Showing papers by "David S. Cannell published in 1991"
TL;DR: Experimental studies of the transitions between conduction, hexagons, and rolls in non-Boussinesq convection of gaseous CO{sub 2} in a cylindrical cell of radius-to-height ratio 86 show that conduction gives way to hexagons via the propagation of a front connecting the two states, while the transition between hexagons and rolls are facilitated at the cell walls which appear to nucleate the minority state.
Abstract: We present experimental studies of the transitions between conduction, hexagons, and rolls in non-Boussinesq convection of gaseous ${\mathrm{CO}}_{2}$ in a cylindrical cell of radius-to-height ratio 86. Except for the transition from conduction to hexagons, transitions occur when the two states involved have nearly the same value of a generalized potential rather than at the stability limits. Conduction gives way to hexagons via the propagation of a front connecting the two states, while the transitions between hexagons and rolls are facilitated at the cell walls which appear to nucleate the minority state.
127 citations
TL;DR: Experimental and theoretical results for the absolute and convective instability boundaries in Taylor-Couette flow with imposed axial flow as a function of the axial Reynolds number confirm that noise-sustained structures of traveling vortices exist in much of the convective unstable regime.
Abstract: We report experimental and theoretical results for the absolute and convective instability boundaries in Taylor-Couette flow with imposed axial flow as a function of the axial Reynolds number. Experiment and theory agree quantitatively. In the downstream region of a large-aspect-ratio system, noise-sustained structures of traveling vortices exist in much of the convectively unstable regime. These structures have a nearly time-independent amplitude, but a noisy phase. The phase noise ceases abruptly upon crossing the absolute instability boundary.
82 citations
TL;DR: The structure of silica hydrogels has been studied by elastic light scattering and these gels show mass fractal behavior at length scales below a crossover length ξ and scatter like a spatially random distribution of fractal objects for length scales >ξ.
Abstract: The structure of silica hydrogels has been studied by elastic light scattering. Like colloidal silica gels and neutrally catalyzed aerogels, these gels show mass fractal behavior at length scales below a crossover length \ensuremath{\xi} and scatter like a spatially random distribution of fractal objects for length scales g\ensuremath{\xi}. Their fractal dimension D depends on \ensuremath{\xi} and, unlike the other gels for which \ensuremath{\xi}\ensuremath{\propto}${\mathrm{\ensuremath{\varphi}}}^{1/(\mathit{D}\mathrm{\ensuremath{-}}3)}$, \ensuremath{\xi} depends on both silica volume fraction \ensuremath{\varphi} and gelation conditions. However, all our data are consistent with the correlation function 〈\ensuremath{\delta}\ensuremath{\varphi}(0)\ensuremath{\delta}\ensuremath{\varphi}(r)〉=A${\mathrm{\ensuremath{\varphi}}}^{2}$${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{r}/\ensuremath{\xi}}$/(r/\ensuremath{\xi}${)}^{3\mathrm{\ensuremath{-}}\mathit{D}}$, with A=1.8\ifmmode\pm\else\textpm\fi{}0.13.
41 citations
TL;DR: The results demonstrate the importance of stochastic effects on pattern formation in convective flows in a thin fluid layer of depth {ital d} that is heated from below, and an explanation of the measured convective heat current requires that the noise source in these models have an intensity that is four orders of magnitude larger than that of thermal noise.
