Order-parameter fluctuations decay rate

The order-parameter fluctuations are temperature- and system-dependent and their decay rate is related to the transport coefficients (5) Usually the magnitude of the fluctuations are characterized by a correlation length . Along a critical isochore or isopleth, the correlation length diverges as... 

The dec8y rate of the order-parameter fluctuations is proportional to the thermal diffusivity in case of pure gases near the vapor-liquid critical point and is proportional to the binary diffusion coefficient in case of liquid mixtures near the critical mixing point (6). Recently, we reported (7) single-exponential decay rate of the order-parameter fluctuations in dilute sugercritical solutions of liquid hydrocarbons in CO for T - T 10 C. This implied that the time scales associated with thermal diffusion and mass diffusion are similar in these systems. 

The above equation provides a basis for correlating the temperature dependence of a transport coefficient such as mass diffusivity in the supercritical region. The effects of composition, solute, and solvent characteristics can also be introduced into the correlations via and A which are system-dependent amplitudes. However, a rigorous ftest of the applicability of equation 5 requires independent measurements of the decay rate of the order-parameter fluctuations, the correlation length, and the viscosity. 

In this study, we employed PCS to measure the decay rate of the order-parameter fluctuations in dilute supercritical solutions of heptane, benzene, and decane in CC - The refractive index increment with concentration is much larger than the refractive index increment with temperature in these systems. Therefore the order-parameter fluctuations detected by light scattering are mainly concentration fluctuations and their decay rate T is proportional to the binary diffusion coefficient, D = V/q. The... 

CO -benzene, and CO -n-decane. The critical densities and the corresponding compositions are plotted in Figure 1. The three hydrocarbons in order of higher to lower solubility in C0 were heptane, benzene, and decane. The measured binary diffusion coefficients or the decay rates of the order-parameter fluctuations at various temperatures and pressures are listed in Tables I, II, and III for CO -heptane, CO -benzene, and CO -decane systems respectively. In Figure 2, the critical lines of the three binary systems in the dilute hydrocarbon range are shown in the pressure-temperature space. dP/dT along the critical lines of CO.-heptane and CO -benzene systems are similar and lower than dP/dT along the critical line of CO -decane system, which indicates that C02 and decane form more asymmetric mixtures relative to CO with heptane or benzene. 

The decay rate (first cumulant) T of the time-dependent correlation function associated with the order parameter fluctuations can be measured by dynamic light scattering. Mode-coupling theories of critical phenomena including dynamical background contributions predict that is the sum of a critical part Tf and a background part Tb, i.e.. 

The scattered light intensity correlation function C (/) has been measured over a very wide range of temperature and wave vectors for various systems. Typical intensity correlation functions C-(/) are depicted in Fig. 4 for the sake of illustration. These graphs show systematic deviations from the usual exponential decay, which are also observed for most of the systems we report in this part. As a remark, nonexponential decays that are small at low concentration, close to the critical point, become large for dense systems. From the initial slope of the time-dependent intensity correlation function, one can deduce the first cumulant F, which is the relaxation rate of the order parameter fluctuations. 

In light-scattering experiments the decay rate of the order parameter is measured. Experiments performed by Chang et al. (1986) on mixtures of carbon dioxide and ethane show that the diffusion coefficient associated with the exponential decay (6.5) of the order-parameter fluctuations again satisfies the Stokes-Einstein law (6.21). However, the diffusion coefficient cannot simply be identified with either the thermal diffusivity a or the mass diffusivity D12, since the order-parameter fluctuations now incorporate fluctuations in both the density and the concentration. 

Swinney, H. L. Henry, D. L. (1973). Dynamics of fluids near the critical point Decay rate of the order-parameter fluctuations. Phys. Rev. A, 8, 2586-2617. 

The width of the Rayleigh central band in a one-component liquid (see Equations 53, 57) or in a solution (see section 2.4) does actually correspond to the decay rate of fluctuations in the order parameter, and can be expressed in the general form as... 

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