Mixing analysis in a coaxial mixer

The performance of a coaxial mixer in the laminar-transitional flow regime was numerically investigated with Newtonian and non-Newtonian fluids. These mixers comprised two shafts: a central fast speed shaft mounted with an open turbine, and a slow speed shaft fitted with a wall scraping anchor arm. To model the complex hydrodynamics inside the vessel, the virtual finite element method (POLY3D^TM software) coupled with a Lagrange multiplier approach to cope with the non-linearity coming from the rheological model was employed. Co-rotation and counter-rotation mode were compared, based on several numerical criteria, namely, mixing time, power consumption and pumping rate. It was found that co-rotating mode is more efficient than counter-rotating mode in terms of energy, pumping rate and homogenization time.     

Theoretical prediction of gas-liquid mass transfer coefficient, specific area and hold-up in sparged stirred tanks

A prediction method for calculating the volumetric mass transfer coefficient, k_La, in gas-liquid sparged stirred tanks is proposed. A theoretical equation based on Hibie's penetration theory and the isotropic turbulence theory of Kolmogoroff is used for k_L determination. The values of the interfacial area have been calculated from a hold-up theoretical equation and the mean size of the gas bubble. Both Ostwald-De Waele and Casson models are used to describe the rheological properties of the fluid. The model predicts the mass transfer coefficient and the interfacial area values in stirred tank reactors, analysing the influence of different variables. The values of the volumetric mass transfer coefficient can be calculated for different geometries of the reactor, different physicochemical properties of the liquid and under different operational conditions. The capability of prediction has been examined using experimental data available in the literature for Newtonian and non-Newtonian fluids, for very different vessel sizes, different numbers and types of stirrers and a wide range of operational conditions, with very good results.     

Dimensional analysis for planetary mixer: Mixing time and Reynolds numbers

Mixing time number is a convenient parameter to characterize mixing performance of stirred tanks. This dimensionless number is now well established for agitated vessels equipped with vertically and centrally mounted impeller for Newtonian as well as for non-Newtonian fluids. To our knowledge, there is more ambiguity concerning its definition for planetary mixers especially when they have dual motion (around two perpendicular axes) to achieve homogenization. In this study, dimensional analysis of mixing time and reliability of the modified Reynolds and mixing time numbers are proposed for such a planetary mixer particularly named as TRIAXE^® system. These two numbers are based on the maximum tip speed of mixer as the characteristic velocity. Modified dimensionless numbers are consistent with the definition of conventional Reynolds and mixing numbers (when only one revolving motion around the vertical axis of the mixing device occurs in the vessel).Mixing time experiments with TRIAXE^® mixer for highly viscous Newtonian fluids showed that the proposed modified Reynolds and mixing time numbers succeeded to obtain a unique mixing curve irrespective of the different speed ratio chosens. This agreement proves that the proposed modified dimensionless numbers can be well adapted for engineering purposes and they can be used to compare the mixing performance of planetary mixers.     

LOCAL OVERALL GAS-LIQUID VOLUMETRIC MASS TRANSFER COEFFICIENTS IN A GAS-LIQUID TWO-PHASE REVERSED FLOW JET LOOP REACTOR

Local overall gas-liquid volumetric mass transfer coefficient profiles at the specified point were experimentally investigated in a gas-liquid two-phase reversed flow jet loop reactor with Newtonian and non-Newtonian systems. It was observed that the local overall gas-liquid volumetric mass transfer coefficient profiles of this reactor with Newtonian and non-Newtonian systems increase with increase in gas jet flow rates and liquid jet flow rates, and with decrease in nozzle diameter and CMC concentration.     

An explicit equation for the terminal velocity of solid spheres falling in pseudoplastic liquids

An explicit equation is proposed which predicts directly the terminal velocity of solid spheres falling through stagnant pseudoplastic liquids from the knowledge of the physical properties of the spheres and of the surrounding liquid. The equation is a generalization of the equation proposed for Newtonian liquids. By properly defining the dimensionless diameter, d_*, a function of the Archimedes number, Ar, and the dimensionless velocity, U_*, a function of the generalized Reynolds number, Re, to account for the non-Newtonian characteristics of the liquid, the final equation relating these two variables has similar form to the Newtonian equation. The predictions are very good when they are compared to 55 pairs of Re—C_D for non-Newtonian data and 37 pairs for Newtonian data published previously. The root mean square error on the dimensionless velocity is 0.081 and much better than the only other equation previously proposed.     