Abstract: We report on computer-enhanced shadowgraph flow-visualization and heat-flux measurements of pattern formation in convective flows in a thin fluid layer of depth {ital d} that is heated from below Most of the experiments were conducted in a cylindrical container of radius {ital r} and aspect ratio {Gamma}=={ital r}/{ital d}=10 The temperature of the top plate of the container was held constant while the heat current through the fluid was linearly ramped in time, resulting in a temperature difference {Delta}{ital T} between the bottom and top plates After initial transients ended, the reduced Rayleigh number {epsilon}=={Delta}{ital T}/{Delta}{ital T}{sub {ital c}}{minus}1, where {Delta}{ital T}{sub {ital c}} is the critical temperature difference for the onset of convection, increased linearly with ramp rate {beta} such that {epsilon}({ital t})={beta}{ital t} When time was scaled by the vertical thermal diffusion time, our ramp rates were in the range 001{le}{beta}{le}030 When the sidewalls of the cell were made of conventional plastic materials, a concentric pattern of convection rolls was always induced by dynamic sidewall forcing When sidewalls were made of a gel that had virtually the same thermal diffusivity as the fluid, pattern formation occurred independent of cell geometry In the earliest stages the patterns were thenmore » composed of irregularly arranged cells and varied randomly between experimental runs The same random cellular flow was also observed in samples of square horizontal cross section The results demonstrate the importance of stochastic effects on pattern formation in this system However, an explanation of the measured convective heat current in terms of theoretical models requires that the noise source in these models have an intensity that is four orders of magnitude larger than that of thermal noise« less
40 citations
TL;DR: An experimental study of the effect of a dilute silica network on critical phenomena in a binary mixture of 2,6-lutidine and water finds that its structure does not differ significantly from that of the gel, but the scattered intensity increases dramatically as the two-phase region is approached.
Abstract: We report the results of an experimental study of the effect of a dilute silica network on critical phenomena in a binary mixture of 2,6-lutidine and water. Light-scattering measurements of this system show that its structure does not differ significantly from that of the gel, but that the scattered intensity increases dramatically as the two-phase region is approached. We interpret these results in terms of a layer of lutidine-rich fluid adsorbed on the silica surface and the resulting changes in concentration of the nonadsorbed fluid
31 citations
TL;DR: It is found that external rotation stabilizes the base flow and decreases the critical wave number of the tilted vortices that form at the onset of the first instability.
Abstract: We report theoretical results for Taylor-vortex flow subjected to external rotation. The system consists of an incompressible viscous fluid between two concentric cylinders with the inner one rotating about their common axis. The two cylinders also rotate together with a dimensionless angular velocity \ensuremath{\Omega} about an axis orthogonal to their axis. We perturbatively calculated the base flow to second order in \ensuremath{\Omega} and carried out a linear stability analysis of this flow. We found that external rotation stabilizes the base flow and decreases the critical wave number of the tilted vortices that form at the onset of the first instability. Our results for the critical Reynolds number, the critical wave number, and the tilt angle, together with the coefficients of linear terms in the relevant Ginzburg-Landau amplitude equation, are presented to order ${\mathrm{\ensuremath{\Omega}}}^{2}$.
11 citations
TL;DR: In this article, an apparatus consisting of two concentric cylinders with the inner one rotating, and with a radius ratio near 0.75, was mounted with its axis horizontal on a table which rotated with angular velocity about a vertical axis.
Abstract: We present experimental results for Taylor-Couette flow subjected to a Coriolis force. We used an apparatus consisting of two concentric cylinders with the inner one rotating, and with a radius ratio near 0.75. It was mounted with its axis horizontal on a table which rotated with angular velocityΩ about a vertical axis. For sufficiently lowΩ, the first bifurcation upon increasing the inner-cylinder rotation rate ω was to tilted vortices. With further increase in ω this bifurcation was followed by a secondary one to time-periodic tilted vortices. The two bifurcation lines met at higherΩ. The initial bifurcation then became one to tilted traveling vortices. For even larger values ofΩ, the flow immediately above the initial transition was disordered, and for sufficiently largeΩ the initial bifurcation was to a featureless turbulent state. We studied these transitions with three different outer cylinders. Two had symmetric spatial ramps terminating both ends of a straight section to reduce the effect of the rigid, nonrotating ends, and one had no ramps. The transition to featureless turbulence in the apparatus with ramps became hysteretic over a range ofΩ.
6 citations
5 citations