The influence of molecular diffusion on mass transfer between turbulent liquids

The influence of molecular diffusion on liquid—liquid mass transfer in a stirred transfer cell has been found by measuring the rates transfer of helium and iso-butane from water to toluene and dekalin. These solutes have very different diffusion coefficients, their presence does not alter the physical properties of the liquids and, because their equilibrium distributions strongly favour the organic phases, the water phase mass transfer coefficient could be determined and was found to depend on the square root of the diffusion coefficient.The results are compared with the predictions of a model for liquid—liquid mass transfer under turbulent conditions, based on the approach of an eddy to the interface being restrained by interfacial tension and gravitational forces and taking into account eddy pressure fluctuations in both phases. This model provides a correlation for these results, as well as water phase mass transfer coefficients for the transfer of iso-butane from water to n-octanol, and previous stirred transfer cell results.     

HEAT EFFECTS FOR PHYSICAL AND CHEMICAL ABSORPTION IN TURBULENT LIQUID FILMS

An eddy diffusivity model was used to describe simultaneous heat and mass transfer for chemical absorption in turbulent liquid films. For absorption accompanied by a first-order reaction an approximate expression for the mass transfer coefficient is derived and shown to be in excellent agreement with exact numerical calculations. An equation is developed for the temperature rise at the free surface due to both the heat of reaction and the heat of solution. Relationships are also developed for the concentration of the liquid phase product at the free surface and the depletion of the liquid phase reactant at the free surface.

The temperature rise at the free surface for gas absorption accompanied by an instantaneous reaction due to both the heat of solution and the heat of reaction was determined. An equation is also derived for the concentration of liquid phase product at the free surface for the case of an instantaneous reaction.     

Performance improving with temperature in liquid–liquid extraction using cumene–isobutyric acid–water chemical system

The performance of single drops was investigated in liquid–liquid extraction while temperature was changed within the range of 15–40 °C. The recommended system of cumene–isobutyric acid–water with mass transfer resistance mainly in aqueous phase was used. An average enhancement of 75.6% in the rate of transfer was revealed. The extraction efficiency is the most influencing term due to molecular diffusivity enhancement. For modeling, a simple correlation was proposed for the effective diffusivity in Newman's equation, while continuous phase mass transfer coefficient was directly included. Using this model, relative deviation of the overall mass transfer coefficient was within only ±5.6%.     

DIRECT CONTACT CONDENSATION OF DILUTE STEAM/AIR MIXTURES ON WAVY FALLING FILMS

Condensation from air-steam mixtures on falling water layers is investigated experimentally and theoretically. The thin film flows on the inner surface of a 5cmi.d. vertical pipe. This film is wavy turbulent while the gas phase is kept saturated with steam. Experiments are conducted with the gas mixture effectively stagnant, compared with the fast moving liquid film. Measurements are also made under a mild vacuum applied on the gas phase. Heat transfer coefficients averaged over the entire length of the condensing surface, tend to increase by decreasing the liquid flowrate, by increasing the steam fraction, and by applying a mild vacuum on the gas phase. However, for the cases examined, there is a liquid flowrate above which the heat transfer coefficient becomes almost constant.

Numerical predictions are made for a fully developed turbulent film using an eddy diffusivity model. The results indicate that for a system with a large amount of noncondensable gases-as in this study-the temperature profile in the liquid film is nearly uniform and that the major resistance to condensation resides in the gas phase. The analysis also shows that the relative contribution of sensible heat transferred through the gas phase is small relative to the latent heat released upon condensation. Comparison of predictions with experimental data suggests that a significant parameter in these analyses is the gas diffusion boundary layer thickness which seems to be comparable in size with the liquid film thickness. Finally, the possibility is discussed of correlating condensation heat transfer coefficients with already available statistical characteristics of the falling wavy layer. Theoretical predictions based on this idea are in good agreement with data.     

Mass transfer from nanofluid drops in a pulsed liquid–liquid extraction column

Mass transfer in gas–liquid systems has been significantly enhanced by recent developments in nanotechnology. However, the influence of nanoparticles in liquid–liquid systems has received much less attention. In the present study, both experimental and theoretical works were performed to investigate the influence of nanoparticles on the mass transfer behaviour of drops inside a pulsed liquid–liquid extraction column (PLLEC). The chemical system of kerosene–acetic acid–water was used, and the drops were organic nanofluids containing hydrophobic SiO₂ nanoparticles at concentrations of 0.01, 0.05, and 0.1 vol%. The experimental results indicate that the addition of 0.1 vol% nanoparticles to the base fluid improves the mass transfer performance by up to 60%. The increase in mass transfer with increased nanoparticle content was more apparent for lower pulsation intensities (0.3–1.3 cm/s). At high pulsation intensities, the Sauter mean diameter (d₃₂) decreased to smaller sizes (1.1–2.2 mm), leading to decreased Brownian motion in the nanoparticles. Using an analogy for heat and mass transfer, an approach for determining the mass diffusion coefficient was suggested. A new predictive correlation was proposed to calculate the effective diffusivity and mass transfer coefficient in terms of the nanoparticle volume fraction, Reynolds number, and Schmidt number. Finally, model predictions were directly compared with the experimental results for different nanofluids. The absolute average relative error (%AARE) of the proposed correlation for the mass transfer coefficient and effective diffusivity were 5.3% and 5.4%, respectively.     

