Hydrodynamics and mass transfer in bubble column: Influence of liquid phase surface tension

According to literature, few experiments are performed in organic solvents which are mostly used in commercial gas–liquid reactors. However, it is commonly accepted that data obtained in aqueous solution allow to predict the surface tension effects, and to model the behaviour of organic solvents. In this work, we examine the validity of this approximation. In this objective, the flows observed in two pure media having similar viscosity but different surface tension—respectively, water (reference) and cyclohexane (solvent)—are successively compared at two scales: in a bubble column and in bubble plumes. In bubble plumes, as expected, the mean bubble size is smaller in the medium having the smallest surface tension (cyclohexane), but for this medium the destabilisation of flow is observed to occur at smaller gas velocity, due to break-up and coalescence phenomena. In bubble column, these phenomena induce the bubbling transition regime at lower gas velocity, whatever the operating conditions for liquid phase: batch or continuous. Consequently, when the two media are used at similar gas superficial velocity, but in different hydrodynamic regimes, greater gas hold-up and smaller bubble diameter can be observed in water; the interfacial area is then not always higher in cyclohexane. This result differs from the behaviour observed in the literature for aqueous solutions. The analysis of bubble plumes in aqueous solutions of butanol shows that this difference is due to a fundamental difference in coalescent behaviour between pure solvents and aqueous mixtures: the surface tension effect is less important in pure liquid than in aqueous solutions, because of the specific behaviour of surfactants. It is then still difficult to predict a priori the bubbling regime or the flow characteristics for a given medium, and all the more to choose an appropriate liquid as a model for industrial solvents

Axial and Radial Investigation of Hydrodynamics in a Bubble Column;Influence of Fluids Flow Rates and Sparger Type

A detailed investigation of local hydrodynamics in a pilot plant bubble column has been performed using various techniques, exploring both axial and radial variations of the gas hold-up, bubble average diameter and frequency, surface area. A wide range of operating conditions has been explored up to large gas and liquid flow rates, with two sparger types. Two main complementary techniques were used: a quasi local measurement of gas hold-up via series of differential pressure sensors to get the axial variation and a double optic probe giving radial variations of gad hold-up, bubble average size and frequency and surface area. According to axial evolutions, three zones, where radial evolutions have been detailed,have been separated: at the bottom the gas injection zone, the large central region or column bulk and the disengagement zone at the column top. It was found that significant axial and radial variations of the two phase flow characteristics do exist even in the so called homogeneous regime. The normalized profiles of bubble frequency appear sparger and gas velocity independent contrary to bubble diameter, gas hold-up and interfacial area normalized profiles. In any case bubbles are larger in the sparger zone than elsewhere. The main result of this work is the very strong effect of liquid flow on bubble column hydrodynamics at low gas flow rate. First the flow regime map observed in batch mode is dramatically modified with a drastic reduction of the homogeneous regime region, up to a complete heterogeneous regime in the working conditions (uG> 0.02 m/s). On the contrary, liquid flow has limited effects at very high gas flow rates. A large data bank is provided to be used for example in detailed comparison with CFD calculations

Mass transfer in bubble column for industrial conditions—effects of organic medium, gas and liquid flowrates and column design

Most of available gas–liquid mass transfer data in bubble column have been obtained in aqueous media and in liquid batch conditions, contrary to industrial chemical reactor conditions. This work provides new data more relevant for industrial conditions, including comparison of water and organic media, effects of large liquid and gas velocities, perforated plates and sparger hole diameter. The usual dynamic O2 methods for mass transfer investigation were not convenient in this work (cyclohexane, liquid circulation). Steadystate mass transfer of CO2 in an absorption–desorption loop has been quantified by IR spectrometry. Using a simple RTD characterization, mass transfer efficiency and kLa have been calculated in a wide range of experimental conditions. Due to large column height and gas velocity, mass transfer efficiency is high, ranging between 40% and 90%. kLa values stand between 0.015 and 0.050 s−1 and depend mainly on superficial gas velocity. No significant effects of column design and media have been shown. At last, using both global and local hydrodynamics data, mass transfer connection with hydrodynamics has been investigated through kLa/G and kLa/a

On the reliability of an optical fibre probe in bubble column under industrial relevant operating conditions

When bubble columns are operated under industrial relevant conditions (high gas and liquid flow rates, large bubbles and vortices,. . .), local data, and especially bubble size values, are difficult to obtain. However, such data are essential for the comprehension of two-phase flow phenomena in order to design or to improve industrial installations. When high gas flow rates and organic liquids are used, intrusive optic probes are considered. This work investigates different ways to derive reliable local information on gas phase from double optic probe raw data. As far as possible, these results have been compared with global data, easier to measure in such conditions. Local gas hold-up, eG, and bubble frequency, fB, are easily obtained, but bubble velocity and bubble diameter determination is not obvious. For a better reliability, the final treatment that is proposed for velocity and size estimation is based on mean values only: the bubble velocity is considered as the most probable velocity ~v issued from raw signals inter-correlation function and the mean Sauter diameter is calculated through dSM ¼ 3~veG 2f B

