Large-scale, unidirectional convection during phase separation of a density-matched liquid mixture

Califano, Filomena; Mauri, Roberto; Shinnar, Reuel

doi:10.1063/1.2065887

Cited by 18 publications

(16 citation statements)

References 25 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: 78%

“…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: 78%

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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“…Mauri et al have examined many systems near consolute points and observed fluid flow caused by gradients in chemical potential (Poesio et al 2006;Gupta et al 1999;Santonicola et al 2001;Mauri et al 2003;Califano et al 2005;Lamorgese and Mauri 2005). Lamorgese and Mauri simulated a two-phase system quenched into the one-phase region and observed that convection coupled to diffusion via the body force slowed down mixing (Lamorgese and Mauri 2006).…”

Section: Introductionmentioning

confidence: 96%

Numerical Simulations of Convection Induced by Korteweg Stresses in a Miscible Polymer–Monomer System: Effects of Variable Transport Coefficients, Polymerization Rate and Volume Changes

Chekanov

Wyatt

Bessonov

et al. 2008

Microgravity Sci. Technol

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We modeled a miscible polymer-monomer system with a sharp transition zone separating the two fluids to determine if convection analogous to Marangoni convection in immiscible fluids could occur because of thermal and concentration gradients. We considered three cases: with a temperature gradient along the transition zone, with a variable transition zone width, and one with a gradient in the conversion of polymerization. Using the Navier-Stokes equations with an additional term, the Korteweg stress term arising from non-local interactions in the fluid, we demonstrated with realistic parameters that measurable fluid flow would result in the absence of buoyancy-driven convection for all three cases. We show that even if the Korteweg stress is not a function of temperature, the increase in the diffusion coefficient with temperature can result in convection because a gradient in the transition zone width develops. We also examine the effects of a polymer viscosity that is not only a function of concentration but also temperature. We demonstrate that a constant flux of heat, as would be realistic for a heating element in contact with the side of the reactor, would produce a greater flow than a linear thermal gradient parallel to the transition zone. We demonstrate that qualitatively different flow patterns can be realized by using unusual initial conditions that could be realized with different masks for the photopolymerization. We also demonstrate that the volume change during polymerization and caused by side heating could not cause significant fluid flow that would confound the observation of Korteweg-stress induced flows. To avoid buoyancy-driven convection, the experiment would have to be performed in microgravity.

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“…8 Temperature-gradient effects on phase-separating binary liquid mixtures have been investigated in the past, both numerically [8][9][10] and experimentally. [11][12][13][14][15] In particular, Marangoni-like migration of droplets undergoing phase separation has been studied numerically under particular flow conditions, 10,16 although none of these works have focused on thermocapillary effects systematically. Other numerical studies [8][9][10] have focused on the effects of temperature gradients on diffusion-driven phase separation and, specifically, on how the morphology of a very viscous binary system, where both the molar and the thermal Peclet numbers of the mixture can be assumed to be negligible, evolves during phase separation with an imposed temperature gradient.…”

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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Large-scale, unidirectional convection during phase separation of a density-matched liquid mixture

Cited by 18 publications

References 25 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

Numerical Simulations of Convection Induced by Korteweg Stresses in a Miscible Polymer–Monomer System: Effects of Variable Transport Coefficients, Polymerization Rate and Volume Changes

Liquid mixture convection during phase separation in a temperature gradient

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