measured typical speeds that are quite larger than the Marangoni velocity. To understand this finding, we then studied the temperature-gradient-induced motion of an isolated droplet of the minority phase embedded in a continuous phase, showing that when the drop is near local equilibrium, its speed is of the same order as the Marangoni velocity, i.e., it is proportional to the unperturbed temperature gradient and the fluidity coefficient. However, far from local equilibrium, i.e., for very large unperturbed temperature gradients, the drop first accelerates to a speed that is larger than the Marangoni velocity, then, later, it decelerates, exhibiting an increase-decrease behavior, as described by Yin et al. ͓"Thermocapillary migration of nondeformable drops," Phys. Fluids 20, 082101 ͑2008͔͒. Such behavior is due to the large nonequilibrium, Korteweg-driven convection, which at first accelerates the droplets to relatively large velocities, and then tends to induce an approximately uniform inside temperature distribution so that the drop experiences an effective temperature gradient that is much smaller than the unperturbed one and, consequently, decelerates.

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“…with Ψ = 2.1. We chose this particular value of Ψ because Vol.79 (2011) that is the Margules parameter of the water-acetonitrile-toluene mixture at 20 • C that we used in our own experimental work [17,18,53,7,46]. The first row of images represents the results for N P e = 0, i.e.…”

Section: Vol79 (2011)mentioning

confidence: 99%

Phase Field Approach to Multiphase Flow Modeling

2011

Self Cite

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We review the phase field (otherwise called diffuse interface) model for fluid flows, where all quantities, such as density and composition, are assumed to vary continuously in space. This approach is the natural extension of van der Waals' theory of critical phenomena both for one-component, two-phase fluids and for partially miscible liquid mixtures. The equations of motion are derived, assuming a simple expression for the pairwise interaction potential. In particular, we see that a non-equilibrium, reversible body force appears in the Navier-Stokes equation, that is proportional to the gradient of the generalized chemical potential. This, so called Korteweg, force is responsible for the convection that is observed in otherwise quiescent systems during phase change. In addition, in binary mixtures, the diffusive flux is modeled using a Cahn-Hilliard constitutive law with a composition-dependent diffusivity, showing that it reduces to Fick's law in the dilute limit case. Finally, the results of several numerical simulations are described, modeling, in particular, a) mixing, b) spinodal decomposition, c) nucleation, d) enhanced heat transport, e) liquid-vapor phase separation

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Drop Size Evolution during the Phase Separation of Liquid Mixtures

Cited by 23 publications

References 31 publications

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

Liquid mixture convection during phase separation in a temperature gradient

Phase Field Approach to Multiphase Flow Modeling

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