HEAT EFFECTS FOR PHYSICAL AND CHEMICAL ABSORPTION IN TURBULENT LIQUID FILMS

An eddy diffusivity model was used to describe simultaneous heat and mass transfer for chemical absorption in turbulent liquid films. For absorption accompanied by a first-order reaction an approximate expression for the mass transfer coefficient is derived and shown to be in excellent agreement with exact numerical calculations. An equation is developed for the temperature rise at the free surface due to both the heat of reaction and the heat of solution. Relationships are also developed for the concentration of the liquid phase product at the free surface and the depletion of the liquid phase reactant at the free surface.

The temperature rise at the free surface for gas absorption accompanied by an instantaneous reaction due to both the heat of solution and the heat of reaction was determined. An equation is also derived for the concentration of liquid phase product at the free surface for the case of an instantaneous reaction.     

Asymmetry of Peak Shapes in Linear Gas—Liquid Chromatography

Abstract

A mathematical model describing axial dispersion, interparticle mass transfer, intraparticle gas diffusion, and diffusion in a uniform thickness liquid film is used systematically to investigate the influence of intraparticle diffusivity, diffusivity in a stationary liquid phase (SLP), partition coefficient, and thickness of liquid film on the shape of the peaks in linear gas—liquid chromatography by converting Laplace transformed equations into time domain. The low diffusivities of intraparticle and/or SLP can cause the asymmetry and long tail in chromatographic peaks. A higher partition coefficient and the film thickness at low diffusivities also give skewed peaks. At a higher mass transfer rate, the peak becomes sharper. From these results a guide can be suggested to avoid the asymmetric condition of long-tailing peaks.     

The Use of Surface Renewal and Eddy Diffusivity Theories in the Ozonation of a THM Precursor: 1,3-Cyclohexanedione

Kinetic equations derived from surface renewal and eddy diffusivity theories for fast and instantaneous kinetic regimes of absorption have been applied to the results of the ozonation of 1,3-cyclohexanedione (CYC) in water. This has allowed the determination of the rate constant of the direct reaction of ozone with CYC and the liquid phase volumetric mass transfer coefficient of the system. The results obtained are close to those reported in the preceding paper (SOTELO et al., 1991) when using the film theory. However, the ozone partial pressure necessary to reach the instantaneous kinetic regime is higher for the case of the theories applied in this work.     

CFD simulations of wall mass transfer for Taylor flow in circular capillaries

Computational fluid dynamics is used to investigate the mass transfer from the liquid phase to the channel wall for Taylor flow of bubbles rising in circular capillaries. The separate influences of the Taylor bubble rise velocity, unit cell length, gas holdup, and liquid diffusivity on mass transfer were investigated for capillaries of 1.5, 2 and 3 mm diameter. A correlation is proposed for estimation of the wall mass transfer coefficient and this correlation has been tested against published experimental data.     

The effect of diffusivity on gas-liquid mass transfer in stirred vessels. Experiments at atmospheric and elevated pressures

Mass transfer has been studied in gas-liquid stirred vessels with horizontal interfaces which appeared to the eye to be completely smooth. Special attention has been paid to the influence of the coefficient of molecular diffusion. The results are compared with those published before. The simplifying assumptions of identical hydrodynamical conditions at the same stirrer speed in one particular geometry, which have been made in some previous investigations, is shown to be wrong and may lead to incorrect conclusions on the influence of the diffusion coefficient. For the gas phase the mass transfer can be described by the penetration theory (Higbie, R., 1935, Trans. Am. Inst. Chem. Engrs35, 36–60) or surface renewal model (Danckwerts, P. V., 1951, Ind. Engng Chem.43, 1460–1467). With the use of a dimensionless equation, Sh, Re and Sc numbers, all data, even experiments carried out at elevated pressures, could be well correlated. For the liquid phase the results indicate that the mass transfer cannot be described by a simple model. The King model (King, C.J., 1976, Ind. Engng Chem. Fundam.5, 1–8), a combination of molecular and eddy diffusivity, is able to explain qualitatively the observed phenomena and the literature data.     

