Express 21 5 Express 18 11 Express 25 8 AA Express 22 19 Alharbi Opt. Express 26 19 Diatta and S. Brun, S. Guenneau, and A.
Germain, and A. Greenleaf, Y. Kurylev, M. Lassas, and G. Zhang, D. Genov, C. Sun, and X. Kohn, H. Shen, M. Vogelius, and M. Nicolet, F. Zolla, and S. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Cummer and D. Chen and C. Huang, Y. Feng, and T. Zolla, S. Guenneau, A. Nicolet, and J. Schurig, J. Mock, B. Justice, S. Cummer, J. Pendry, A. Starr, and D. Pendry, D. Schurig, and D. Milton, M.
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Briane, and J. Alu and N. Greenleaf, M. Pure Appl. An approximate description would be a "random counter-current flow". Although diffusion always affects the recorded values, the transit time through this intermediate region is too short to homogenize the mixture.
Farther from the surface, the mixture produced by turbulent movements turbulent diffusion is superimposed by the homogenization at the molecular level produced by molecular diffusion which allows one to use a reference value C b for the bulk liquid. Complementary Aspects of the Different Profiles. Experimental evidence of this affirmation is needed to confirm the adequacy of the use of p c as a measure of the diffusive layer considering, for example, the numerical results of Maganaudet and Calmet, Experiments on oxygen absorption by water were conduced by Janzen at the Institute of Hydromechanics, University of Karlsruhe, Germany.
The data permitted description of the mean characteristics of the oxygen concentration in the liquid phase very close to the surface and a check on the theoretical concepts previously described. Figure 4 shows a sketch of the turbulence-generating system composed of a tank made of Perspex, with a 0. Water was filled until a depth of For the concentration field experiments, a 6.
The center of oscillation of the grid was positioned Full descriptions of this oscillating-grid tank may be found in Herlina and Janzen The grid was operated with strokes S of 5. The mean water temperature was Table 1 presents experimental parameters, where Re is the Reynolds number for the equipment.
The frequency ranges for both strokes were chosen based on the quality of the recorded images, to assure a high quality for the calculated statistical functions. The runs were performed sequentially to approach similar environmental and surface conditions , with unbroken and visually clean surfaces.
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Data acquisition began 10 min after the onset of oscillation. PBA, which fluorescence changes in the presence of oxygen, was used to determine the dissolved oxygen concentration in water, as described by Vaughan and Weber Figure 4 shows the LIF setup used in this study.
For the experiments, the tank was filled with water and 2x10 -5 M PBA. Nitrogen was bubbled into the water during 20 minutes to attain an oxygen concentration of about 0. A pulsed nitrogen laser MNL with a mean energy power of 0. The laser beam was guided into the centre of the tank through a UV-mirror and a combination of lenses. A FlowMaster CCD camera x pixels and 12 bit , with a macro objective was used to obtain images of approximately 9.
Nine hundred images were taken for each run, in three sets of images. Image processing was performed, involving noise removal, water surface detection, correction of laser attenuation, and correction of optical blurring near the interface. The image processing procedure is described in details by Janzen , being the same of that described by Woodrow and Duke and Herlina and Jirka The c' profiles of the oxygen concentration are presented in Figure 5 a.
All profiles show a well defined peak. Steep slopes are observed close to the surface and long tails after the peak. Figure 5 b shows that the measured values of p c varied in the range from to m, decreasing for higher Reynolds number or, in other words, presenting c'-peaks closer to the surface. This behavior agrees with the general understanding that the thickness of the "diffusive region" close to the surface must be lower for higher agitation levels of the liquid. The experimental amplitudes of the peaks vary in the range from 0.
Peaks of c' were also reported by several authors: Lee and Luk presented values in the range of about 0. As can be seen, all reported values are lower than the proposed limit of 0. Figure 6 a shows the normalized mean oxygen concentration profiles n see Eq. All measured curves merged together, showing that p c is a good choice to normalize the mean concentration profiles. Figure 6 c also reproduces the data of Figure 6 b , to permit comparisons. As the profiles for n and c' are known experimentally determined , Eq. Figure 7 b shows that the peak values decreased strongly, from 0.
Although the near-surface dominance of molecular diffusion over turbulent transport is amply mentioned in the literature e. Comparisons between values of molecular and turbulent fluxes were presented by Janzen and Herlina and Jirka , showing that the present results are consistent with previous observations. The subsuperficial structure composed by a diffusive layer in the region mainly affected by the surface and an outer turbulent region is well evidenced by the present data and analysis.
The frontier between both regions is conveniently quantified using the vertical coordinate p c. It was shown theoretically that the subsurface region of interfacial mass transfer may be adequately described by the random square wave approximation. It was also shown theoretically that the amplitude of the peak of c' must be lower than 0. The amplitudes of the peaks of c' oscillated in the range from 0.
RMS of the concentration fluctuation function of z. Reynolds number at the surface. Reynolds number of the equipment. Atmane, M. Bender, C. Calmet, I. Fluids, 9, p. Chu, C. Germano, M.
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Fluids, 29, p. Handler, R. Fluids, 11, p. Herlina, Gas transfer at the air-water interface in a turbulent flow environment, p. Doktor Thesis, University of Karlsruhe, Karlsruhe Herlina and Jirka, G.
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Janzen, J. Kumar, S. Fluids 10, p. Komori, S. Direct numerical simulation of three-dimensional open-channel flow with zero-shear gas-liquid interface, Phys. Lam, K. Fluids, A 4, p. Lee, Y. Lewis, W. Industrial and Engineering Chemistry, v. Magnaudet, T. Fluid Mech. Momesso, A. Nagoaosa, R. Fluids 11, p. Ramshankar, R. Scalar dispersion and the structure of the concentration field, Phys.
Fluids A. Saylor, J. Schulz, H. E and Schulz, S. Computational Mechanics Publications, p. Vaughan, W. Woodrow, P. In: Donelan, M.