Comparison of Experiments with the Modified Mode-Mode Coupling Theory of Kawasaki in Binary Fluids

Chu, Benjamin; Lee, S. P.; Tscharnuter, W.

doi:10.1103/physreva.7.353

Cited by 72 publications

(10 citation statements)

References 27 publications

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“…Further checks of the performance of the apparatus were measurements of the equilibrium scattering at small angles (1.6°-11°) at temperatures from 2 to 5 mK above T C9 which are well represented by the Ornstein-Zernike expression and give values of | consistent with those reported by Chu, Lee, and Tscharnuter. 5 These studies also confirm that for the geometry employed the effect of multiple scattering is small at low angles. 6 In the neighborhood of the maxima, the scatter in the relative intensity is 5% 0 Figure 2 shows the scattered intensity as a function of k and t for two jump experiments nominally equivalent to those for which the curves in Fig.…”

Section: Pressure-jump Studies In Supercritical Mixturessupporting

confidence: 60%

“…At these angles g{k£)-l, and hence the slope of line gives directly D = 1.7 x 10" 8 cm 2 s" 1 , in good agreement with the value D =1.6X10" 8 cm 2 s" 1 at T c + 70 mK calculated from the light-beating results. 5 An interesting detail of Fig. 4 is the spike that appears immediately after the pressure jump.…”

Section: Pressure-jump Studies In Supercritical Mixturesmentioning

confidence: 98%

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Pressure-Jump Studies in Supercritical Mixtures

Wong

Knobler

1979

Phys. Rev. Lett.

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FIG. 3. Superbanana orbit of a particle trapped in a localized magnetic well in the stellarator. the well boundary prevented the periodic motion necessary for the conservation of the action.The existence of the stellarator superbananas corresponds to the localization of the magnetic wells B = W/p.. Furthermore, the remainder of the stellarator magnetic wells, which are not localized, produced no superbananas. No superbananas were found in the torsatron configuration, for which no localized magnetic wells exist.From this work, we have found the following conclusions valid for single-charged-particle Although recent theoretical 1 and experimental 2 investigations of the nonequilibrium behavior of mixtures near a critical point have focused on the processes involved in phase separation, the dynamical behavior of systems that relax to states in a one-phase region of the phase diagram is of interest as well. Binder 1 has used the Kawasaki spin-exchange model to derive a kinetic motion in vacuum magnetic fields for the classical stellarator and torsatron:(1) Action is not conserved in classical stellarators and torsatrons.(2) Superbananas are a property of the magnetic well topology of the stellarator, and appear on the exterior of the torus only.(3) Superbananas do not appear in the classical torsatron. equation for the structure factor S(k,t) in binary mixtures with conserved order parameter For a temperature jump within the one-phase region from T to T' he finds, in the hydrodyhamic limit S(k,t)=SPressure jump experiments have been performed to study the relaxation of isobutyric acid and water mixtures to equilibrium states in the one-phase region near a critical point. Small-angle light-scattering measurements have been used to monitor the aproaeh to equilibrium. The observed time dependence of the scattered intensity is in good agreement with a model proposed by Binder.

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Section: Pressure-jump Studies In Supercritical Mixturessupporting

confidence: 60%

Section: Pressure-jump Studies In Supercritical Mixturesmentioning

confidence: 98%

Pressure-Jump Studies in Supercritical Mixtures

Wong

Knobler

1979

Phys. Rev. Lett.

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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: 95%

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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“…6. Where 5 (7) represents the normalized correlation function 5(7) = C(7) -1, the dashed straight line represents the single exponential fit and gives an unrea- 1.2 1.5 1.8…”

Section: Performance Application and Future Possibilitiesmentioning

confidence: 99%

“…A 32 bit storage per channel is being used to ensure data precision. Also, the accidental counts [L j n(j)] are determined exactly in calculating the normalized correlation function 5 (7). Since this is a full photon-counting instrument, it can handle a system with nonGaussian statistics 23 without distortion.…”

Section: Performance Application and Future Possibilitiesmentioning

confidence: 99%

Full-photon-counting Rayleigh spectrometer: a correlation and/or fast Fourier transform instrument

Han

1978

Review of Scientific Instruments

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A fast, flexible, and relatively inexpensive minicomputer based Rayleigh spectrometer has been constructed. This spectrometer can utilize photon pulses in a most efficient way by performing autocorrelation and/or FFT with any desired number of channels. Its capability has been demonstrated by measuring large latex particles, small sodium dodecyl sulfate micelles, and a polydisperse latex-gamma-globulin system. Detailed timing diagrams and circuit schematics are also included.

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Comparison of Experiments with the Modified Mode-Mode Coupling Theory of Kawasaki in Binary Fluids

Cited by 72 publications

References 27 publications

Pressure-Jump Studies in Supercritical Mixtures

Pressure-Jump Studies in Supercritical Mixtures

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

Full-photon-counting Rayleigh spectrometer: a correlation and/or fast Fourier transform instrument

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