Mass transfer and hydrodynamic characteristics of a high aspect ratio self-ingesting reactor for gas-liquid operations

The mass transfer performance of a gas-liquid self-ingesting stirred reactor is reported both for coalescing and non-coalescing systems. The vessel features are a high aspect ratio and a rather narrow multiple-impeller draft tube, through which the gas phase is ingested and led down to the vessel bottom, where it is finely dispersed into the liquid rising in the annular portion of the vessel. Comparison is made between k_La values determined by several variants of the dynamic method, among which pure oxygen absorption in a previously de-gassed liquid phase. Results show that the gas-liquid mass transfer coefficient values obtained with the last approach are remarkably larger than those measured with all other techniques in which nitrogen is initially dissolved in the liquid phase. Possible reasons behind this discrepancy are discussed.The gas-liquid mass transfer performance of the investigated gas inducing contactor is finally compared with literature data on other self-inducing/ingesting devices. Comparison results encourage further development of the investigated apparatus.     

Gas absorption into non-newtonian fluids in rotating disc contactors

Mass transfer characteristics (k_Ia and a) for rotating disc contactor where a number of discs are mounted on a horizontal shaft and are partially submerged in a pool of liquid, are determined experimentally for Newtonian and non-Newtonian fluids. A simple model based on wetted area is developed which correlates the data within 10%.     

Gas-liquid mass transfer studies: The influence of single- and double-impeller configurations in stirred tanks

The influence of impeller structure on the mass transfer characteristics was studied with the steady-state method for gas-liquid volumetric mass transfer coefficient (k _L a). The single-impeller configurations included eight impeller types (three radial flow impellers, four axial flow impellers and one mixed flow impeller), and the doubleimpeller included three configurations (RT+RT, RT+WH _D , WH _D +WH _D ). For single-impeller, the gas-liquid mass transfer rates of radial flow impellers were better than those of axial flow impellers under the same rotation speed and gas flow rate. The mass transfer performance (defined as the volumetric mass transfer coefficient per unit power input) of radial flow impellers were also better than that of axial flow impellers. With the same kLa value under a certain gas flow rate, the local bubble size distribution between radial flow impeller and axial flow impeller was similar. As for double impellers, RT+RT provided the highest mass transfer rate under certain rotation speed and gas flow rate, while WH _D +WH _D gave the highest values of gas-liquid mass transfer coefficient with the same power consumption.     

Gas—liauid mass transfer in three-phase stirred tank reagors: Newtonian and non-newtonian fluids

Gas—liquid mass transfer has been investigated in gas—liquid-solid three-phase stirred tank reactors with Newtonian and non-Newtonian liquids. Volumetric mass transfer coefficients and gas hold-ups were measured in a 0.2 m i.d. stirred tank reactor and the effects of low-density polymeric particles (ρ_s, =1030 and 1200 kg/m³; up to 15 vol%) on gas—liquid mass transfer were examined. The volumetric mass transfer coefficients in water were found to decrease due to the presence of solid particles at constant impeller speed and superficial gas velocity. On the other hand, solids loading led to higher mass transfer rates in non-Newtonian carboxymethyl cellulose aqueous solutions. Our previously proposed model for mass transfer in gas—liquid two-phase systems was extended to gas—liquid—solid three-phase systems. Reasonable agreement was found between the predictions of the proposed model and the experimental data.     

Mass transfer of carbon dioxide in aqueous polyacrylamide solution with methyldiethanolamine

Carbon dioxide was absorbed into aqueous polyacrylamide (PAA) solution containing methyl-diethanolamine (MDEA) in a flat-stirred vessel to investigate the effect of non-Newtonian rheological behavior of PAA on the rate of chemical absorption of CO₂, where the reaction between CO₂ and MDEA was assumed to be a first-order reaction with respect to the molar concentration of CO₂ and MDEA, respectively. The liquid-side mass transfer coefficient (k_L), which was obtained from the dimensionless empirical equation containing the viscoelasticity properties of a non-Newtonian liquid, was used to estimate the enhancement factor due to chemical reaction. PAA with elastic property of non-Newtonian liquid made the rate of chemical absorption of CO₂ accelerate compared with a Newtonian liquid     

Zur Fluiddynamik und zum Stoffübergang newtonscher und nichtnewtonscher Gemische auf Siebböden

