Showing papers by "David S. Cannell published in 1995"
TL;DR: The structure factor of the fluctuating convection rolls is consistent with the expected rotational invariance of the system and the fluctuation intensity is found to be proportional to 1/{radical}{minus}{epsilon}.
Abstract: We report quantitative experimental results for the intensity of noise-induced fluctuations below the critical temperature difference {Delta}{ital T}{sub {ital c}} for Rayleigh-Benard convection. The structure factor of the fluctuating convection rolls is consistent with the expected rotational invariance of the system. In agreement with predictions based on stochastic hydrodynamic equations, the fluctuation intensity is found to be proportional to 1/{radical}{minus}{epsilon}, where {epsilon}{equivalent_to}{Delta}{ital T}/{Delta}{ital T}{sub {ital c}}{minus}1. The noise power necessary to explain the measurements agrees with the prediction for thermal noise.
86 citations
TL;DR: By interpreting the adsorption as the response of the order parameter to an imposed field due to the gel, it is found that the q dependence of the response is consistent with linear response theory on all length scales accessible in these experiments.
Abstract: We report the results of neutron-scattering experiments designed to probe structure in binary mixtures confined in silica gels over the wavelength range 60\char21{}2000 \AA{}. In what would be the one-phase region of the pure system, the scattering can be fit very well to the sum of three contributions: critical fluctuations of the mixture, preferentially adsorbed fluid, and the silica gel itself. By interpreting the adsorption as the response of the order parameter to an imposed field due to the gel, we find that the q dependence of the response is consistent with linear response theory on all length scales accessible in these experiments, although the amplitude of the response does not diverge as strongly as does the order-parameter susceptibility. In what would be the two-phase region of the pure system, we observe changes in the scattering that are consistent with the existence of large, slowly coarsening domains. The results are discussed in the context of the random-field Ising model and its magnetic realizations.
28 citations
TL;DR: It is deduced that the critical fluctuations are suppressed in amplitude relative to those of the pure system as the consolute point is approached, and the effect of the time-independent response of the mixture to the silica gel into account is taken into account.
Abstract: We report details of experimental studies of the effect of dilute silica networks on critical phenomena for two binary fluid mixtures: lutidine-water (LW) and isobutyric acid\char21{}water (IBAW). For both mixtures, the primary effect of the silica is to induce a time-independent perturbation of the mixtures' concentration, making it spatially nonuniform. We interpret this as the static response of the critical system to the spatial nonuniformities of the silica concentration. We have measured this response by light scattering and find it is both temperature and concentration dependent, becoming strongly so in the vicinity of the consolute points of the mixtures. We observed no critical fluctuations for the LW-gel system. For the IBAW-gel system, time-dependent scattering was observed, and the temporal autocorrelation function of the scattered intensity revealed three regimes. Well away from the consolute point, the decay was exponential. By taking the effect of the time-independent response of the mixture to the silica gel into account, we found that the decay rates were comparable to those of the pure system. Correlation functions measured closer to the consolute point contained a significant nonexponential component for sufficiently large values of the scattering wave vector. This component is well fitted by either a stretched exponential or an activated form. From the amplitude of the normalized autocorrelation function we deduce that the critical fluctuations are suppressed in amplitude relative to those of the pure system as the consolute point is approached. Sufficiently near the phase boundary of the pure system, a very slowly decaying mode was also observed in the autocorrelation function. This mode died away hours after the small temperature change that induced it. A further temperature change toward the two-phase region induced it agian, while a change in the opposite direction did not. We interpret this behavior as resulting from a phase separation process. IBAW-gel samples held deep in the two-phase region of the pure system for months ordered macroscopically, proving that this system has long-range order in the presence of such silica networks.
27 citations
TL;DR: Determinations of the wave numbers of the patterns near onset are consistent with the theoretically predicted small critical wave numbers at positive {Psi} and the modelmore predicts a cancellation between contributions to the refractive index from concentration and temperature variations, which does not seem to occur in the physical system.
Abstract: We present an experimental study of convection in binary mixtures with separation ratios {Psi} close to zero. Measurements of the Hopf frequency for {Psi}{lt}0 were used to determine the relationship between {Psi} and the mass concentration {ital x} with high precision. These results are consistent with but more precise than earlier measurements by conventional techniques. For {Psi}{gt}0, we found that the pattern close to onset consisted of squares. Our data give the threshold of convection {ital r}{sub {ital c}}{equivalent_to}{ital R}{sub {ital c}}/{ital R}{sub {ital c}0} ({ital R}{sub {ital c}} is the critical Rayleigh number of the mixture and {ital R}{sub {ital c}0} that of the pure fluid) from measurements of the refractive-index power of the pattern as revealed by a very sensitive quantitative shadowgraph method. Over the range {Psi}{approx_lt}0.011, corresponding to {ital r}{sub {ital c}}{approx_gt}0.2, these results are in good agreement with linear stability analysis. The measured refractive-index power varies by six orders of magnitude as a function of {ital r} and for {ital r}{approx_gt}0.55 is in reasonable agreement with predictions based on the ten-mode Lorenz-like Galerkin truncation of Mueller and Luecke [H. W. Mueller and M. Luecke, Phys. Rev. A 38, 2965 (1988)]. For smaller {ital r}, the modelmore » predicts a cancellation between contributions to the refractive index from concentration and temperature variations, which does not seem to occur in the physical system. Determinations of the wave numbers of the patterns near onset are consistent with the theoretically predicted small critical wave numbers at positive {Psi}. As {ital r} approaches one, we find that {ital q} approaches the critical wave number {ital q}{sub {ital c}0}{congruent}3 of the pure fluid. (c) 1995 The American Physical Society« less
15 citations
TL;DR: In this paper, the electroconvection patterns in the liquid crystal 4-ethyl-2-fluoro-4′-[2-(trans-4-pentylcyclohexyl)-ethyl]biphenyl (152) for two values of the parameter Td/T[sgrave, where Td is the director relaxation time and T[ sgrave] is the charge relaxation time, as a function of the rms voltage and frequency of an applied AC electric field.
Abstract: We report on electroconvection patterns in the liquid crystal 4-ethyl-2-fluoro-4′-[2-(trans-4-pentylcyclohexyl)-ethyl]biphenyl (152) for two values of the parameter Td/T[sgrave], where Td is the director relaxation time and T[sgrave] is the charge relaxation time, as a function of the rms voltage and frequency of an applied AC electric field. For Td/T[sgrave] = 180, we observe a forward Hopf bifurcation to a superposition of the two degenerate oblique roll states. The envelopes of these patterns are chaotic in space and time. There exists a secondary transition to a state which oscillates between the two degenerate modes. For Td/T[sgrave] = 620, the initial instability is to a state of stationary oblique rolls. The secondary transition is to a superposition of the already existing oblique rolls and rolls of the same wavenumber which are perpendicular to the existing rolls. This forms stationary oblique squares.
12 citations