Spatial and time-dependent concentration fluctuations of the isobutyric acid-water system in the neighborhood of its critical mixing point

Chu, B.; Schoenes, F. J.; Kao, W. P.

doi:10.1021/ja01014a009

Cited by 81 publications

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“…where m ¼ 0:664 and D 0 ¼ 5:9 Â 10 À10 m 2 s À1 [41,[48][49][50][51]. The diffusion coefficient equals 1:3 Â 10 À11 m 2 s À1 at 27 C and 2:8 Â 10 À11 m 2 s À1 at 30 C. We could not find in the literature values of the IBA/water diffusion coefficient for temperatures below the critical point.…”

Section: Binary Mixturesmentioning

confidence: 60%

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Shapes and dynamics of miscible liquid/liquid interfaces in horizontal capillary tubes

Stevar

Vorobev

2012

Journal of Colloid and Interface Science

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We report optical observations of the dissolution behaviour of glycerol/water, soybean oil/hexane, and isobutyric acid (IBA)/water binary mixtures within horizontal capillary tubes. Tubes with diameters as small as 0.2mm were initially filled with one component of the binary mixture (solute) and then immersed into a solvent-filled thermostatic bath. Both ends of the tubes were open, and no pressure difference was applied between the ends. In the case of glycerol/water and soybean oil/hexane mixtures, we managed to isolate the dissolution (the interfacial mass transfer) from the hydrodynamic motion. Two phase boundaries moving from the ends into the middle section of the tube with the speeds v∼D(1/3)t(-2/3)d(2) (D,t and d are the coefficient of diffusion, time and the diameter of the tube, respectively) were observed. The boundaries slowly smeared but their smearing occurred considerably slower than their motion. The motion of the phase boundaries cannot be explained by the dependency of the diffusion coefficient on concentration, and should be explained by the effect of barodiffusion. The shapes of the solute/solvent boundaries are defined by the balance between gravity and surface tension effects. The contact line moved together with the bulk interface: no visible solute remained on the walls after the interface passage. Changes in temperature and in the ratio between gravity and capillary forces altered the apparent contact angles. The IBA/water system had different behaviour. Below the critical (consolute) point, no dissolution was observed: IBA and water behaved like two immiscible liquids, with the IBA phase being displaced from the tube by capillary pressure (the spontaneous imbibition process). Above the critical point, two IBA/water interfaces could be identified, however the interfaces did not penetrate much into the tube.

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Section: Binary Mixturesmentioning

confidence: 60%

“…The IBA/water mixture is characterized by the upper critical solution temperature, T ¼ 26:2 C [41,42,15]. At temperatures above the critical point, the mixture components are miscible in any proportions.…”

Section: Binary Mixturesmentioning

confidence: 99%

Shapes and dynamics of miscible liquid/liquid interfaces in horizontal capillary tubes

Stevar

Vorobev

2012

Journal of Colloid and Interface Science

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“…Light-scattering techniques have further shown that the rate at which the diffusion coefficient goes to zero as the critical temperature is approached from above at constant critical composition is not the same as the rate a t which the thermodynamic factor approaches zero (Chu et al, 1968, 1969, 1973, and Burstyn and Sengers, 1982, are a few of many studies). While the thermodynamic factor has been found to approach zero with a critical exponent of nearly 4/3, the critical exponent of the diffusion coefficient appears to be approximately ' /3.…”

