Physical optics treatment of the shadowgraph

Trainoff, Steven P.; Cannell, David S.

doi:10.1063/1.1449892

Cited by 131 publications

(140 citation statements)

References 18 publications

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“…Different setups show different responses to the acquired signal as a function of the wave vector q, which is described by the so-called transfer function T (q) of the technique. It has been shown that the shadowgraph transfer function dependence upon the wave vector shows a sinusoidal behavior [48,53,54]:…”

Section: Dynamic Near-field Imagingmentioning

confidence: 99%

Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

Croccolo

Scheffold

Bataller

2013

Comptes Rendus. Mécanique

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We present preliminary near-field light scattering (NFS) data concerning the analysis of the static power spectrum and of the relaxation time constant as a function of the wave vector for non-equilibrium fluctuations (NEFs). The goal of these measurements is to obtain information about the Soret and the mass diffusion coefficients of a binary mixture undergoing thermodiffusion. In particular, we show how the interaction between NEFs and the gravity force gives rise to a critical wavelength that provides additional information about the Soret coefficient. We suggest that a quantitative analysis can be performed by means of this non-invasive optical technique. In our setup, the sample is monitored parallel to the imposed temperature gradient, thus being insensitive to the refractive index profile along the vertical axis, while at the same time we are able to detect the light scattered by the refractive index fluctuations in horizontal planes. We select a shadowgraph layout for the NFS setup due to the extremely small wave vectors we aim to analyze. From a double-frame differential analysis of the acquired images, we obtain both the static power spectrum and the dynamics of NEFs. As a proof-of-principle experiment, we present Soret and diffusion coefficient data on a liquid mixture of tetrahydronaphthalene/n-dodecane.

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Section: Dynamic Near-field Imagingmentioning

confidence: 99%

Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

Croccolo

Scheffold

Bataller

2013

Comptes Rendus. Mécanique

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“…When the penetration depth is a macroscopic length ͑as it often is 9 ͒ shadowgraphy would be needed. 4,29 However, for a quantitative interpretation of experimental shadowgraphs, we shall need to also consider the effects of buoyancy and of the boundary conditions on the fluctuations. 4 Our theory can also provide a way to probe whether chemical equilibrium has been reached in the temperature gradient.…”

Section: A Light Scattering and Shadowgraphymentioning

confidence: 99%

“…͑39a͒ and ͑39b͒ that the decay rates of the fluctuations depend explicitly on the rate constant L r . Hence, measuring these fluctuations by light scattering 4,27 or shadowgraphy 4,29,30 in a reacting mixture provides information about the rate constant of the reaction. For instance, Letamendia et al 31,32 measured light scattering in various liquids with chemical equilibrium between two isomers.…”

Section: ͑33͒mentioning

confidence: 99%

Concentration fluctuations in nonisothermal reaction-diffusion systems

Zárate

Sengers

Bedeaux

et al. 2007

The Journal of Chemical Physics

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In this paper a simple reaction-diffusion system, namely a binary fluid mixture with an association-dissociation reaction between the two components, is considered. Fluctuations at hydrodynamic spatiotemporal scales when a temperature gradient is present in this chemically reacting system are studied. First, fluctuating hydrodynamics when the system is in global equilibrium ͑isothermal͒ is reviewed. Comparing the two cases, an enhancement of the intensity of concentration fluctuations in the presence of a temperature gradient is predicted. The nonequilibrium concentration fluctuations are spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a ϰq −4 to a ϰq −2 behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion-or activation-controlled regimes of the reaction by measuring these fluctuations. In addition, the possible observation of these fluctuations in nonequilibrium molecular dynamics simulations is considered.

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“…All experiments were performed at a fixed inclination of γ = 30 • , within the regime of buoyancyinstability. Images of the convection pattern were collected using a digital CCD camera, via the usual shadowgraph technique [21,22]. Images were collected at 3 frames per second in one of two formats.…”

Section: Inclined Layer Convectionmentioning

confidence: 99%

Statistics of defect motion in spatiotemporal chaos in inclined layer convection

Daniels

Bodenschatz

2003

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We report experiments on defect-tracking in the state of undulation chaos observed in thermal convection of an inclined fluid layer. We characterize the ensemble of defect trajectories according to their velocities, relative positions, diffusion, and gain and loss rates. In particular, the defects exhibit incidents of rapid transverse motion which result in power law distributions for a number of quantitative measures. We examine connections between this behavior and Lévy flights and anomalous diffusion. In addition, we describe time-reversal and system size invariance for defect creation and annihilation rates. Topological defects within patterns are observed in many systems to move in a spatiotemporally chaotic fashion. We examine the motion of such defects within a defect-turbulent state observed in thermal convection of an inclined fluid layer. We characterize the trajectories of the defects both by analogy to fluid turbulence -velocity distributions, diffusion, and power spectra -and by properties dependent upon the topological characteristics of the defects: pair creation/annihilation and interactions.

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Physical optics treatment of the shadowgraph

Cited by 131 publications

References 18 publications

Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

Concentration fluctuations in nonisothermal reaction-diffusion systems

Statistics of defect motion in spatiotemporal chaos in inclined layer convection

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