Fluiddynamics and Mass Transfer of Newtonian and non-Newtonian Mixtures on Sieve Trays Highly viscous media are processed in a number of industries such as the chemical, pharmaceutical, petrochemical and food industries, whereby a great number of the used systems has an non-Newtonian behaviour. To improve the knowledge of mass transfer processes in Newtonian and non-Newtonian mixtures systematic experiments for fluiddynamics and mass transfer were carried out on various sieve trays. The realised results show that the separation performance of tray columns can be increased significantly by a suitable choice of operating conditions and sievetray lay-out. This paper summarizes results on the absorption of oxygene into water and in non-Newtonian liquids like carboxyl-methylcelluose/water and polyacrylamide/water. In parallel to the experimental measurements new correlations for the mass transfer of tray columns operating with average and high-viscous media were developed.     

Influence of polyethylene oxide on absorption of carbon dioxide into aqueous <Emphasis Type="Italic">N</Emphasis>-methyldiethanolamine solution

Carbon dioxide was absorbed into aqueous polyethylene oxide (PEO) solution containing N-methyldiethanolamine (MDEA) in a flat-stirred vessel to investigate the effect of non-Newtonian rheological behavior of PEO on the chemical absorption rate of CO₂, where the reaction between CO₂ and MDEA was assumed to be a first-order reaction with respect to the concentration of CO₂ and MDEA, respectively. A unified correlation equation containing the Deborah number, which reflects the viscoelastic properties of a non-Newtonian liquid, was used to obtain the volumetric liquid-side mass transfer coefficient of carbon dioxide in aqueous PEO solution. The elastic properties of PEO accelerated the absorption rate of CO₂ compared with that of a Newtonian liquid based on the same values of viscosity.     

A review on single bubble gas–liquid mass transfer

It is common to empirically correlate volumetric mass transfer coefficient k_La for predicting gas–liquid mass transfer in industrial applications, and the investigation of single bubble mass transfer is crucial for a detailed understanding of mass transfer mechanism. In this work, experiments, models and simulations based on the experimental results were highlighted to elucidate the mass transfer between single bubbles and ambient liquid. The experimental setups, measurement methods, the mass transfer of single bubbles in the Newtonian and the non-Newtonian liquid, models derived from the concept of eddy diffusion, the extension of Whitman's, Higbie's and Danckwerts' models, or dimensionless numbers, and simulation methods on turbulence, gas–liquid partition methods and mass transfer source term determination are introduced and commented on. Although people have a great knowledge on mass transfer between single bubbles and ambient liquid in single conditions, it is still insufficient when facing complex liquid conditions or some phenomena such as turbulence, contamination or non-Newtonian behavior. Additional studies on single bubbles are required for experiments and models in various liquid conditions in future.     

Trickle bed hydrodynamics and flow regime transition at elevated temperature for a Newtonian and a non-Newtonian liquid

Despite the hydrodynamics of trickle beds experiencing high pressures has become largely documented in the recent literature, trickle bed hydrodynamic behavior at elevated temperatures, on the contrary, largely remains terra incognita. This study's aim was to demonstrate experimentally the temperature shift of trickle-to-pulse flow regime transition, pulse velocity, two-phase pressure drop, liquid holdup and liquid axial dispersion coefficient. These parameters were determined for Newtonian (air-water) and non-Newtonian (air-0.25% Carboxymethylcellulose (CMC)) liquids, and the various experimental results were compared to available literature models and correlations for confrontation and recommendations. The trickle-to-pulse flow transition boundary shifted towards higher gas and liquid superficial velocities with increasingly temperatures, aligning with the findings on pressure effects which likewise were confirmed to broaden the trickle flow domain. The Larachi-Charpentier-Favier diagram [Larachi et al., 1993, The Canadian Journal of Chemical Engineering 71, 319-321] provided good predictions of the transition locus at elevated temperature for Newtonian liquids. Conversely, everything else being kept identical, increasingly temperatures occasioned a decrease in both two-phase pressure drop and liquid holdup; whereas pulse velocity was observed to increase with temperature. The Iliuta and Larachi slit model for non-Newtonian fluids [Iliuta and Larachi, 2002, Chemical Engineering Science 46, 1233-1246] predicted with very good accuracy both the pressure drops and the liquid holdups regardless of pressure and temperature without requiring any adjustable parameter. The Burghardt et al. [2004, Industrial and Engineering Chemistry Research 43, 4511-4521] pulse velocity correlation can be recommended for preliminary engineering calculations of pulse velocity at elevated temperature, pressure, Newtonian and non-Newtonian liquids. The liquid axial dispersion coefficient (D_ax) extracted from the axial dispersion RTD model revealed that temperatures did not affect in a substantial manner this parameter. Both Newtonian and power-law non-Newtonian fluids behaved qualitatively similarly regarding the effect of temperature.     