On quasianalytic local rings

This expository article is devoted to the local theory of ultradifferentiable classes of functions, with a special emphasis on the quasianalytic case. Although quasianalytic classes are well-known in harmonic analysis since several decades, their study from the viewpoint of differential analysis and analytic geometry has begun much more recently and, to some extent, has earned them a new interest. Therefore, we focus on contemporary questions closely related to topics in local algebra. We study, in particular, Weierstrass division problems and the role of hyperbolicity, together with properties of ideals of quasianalytic germs. Incidentally, we also present a simplified proof of Carleman's theorem on the non-surjectivity of the Borel map in the quasianalytic case.Comment: Final Manuscrip

Application of the double optic probe technique to distorted tumbling bubbles in aqueous or organic liquid

The optic probe technique is widely used to investigate bubble reactors. To derive values of bubble local velocities and bubble local sizes, a specific signal treatment is usually applied under severe assumptions for bubble path and shape. However, in most industrial reactors, bubble motion is chaotic and no common shape can be assumed. In this work, the reliability of the signal treatment associated with the optic probe technique is examined for distorted and tumbling bubbles. A double-tip optic probe is settled in a glass tank and the rise of bubbles is filmed simultaneously. Several trains of bubbles are studied, interactions between bubbles being gradually increased. Referring to image analysis, several ways to derive mean bubble velocities from optic probe data have been compared. Crenels from front tipand rear tipra w signals are associated and individual bubble velocities are derived. Nevertheless, complete velocity distributions are difficult to obtain, as they depend on the choice of the time within which the bubble is searched on the second tip. Using a simpler approach it is shown that the most probable velocity, calculated through the raw signals inter-correlation, is a correct estimation of the average bubble velocity. Concerning bubble size, bubble chord distributions show too high values due to bubble distortion and deviation. A simplified estimation of bubble mean Sauter diameter, using the most reliable measurements only (i.e., local gas hold-up, local mean bubbling frequency, and most probable bubble velocity), was tested for highly distorted bubbles; this method was validated both in water and cyclohexane

Heat transport in turbulent Rayleigh-Benard convection: Effect of finite top- and bottom-plate conductivity

We describe three apparatus, known as the large, medium, and small apparatus, used for high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of fluid and present results illustrating the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid. We used water samples at a mean temperature of 40 degrees C (Prandtl number sigma = 4.4). The samples in the large apparatus had a diameter D of 49.69 cm and heights L = 116.33, 74.42, 50.61, and 16.52 cm. For the medium apparatus we had D = 24.81 cm, and L = 90.20 and 24.76 cm. The small apparatus contained a sample with D = 9.21 cm, and L = 9.52 cm. For each aspect ratio Gamma = D/L the data covered a range of a little over a decade of R. The maximum R = 10^12 with Nusselt numbers N = 600 was reached for Gamma = 0.43. Measurements were made with both Aluminum and Copper top and bottom plates of nominally identical size and shape. For the large and medium apparatus the results with Aluminum plates fall below those obtained with Copper plates, thus confirming qualitatively the prediction by Verzicco that plates of finite conductivity diminish the heat transport in the fluid. The Nusselt number N_infinity for plates with infinite conductivity was estimated by fitting simultaneously Aluminum- and Copper-plate data sets to an effective powerlaw for N_infinity multiplied by a correction factor f(X) = 1 - exp[-(aX)^b] that depends on the ratio X of the thermal resistance of the fluid to that of the plates as suggested by Verzicco. Within their uncertainties the parameters a and b were independent of Gamma for the large apparatus and showed a small Gamma-dependence for the medium apparatus. The correction was larger for the large, smaller for the medium, and negligible for the small apparatus.Comment: 35 pages, 11 figures. Under consideration for publication in Phys. of Fluid

Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale

Given a subring of the ring of formal power series defined by the growth of the coefficients, we prove a necessary and sufficient condition for it to be a noetherian ring. As a particular case, we show that the ring of Gevrey power series is a noetherian ring. Then, we get a spectral synthesis theorem for some classes of ultradifferentiable functions

Scalable synthesis of ionic liquids: comparison of performances of microstructured and stirred batch reactors

A range of alkylpyridinium bromide ionic liquids have been synthesized in a stirred reactor at multigram scale and characterized by physical methods (viscosity, conductivity, melting point, electrochemical window, and water content). One ionic liquid, octylpyridinium bromide, was chosen to be synthesized in both macro and reduced scale reactors, in order to compare its performance and to afford evidence of the advantages of a cross channel micro reactor (channel width = 1 mm) compared to a stirred reactor

A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux

We report the results of high resolution direct numerical simulations of two-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to \Ra=10^{10} in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we considered the extreme cases of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law \Nu \approx 0.138 \times \Ra^{.285} with a scaling exponent indistinguishable from $2/7 = .2857...$ above \Ra = 10^{7}. The overall flow dynamics for both scenarios, in particular the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers. The findings are compared and contrasted with results of recent three-dimensional simulations.Comment: 4 page, two column RevTex4 format, 5 figure