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• W2010482774 abstract "The distribution of residence times of a tracer injected into a falling water film on the outside of a cylindrical tube has been measured by the frequency response method. A frequency range of about 4 decades is covered, giving phase angles up to 3600° and amplitudes attenuated in the ratio of about 3 × 10−3. High accuracy and reproducibility in this wide range are obtained by connecting a Fourier analyser to the measuring equipment. The effect of the Reynolds number and the film length on the distribution function has been studied in the region of the Reynolds number from 50 to 600 for pure water and up to 1600 with surface active agents present. The dimensionless frequency response is found to change little with the Reynolds number and with the film length, the latter observations indicating that end effects are negligible. Characteristic parameters of the distribution function such as the mean residence time and the minimum residence time are compared with other measurements of velocities and film thickness. The mean residence time of the tracer is found to be from 2 to 7 per cent greater than the mean residence time of the water derived from the laminar film theory. This is to be expected when eddy and molecular diffusion effects are present to some extent. The minimum residence time of the tracer corresponds well to the surface velocity measured by Friedman and Miller and Brauer up to Re = 400. Above Re = 400 there is a deviation from the surface velocity measured by Brauer. When the surface is rippling, the experimental results agree with the conclusion of Stirba and Hurt concerning turbulence in the outer part of the film. It is thus found that the deviation from laminar theory in the distribution function for the residence times of a tracer in pure water, is caused mainly by the ripples on the air-water interface. When surface active agents are added in a sufficient concentration, the ripples practically disappear, and the distribution function approaches closely to a pure laminar film distribution, even up to Reynolds number of about 1600. This agrees with the conclusions drawn by Emmert and Pigford from their absorbtion experiments. The experimental distribution functions obtained in the present paper are compared to different flow models, such as pure laminar flow with no diffusion, rodlike flow with superimposed longitudinal diffusion and to the model consisting of mixing stages in cascade. None of these models gave satisfactory agreement with the experimental results. A double layer flow model is proposed with an outer turbulent layer described by a diffusion model similar to that applied by Taylor and Tichacek to turbulent flow in pipes, superimposed on an inner laminar layer. The thicknesses of the two layers and the equivalent longitudinal diffusivity of the turbulent layer have been calculated. Some calculations on the transverse mass transfer and the velocity profile in the turbulent layer will follow in a subsequent publication. On a étudié l'écoulement de couches d'eau à l'extérieur de tubes cylindriques, en appliquant la méthode de réponse harmonique. Les temps de séjours moyens correspondent avec des valeurs dérivées de la théorie d'écoulement laminaire. Les temps de séjour minimums concordent assez bien avec les vitesses de la surface d'eau mesurées par quelques auteurs. Cependant, les fonctions de distribution sont complètement différentes de celles calculées pour l'écoulement laminaire. Cela est causé par la formation d'ondes à la surface de l'eau. L'écart disparut à l'addition de petites quantités de substances superficiellement actives. Die Strömung von Flüssigkeitsschichten an der Aussenseite von zylindrischen Rohren wurde mit Hilfe der Frequenzganganalyse untersucht. Die gemessenen Werte für die mittlere Verweilzeit stimmen gut überein mit denjenigen, die auf Grund der laminaren Strömungstheorie berechnet wurden. Die minimale Verweilzeiten entsprechen den von einigen Verfassern gemessenen Oberflächengeschwindigkeiten. Die gemessenen Verweilzeitverteilungen aber sind ganz verschieden von den für Laminarströmung berechneten Verteilungen. Dies ist der Bildung von Oberflächenwellen zuzuschreiben. Diese Abweichung verschwand nach der Zugabe oberflächenaktiver Stoffe." @default.
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• W2010482774 date "1961-01-01" @default.
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• W2010482774 title "G2. The distribution of residence times in a falling water film" @default.
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• W2010482774 doi "https://doi.org/10.1016/0009-2509(61)85077-x" @default.
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