Section: Introductionmentioning

confidence: 99%

The mutual diffusion coefficient of methanol–n‐hexane near the consolute point

Clark¹,

Rowley²

1986

AIChE Journal

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The composition and temperature dependence of the mutual diffusion coefficient near the liquid-liquid critical point of methanol-n-hexane mixtures has been determined by Gouy interferometry. The critical exponent was found to be 0.685. Constant-temperature extrapolation to zero diff usivity located the spinodal curve. Spinodal loci calculated from the NRTL model are inconsistent with the experimentally determined values. W. M. Clark and R. L. Rowley Department of Chemical EngineeringRice University Houston, TX 7725 1 SCOPEMutual diffusion coefficients can be separated into two parts: a mobility or Onsager term and a thermodynamic factor. The mathematical criterion, which defines the spinodal curve and demarcates the unstable region interior to the equilibrium coexistence curve, can be expressed as the loci of points where the thermodynamic factor is identically zero. Classical and light-scattering experiments have shown that the diffusion coefficient goes to zero as the temperature approaches the liquid-liquid critical point at constant critical composition. Although Skripov et al. (1980) concluded that the diffusion coefficient for the methanoln-hexane system vanished at the same rate as the thermodynamic factor, indicating a finite Onsager term, it has been fairly well established by studies on other systems that the Onsager coefficient actually diverges as the critical point is approached. One purpose of this study was to determine the critical exponent in the methanol-n-hexane system by a series of temperaturejump-initiated diffusion experiments in a Gouy interferometer. The diffusion critical exponent has significant implications in terms of universality and scaling theories.The second purpose was to use diffusion coefficient measurements to determine the spinodal curve. Since the diffusion coefficient must be zero at the spinodal, extrapolation of measured diffusivities to zero could be used to determine its location. No methods have heretofore been able to provide spinodal information in liquid-liquid phase-splitting systems. Classical equilibrium studies provide only coexistence information. Nevertheless, the location of the spinodal curve could be extremely valuable in developing and testing liquid mixture models for the Gibbs free energy since it is related to the second derivative with respect to composition, as shown in Eq. 7. Generally, liquid-mixture model parameters are fitted from the solubility or equilibrium concentration information. No other data have been available to test the model at other compositions at the same temperature. The spinodal criterion on the other hand provides additional restrictions that a satisfactory and consistent liquid-mixture model must satisfy. CONCLUSIONS AND SIGNIFICANCEDiffusion coefficients were measured in methanol-nhexane mixtures as a function of temperature along the critical composition in a temperature-jump cell using a Gouy interferometer. The critical exponent was found to be 0.685, in good agreement with previous studies on other systems, indicating that...

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“…If these shifts become sufficiently large, wave growth will terminate. 5 In the case of interactions between waves of a wide frequency spectrum, frequency shifts will probably not lead to saturation unless they change (at high field levels) the dispersion relation from the decay type to the nondecay type for which the resonance conditions cannot be met. The opposite case of nonlinear frequency shifts which lead to the fulfillment of resonance conditions has been considered by several authors.…”

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confidence: 99%

Angular Distribution of the Intensity of Light Scattered from Xenon Near Its Critical Point

Giglio

Benedek

1969

Phys. Rev. Lett.

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We have measured the angular dependence of the intensity of light scattered from xenon near its critical point, verified the Ornstein-Zernike theory, and determined the temperature dependence of the isothermal compressibility K T , the long-range correlation length £, and the direct correlation range R. The exponents describing the divergences of /c^andl are, respectively, y iquid '=1.228±0.028, y vapcr '= 1.244 ±0.017, and v vapor '=0.57 ±0.05. R is essentially constant at ~6 A.Over fifty years ago, Ornstein and Zernike 1 proposed that, near the critical point of a singlecomponent fluid, spatial correlations in the density fluctuations would produce angular anisotropy in the intensity of the scattered light. Nevertheless, there has been no direct experimental evidence of this effect. 2 "" 4 In binary critical mixtures, spatial correlations in the concentration fluctuations also produce anisotropy in the scattered intensity. This effect is large and has been carefully studied. 2 ' 3 * 5This Letter reports measurements of the angular anisotropy in the intensity of light scattered from xenon near its critical point. We find, at all temperatures and densities studied, that the reciprocal of the scattered intensity varies linearly with sin 2 (0/2) (where 9 is the scattering angle) as Ornstein and Zernike predicted. Our data provide an accurate measurement of the longrange correlation length £, the isothermal compressibility K Ti and the direct correlation range R along paths near the critical point.The experimental setup we use consists of a helium-neon laser source and associated focusing optics, a high-pressure optical cell having a high-quality cylindrical glass window, collecting optics, and a phototube mounted on a rotating arm whose axis is the same as that of the cylindrical window. The laser power is stabilized to better than 0.5% by a servomechanism which controls the plasma current in response to a solarcell sensor. The electric field of the laser beam is parallel to the axis of the window. When the cell is sealed, stresses are applied only along the cylinder axis; thus the stress-induced birefringence does not alter the polarization of the field. The temperature of the cell was maintained to within ±0.001°K using a two-stage servomechanism. A platinum resistance thermometer, calibrated relative to the National Bureau of Standards (NBS) secondary standards, was used to measure the temperature. The pressure cell was constructed of beryllium copper and stainless steel. The critical fluid was contained in a volume of height 1.986 in. and diam 0.250 in. Of this, a central region • § in. in height is surrounded by the cylindrical window whose specifications are i.d. =0.250± 0.001 in., o.d.=0.709± 0.001 in., and concentricity better than 0.001 in. Indium is used throughout as sealing material. No organic 1145

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Spatial and time-dependent concentration fluctuations of the isobutyric acid-water system in the neighborhood of its critical mixing point

Cited by 81 publications

References 0 publications

Shapes and dynamics of miscible liquid/liquid interfaces in horizontal capillary tubes

Shapes and dynamics of miscible liquid/liquid interfaces in horizontal capillary tubes

The mutual diffusion coefficient of methanol–n‐hexane near the consolute point

Angular Distribution of the Intensity of Light Scattered from Xenon Near Its Critical Point

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