Dynamic scaling function for critical fluctuations in classical fluids

Abstract

A closed-form approximant is proposed for the dynamic scaling function that characterizes the behavior of the wave-numberdependent diffusion of the order-parameter fluctuations in a fluid near a critical point. The expression contains two parameters that determine the expected behavior of the diffusion coefficient in the hydrodynamic and in the nonlocal critical limits. The proposed scaling function yields an accurate representation of our recent experimental data for the 3methylpentane and nitroethane mixture near the critical mixing point with parameter values that are in good agreement with the values predicted from theory. the last 10 mK from the critical temperature and the effect on the actual value deduced for the diffusion coefficient remains small.In a previous paper we demonstrated that the experimental decay-rate data are consistent with the predictions of the mode-coupling theory for dynamic critical phenomena. ' For that purpose we solved two coupled integral 28 1567 1983 The American Physical Society 1568 BURSTYN, SENGERS, BHATTACHARJEE, AND FERRELL 28

Finite-size scaling study of dynamic critical phenomena in a vapor-liquid transition

“…We observe that the simulation data are in disagreement with the theoretically predicted solid line (having exponent x ζ ν = 1.82). The reasons for the disagreement could be the finite-size effects as well as the presence of a background contribution [57], the latter arising from small wavelength fluctuations. We observe similar disagreement for λ, presented in the inset of Fig.…”

“…These two serious issues, viz., finite-size effects and background contributions, have to be appropriately taken care of during the estimation of the critical exponents, along the line discussed below. A quantity, say X, that exhibits singularity at the critical point, can be decomposed into two parts [19,29,30,57] as…”

Critical light scattering in liquids

“…(3.21) to compare our asymptotic result for the characteristic frequency with other theories: In Fig. 3 we have plotted the asymptotic result for Ω(x)/x (which is only a function of x as we have c na (k, x) = 1) as well as the theoretical results of Kawasaki and Lo [12], Paladin and Peliti [13] and Burstyn et al [14]. As the other authors have a different prefactor for Ω(x) we have normalized Ω(x) so that the curves coincide for x → 0.…”

“…As we can see in these figures the experimental data are not described correctly by our asymptotic expressions but only by the non-asymptotic expressions which show the crossover to the van Hove theory for large values of the reduced temperature t or small values of the variable x respectively. Analogously any asymptotic theory [12][13][14] fails to describe the experimental data correctly. In Ref.…”

Does the Viscosity Exponent Derive from Ultrasonic Attenuation Spectra?

“…16), treating τ 0 as the only adjustable parameter. With the n-pentanol-nitromethane mixture of critical composition, the relaxation times τ (T ), and thus the reduced frequencies Ω, were obtained from a combined evaluation of shear viscosity and quasi-elastic light scattering data [24], taking effects of crossover from singular to mean-field behavior into account [38].…”