Concentration profiles in a packed distillation column

Concentration profiles in a pilot plant-sized packed distillation column were measured by sampling both the liquid and the vapour in ten positions along the column. The results were compared with the profiles obtained by computer simulation from the plug flow and backmixing models. It was found that the stagewise backflow model reproduced the experimental profiles well. The corresponding mass transfer coefficients were greater than those calculated for the plug-flow model and could be better correlated with the vapour velocity. However, the corresponding backmixing coefficients were rather low, the equivalent eddy diffusivity in the liquid phase being of the order of 10^?3m²/s.     

Experimental studies of interphase mass transfer with chemical reaction — Saponification of esters

This study concerns the transfer of ethyl acetate from a supernatant still liquid into a lower layer of caustic solution in which a saponification reaction occurs. Apparatus and techniques for measuring the concentration profiles which develop in the turbulent reaction layer in the aqueous phase at the liquid-liquid interface are described. In particular, the effects of turbulence on the reaction layer propagation, the reaction zone in the turbulent layer, and the concentration distribution of various components of the system were observed and measured. From these data, mass transfer rates and enhancement factors were deduced. The effects of turbulence in the aqueous phase were presented in terms of an eddy diffusivity model.     

Liquid phase axial mixing in bubble columns operated at high pressures

Liquid phase axial mixing was measured in a 100 mm i.d. bubble column operated in the pressure range of 0.1-0.5 MPa. Water, ethanol and 1-butanol were used as the liquid phase and nitrogen as the gas phase. The temperature and superficial gas velocity were varied in the range of 298-323 K and 0.01-0.21 m/s, respectively. The axial dispersion coefficient increased with an increase in the gas density due to pressure. The temperature had surprisingly a small effect. A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient (D_L). The predictions of axial dispersion coefficient agree favorably with all the experimental data collected in this work as well as published in the literature. The model was extended for different gas-liquid systems. The predicted values of axial dispersion coefficient were found to agree very well with all the experimental data.     

大型液相色谱分离过程参数辨识新方法

本文提出大型液相色谱分离过程流体轴向扩散系数、吸附相平衡常数和总传质系数参数辨识模型,用惰性物为示踪剂扰动应答实验技术和色谱测量技术测定参数。结果表明:在轴向扩散中,涡流扩散占主导地位;轴向扩散系数随流体流速以及装填密度的增大而增大;相平衡常数比总传质系数有较高灵敏度;葡萄糖果糖的相平衡常数随温度的升高而降低,而总传质系数随流体流速和温度的增大而增大;得到理论流出曲线与实验流出曲线一致的结果。     

Modeling the axial distribution of mass transfer coefficient in an agitated-pulsed extraction column

The dispersed phase holdup and drop size in solvent extraction columns vary along the column height and this affects the mass transfer coefficient and interfacial area. In this article, mass transfer study was performed experimentally using a 25 mm diameter agitated pulsed column. The axial distribution of mass transfer coefficient was determined by coupling population balance equation and axial dispersion model by taking the longitudinal variation in hydrodynamic performance into consideration. Feasibility of different mass transfer models in predicting concentration profiles was evaluated and a novel correlation based on effective diffusivity was developed. The results showed that both overall and volumetric mass transfer coefficients have significant change along the column height and greatly depends on the agitation speed and pulsation intensity. Increasing dispersed phase velocity also augments the overall mass transfer coefficient. The maximum number of transfer unit was measured to be 10 m⁻¹ at agitation speed of 1000 rpm.     

Estimation of diffusion coefficient for solute–polymer systems

Diffusion coefficients are needed for the analysis of many mass transfer problems involving polymers. Since the diffusivity for such systems are strong functions of temperature and concentration, the analysis of these problems is greatly facilitated if predictive methods are available for the determination of the required diffusion coefficient. Because of the limitations of the theoretical approaches for estimating diffusivity, empirical correlation of solute–polymer diffusion coefficient data with physical properties of the solute were investigated. Chemical permeation measurements were made for several organic liquids through three elastomers (polychoroprene, butyl and nitrile rubber) at five different temperatures, ranging from 25 to 65°C. The collected diffusivities were correlated with liquid kinematic viscosity. Diffusivities (at different temperatures) depend mainly on the kinematic viscosity of solutes. The results also indicate a close relation between the variation of diffusivity and viscosity with temperature.     

