Dynamical relaxation of the surface tension of miscible phases

Ma, Wen-Jong; Keblinski, Pawel; Maritan, Amos; Koplik, Joel; Banavar, Jayanth R.

doi:10.1103/physrevlett.71.3465

Cited by 21 publications

(12 citation statements)

References 10 publications

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“…These data are not affected by bulk fluctuations, since their amplitude is very small at equilibrium. The q −2 dependence is also apparent at large wave vectors in the subsequent intensity distributions This shows that an effective surface tension is present during the nonequilibrium diffusive remixing, in agreement with the suggestion by some authors that an effective surface tension should exist between miscible fluids in the presence of a composition gradient [3][4][5][6][7][8]25,26]. This surface tension is usually assumed to be related to the concentration gradient by the mean-field equilibrium Cahn-Hilliard relation [27] …”

Section: Resultssupporting

confidence: 66%

Capillary-to-bulk crossover of nonequilibrium fluctuations in the free diffusion of a near-critical binary liquid mixture

2001

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We have studied the nonequilibrium fluctuations occurring at the interface between two miscible phases of a near-critical binary mixture during a free diffusion process. The small-angle static scattered intensity is the superposition of nonequilibrium contributions due to capillary waves and to bulk fluctuations. A linearized hydrodynamics description of the fluctuations allows us to isolate the two contributions, and to determine an effective surface tension for the nonequilibrium interface. As the diffuse interface thickness increases, we observe the cross-over of the capillary-wave contribution to the bulk one.OCIS: 240.6700, 290.5870

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Section: Resultssupporting

confidence: 66%

Capillary-to-bulk crossover of nonequilibrium fluctuations in the free diffusion of a near-critical binary liquid mixture

2001

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“…(2) is not necessarily confined to systems at thermodynamic equilibrium. In fact, a similarly defined nonequilibrium surface tension had already been introduced in Ma et al (1993) , Osborn et al (1995) and Swift et al (1996) , particularly for checking their lattice Boltzmann scheme in terms of the rate of decay of a flat interface (initially at equilibrium) which is instantaneously brought from the two-phase to the one-phase region. However, these authors did not clarify the role of the nonequilibrium surface tension in diffuse-interface models of emulsion flows far from the critical point, which is the primary objective of the work reported herein.…”

Section: Model Descriptionmentioning

confidence: 98%

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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“…To our knowledge, the only comparable study in the past has been the disappearance of an interface in a vapour-liquid or binary liquid mixture after an 'antiquench' (sudden increase in temperature) [13]. It is indeed striking that we do not find any evidence of the delayed appearance of mesophases due to metastability, unlike that seen experimentally in temperature-jump experiments [14], nor do we find any systematic displacement of the mesophase boundaries by the strong concentration gradients present at such early times.…”

Section: Eigenvalues Ofmentioning

confidence: 99%

Mesoscale Simulations of Surfactant Dissolution and Mesophase Formation

2002

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The evolution of the contact zone between pure surfactant and solvent has been studied by mesoscale simulation. It is found that mesophase formation becomes diffusion controlled and follows the equilibrium phase diagram adiabatically almost as soon as individual mesophases can be identified, corresponding to times in real systems of order 10 µs.When pure surfactant comes into contact with water, mesophases appear at the interface. This is an important process not only for the practical use of surfactants, but also from the point of view of fundamental surfactant phase science. Indeed, contact 'flooding' or penetration scan experiments can yield quantitative information on mesophases as a function of composition [1]. The phenomenon is invariably diffusion controlled in the sense that the widths of the mesophases follow t 1/2 growth laws, and adiabatic in the sense that the local composition determines the mesophase boundaries according to the equilibrium phase diagram [2,3,4]. But penetration scan experiments are restricted to observation times of minutes to hours: what happens on time scales shorter than this? How early does diffusion control set in, and how soon can one expect the mesophase boundaries to track the local composition adiabatically? Such questions are not just of scientific interest since time scales of seconds or less are important in modern processing and the everyday use of surfactants, for instance determining how rapidly washing powder dissolves. Experimentally, this regime is very difficult to access because of the short time scales and the relatively small amounts of mesophase involved. To probe these questions therefore, we have therefore undertaken novel mesoscale simulations of surfactant dissolution. We find adiabatic diffusion control is established remarkably rapidly in our model, on time scales in which only a few repeat units of the growing mesophases have appeared, corresponding to times in the real systems of order 10 µs.The model we have used is a 'minimalist' particlebased model of a binary surfactant / water mixture, based on the dissipative particle dynamics (DPD) method [5,6]. In DPD, the particles are soft spheres, interacting with pairwise soft potentials of the form U = 1 2 A(1 − r/r c ) 2 (r < r c ) where r is the particle separation, r c is the range of the interaction, and A the amplitude. In the model we have three species of particles: A, B and C. The A and B particles are bound together in pairs as dimers with a fixed separation r d , and represent the surfactants. The C particles are monomers representing the solvent (water). The different species are distinguished by their interaction amplitudes, and the trick is to find a set of amplitudes which recover suitable phase behaviour. Following earlier work [6], we use A AA = A BB = A CC = 25, A AB = 30, A AC = 0, A BC = 50 and r d = 0.5 which gives phase diagram features lying in a convenient temperature range around k B T ∼ 1 (we fix units by choosing m = r c = 1 where m is the mass of the particles). Fig. 1 shows the...

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Dynamical relaxation of the surface tension of miscible phases

Cited by 21 publications

References 10 publications

Capillary-to-bulk crossover of nonequilibrium fluctuations in the free diffusion of a near-critical binary liquid mixture

Capillary-to-bulk crossover of nonequilibrium fluctuations in the free diffusion of a near-critical binary liquid mixture

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

Mesoscale Simulations of Surfactant Dissolution and Mesophase Formation

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