Showing papers by "David S. Cannell published in 1992"

Critical dynamics in the presence of a silica gel.

Abstract: Dynamic and static light scattering results are reported for isobutyric acid and water in a 4 wt.% silica network with a crossover length of 300 A. In the one-phase region, well away from the critical point, the decay rate for order parameter fluctuations is unaffected by the network. Near the critical point, the order-parameter correlation function is well fitted by the sum of an exponential with decay rate Γ 1 and a term of the form exp{ln(τ/t 0 )/ln(Γ 2 t 0 )] 3 , with Γ 2 ≃Γ 1

Hexagonal and roll flow patterns in temporally modulated Rayleigh-Bénard convection.

Abstract: We present experimental results for pattern formation in a thin fluid layer heated time periodically from below. They were obtained with computer-enhanced shadowgraph flow visualization and with heat-flux measurements. The experimental cell was cylindrical, with a radius-to-height ratio of 11.0. The temperature of the top plate was held constant while that of the bottom plate was modulated sinusoidally so that the reduced Rayleigh number {epsilon}{equivalent to}{Delta}{ital T}/{Delta}{ital T}{sub {ital c}}{minus}1 had the form {epsilon}({ital t})={epsilon}{sub 0}+{delta} sin({omega}{ital t}). Here the time {ital t} and frequency {omega} are scaled by the vertical thermal diffusion time. Experiments were performed within the ranges 8.0{le}{omega}{le}18.0, 0.4{le}{delta}{le}3.3, and {minus}0.2{le}{epsilon}{sub 0}{le}0.6. Measurements of the convective threshold shift {epsilon}{sub {ital c}}({delta},{omega}) were in good agreement with theoretical predictions. Comparisons were made with theoretical predictions of a range {epsilon}{sub {ital A}}({delta},{omega}){le}{epsilon}{sub 0}{lt}{epsilon}{sub {ital R}}({delta},{omega}) ({epsilon}{sub {ital A}}{lt}{epsilon}{sub {ital c}},{epsilon}{sub {ital R}}{gt}{epsilon}{sub {ital c}}) where only a hexagonal pattern with downflow at the cell centers is predicted to be stable, a range {epsilon}{sub {ital R}}{le}{epsilon}{sub 0}{lt}{epsilon}{sub {ital B}}({delta},{omega}) where both hexagonal and roll patterns are expected to be stable, and a range {epsilon}{sub 0}{ge}{epsilon}{sub {ital B}} where only a roll pattern should be stable.

On the Stability of Taylor-Couette Flow Subjected to External Rotation

Abstract: Circular Couette flow1 is the flow between two concentric cylinders with one or both of them rotating about their geometric axis. We consider here a modified Couette flow, which occurs when only the inner cylinder rotates about this axis, and both cylinders rotate about a second external axis which is orthogonal to the first. In this paper we present theoretical results for the linear stability of this modified flow. This system is of particular interest because the external rotation breaks the cylindrical symmetry of Couette flow and leads to instabilities and spatio-temporal patterns which do not occur without it. Experimental studies of this system2–5 have revealed a surprising richness of bifurcation phenomena. The first theoretical results for this problem were obtained by Ning et al.6 and Wiener et a1.,7 who calculated the modified base flow and determined its stability for small values of the external rotation rate Ω. Using Ω as an expansion parameter, these authors carried out the analysis to O(Ω2). The calculated values of the critical Reynolds number, the critical wavenumber, and the tilt angle of the vortices were in quantitative agreement with experiments.6

Consolute Critical Phenomena in Dilute Silica Gel

Abstract: The effect of even dilute silica networks on the critical phenomena of binary liquid mixtures is profound. The network preferentially adsorbs one component, preventing a portion of the mixture from participating in critical fluctuations. Fluctuations in the remaining mixture are found to decay with a non-exponential correlation function near the consolute point. A correlation function consisting of the sum of an exponential decay and a non-exponential term of either an activated or stretched exponential form fits the data well. In the presence of the silica network, the mixtures are observed to phase separate near the critical temperature of the pure system, but while still in the one-phase region of the pure system.