降液管内液体混合的模拟计算

<正>自五十年代末以来,塔板效率的模拟计算工作已有了长足的进展.但迄今的模拟工作都是在降液管内液体完全混合的假定下进行的.在大直径塔板上,由于液流不匀和二维返混,沿塔板出口堰的液体浓度是不相等的.由于假定液体在降液管内完全混合,则进入塔板的液体为均一的浓度,这对模型的求解和逐板计算都大为简便.八十年代初才见到Weiler和Lockett等关于降液管混合研究的报道.他们在矩形冷模装置上实测了降液管内液体的混合,并用涡流扩散模型求出了涡流扩散系数D’_e,证实在垂直方向上混合剧烈,可以为完全混合;但沿堰长则更接近于完全不混.工业上广泛应用弓形降液管的塔板,本研究在冷模塔弓形降液管内测得大量反映液体混合状态的数据,并运用混合池和涡流扩散两种模型,对降液管内的液体混合进行了模拟计算.     

A qualitative computational study of mass transfer in upward bubble train flow through square and rectangular mini-channels

In this paper we present a new method for numerical simulation of conjugate mass transfer of a dilute species with resistance in both phases and an arbitrary equilibrium distribution coefficient. The method is based on the volume-of-fluid technique and accounts for the concentration jump at the interface by transforming the discontinuous physical concentration field into a continuous numerical one. The method is validated by several test problems and is used to investigate the mass transfer in upward bubble train flow within square and rectangular channels. Computations are performed for a single flow unit cell and a channel hydraulic diameter of 2 mm. The simulations consider the transfer of a dilute species from the dispersed gas into the continuous liquid phase. Optionally, the mass transfer is accompanied by a first-order homogeneous chemical reaction in the liquid phase or a first-order heterogeneous reaction at the channel walls. The results of this numerical study are qualitative in nature. First, because periodic boundary conditions in axial direction are not only used for the velocity field but also for the concentration field and second, because the species diffusivity in the liquid phase is arbitrarily increased so that the liquid phase Schmidt number is 0.8 and the thickness of the concentration and momentum boundary layer is similar. Two different equilibrium distribution coefficients are considered, one where the mass transfer is from high to low concentration, and one where it is vice versa. The numerical study focuses on the influence of the unit cell length, liquid slug length and channel aspect ratio on mass transfer. It is found that for the exposure times investigated the liquid film between the bubble and the wall is saturated and the mass transfer occurs by the major part through the bubble front and rear so that short unit cells are more efficient for mass transfer. Similar observations are made for the homogeneous reaction and for the heterogeneous reaction when the reaction is slow. In case of a fast heterogeneous reaction and when the main resistance to mass transfer is in the gas phase, it appears that for square channels long unit cells are more efficient, while large aspect ratio rectangular channels are more efficient than square channels, suggesting that for these conditions they might be more appropriate for use in monolithic catalysts.     

Residence time distribution in a packed bed bioreactor containing porous glass particles: Influence of the presence of immobilized cells

An experimental investigation of the liquid phase residence time distribution (RTD) in a packed bed bioreactor containing porous glass particles is presented. For Re < 1, intraparticle forced convection is negligible and only diffusion, characterized by an effective diffusion coefficient, must be considered to describe the mass transfer process between the extraparticle and the intraparticle fluid phase. For Re > 1, the mass transfer rate becomes dependent on the liquid flow rate, indicating the existence of intraparticle convection. A model including axially dispersed flow for the external fluid phase and an ‘apparent’ effective diffusivity that combines diffusion and convection, predicts experimental RTD data satisfactorily. Yeast cells immobilized inside the porous glass beads did not affect the mass transfer rate at low biomass loading. At high biomass loading (0·02 g yeast cells g^?1 carrier), the mass transfer rate between the extraparticle and intraparticle fluid phase was significantly decreased. Comparison of the RTD data from experimets performed in the presence and absence of cells in the external fluid phase revealed that the mass transfer rate is influenced by the cells immobilized inside the porous particles and not by the cells present in the external fluid phase.     

MASS TRANSFER INTO A FREE LIQUID SURFACE EFFECTED BY SUBMERGED JETS

A theoretical and experimental analysis of mass transfer into a turbulent free liquid surface effected by submerged jets has been presented. Theoretical considerations concentrated on hydrodynamic characteristics of the system which enabled us to derive the radial velocity distribution in the surface jet flow. Some conclusions have been drawn from the two-parameter models of turbulence. The results of experimental measurements of the average mass transfer coefficients have been interpreted in terms of our own model of mass transfer accounting for eddy diffusivity. The model parameters were correlated with the basic hydrodynamic parameters of the system. Radial distributions of the local values of the mass transfer coefficients were estimated. The applicability of other models of mass transfer has also been verified. It has been shown that the model presented here is the most general and applicable for interpretation of the experimental data obtained when studying the system under consideration