THEORETICAL PREDICTION OF GAS HOLDUP IN BUBBLE COLUMNS WITH NEWTONIAN AND NON-NEWTONIAN LIQUIDS

A simple model based on an energy balance which takes into account the friction losses at the gas-liquid interface and the slip velocity of single bubble is used to simulate the gas holdup in bubble columns containing Newtonian and non-Newtonian liquids which circulate in both laminar and turbulent flows. Experimental data available from the literature for bubble columns up to 7 m height and 1 m diameter with water and glycerol as Newtonian liquids and different solutions of CMC in a wide range of concentrations as non-Newtonian liquids are simulated with good agreement despite the simplifications made to describe the gas liquid flow regimes. Most of the differences between experimental and calculated gas holdup are justified on the basis of the simplifying assumptions.     

鼓泡反应器中幂律型流体流动与传质特性

很多废水处理装置涉及非牛顿型流体中的多相流动和传质问题,研究其中的气液传质过程有助于实现装置的优化设计和高效节能运行。以鼓泡反应器内清水和不同质量分数的羧甲基纤维素钠（CMC）水溶液为实验对象,分别研究气相表观气速和液相流变特性对气泡尺寸分布、全局气含率和体积氧传质系数的影响。实验结果表明,液相的流变特性对其传质特性参数均有较大影响。与清水相比,CMC水溶液中气泡平均直径和分布范围更大;清水和CMC水溶液的全局气含率均随表观气速的增加而增大;CMC水溶液的体积氧传质系数随CMC水溶液质量分数的增加而减小。基于实验研究,得出修正的体积氧传质系数公式和适用于幂律型非牛顿流体流动体系氧传递过程的无量纲关联式,可很好地实现非牛顿流体流动的废水处理装置中气液传质参数的计算。     

Oxygen transfer into newtonian and non-newtonian fluids in mechanically agitated vessels

Oxygen transfer into Newtonian and non-Newtonian fluids was studied in stirred tank vessels of 0.0018, 0.006 and 0.036 m³ operating volumes. Emphasis was given to the rheological effects of the pseudoplastic medium on the volumetric oxygen transfer coefficient, K_La. Results indicate that K_La is a strong function of gassed power input per unit volume (P_g/V) for the Newtonian fluid, but a weak function of P_g/V for the non-Newtonian fluid, and a strong function of superficial gas velocity (V_s) for both fluids for paddle-type impellers. K_La is found to decrease rapidly with an increase in apparent viscosity for values of μ_a greater than 2.0 Pa · s. In addition to various correlations, a dimen-sionless correlation including the impeller Reynolds number, impeller Weber number, and the aeration number is presented for the prediction of K_La in a gas-liquid non-Newtonian system.     

Hydrodynamics and volumetric gas-liquid mass transfer coefficient of a stirred vessel equipped with a gas-inducing impeller

Hydrodynamic and mass transfer characteristics of a gas-liquid stirred tank provided with a radial gas-inducing turbine were studied. The effect of the rotation speed and the liquid submergence on global hydrodynamic and mass transfer parameters such as the critical impeller speed, the induced gas flow rate, the gas holdup, the power consumption and the volumetric gas-liquid mass transfer coefficient were investigated. The experiments are mainly conducted with air-water system. In the case of critical impeller speed determination, two liquid viscosities have been used. The volumetric gas-liquid mass transfer coefficient k_La has been obtained by two different techniques. The gas holdup, the induced gas rate and the volumetric gas-liquid mass transfer coefficient are increasing functions with the rotation speed and decreasing ones with the liquid submergence. The effects of these operating parameters on the measured global parameters have been taken into account by introducing the dimensionless modified Froude number and correlations have been proposed for this type of impeller.     

Effect of mixing behaviour on gas-liquid mass transfer in highly viscous,stirred non-newtonian liquids

When declaring and using process engineering data such as, for exmple, mixing times or k_La values, it is assumed that these apply to the entire reactor contents. The condition of uniform mixing, necessary for this, is generally met in the regime of turbulent flow. When highly viscous and, above all, strongly non-Newtonian liquids are stirred in small reactors, there are frequently also regions of laminar flow and completely stagnant zones, which are only partially mixed or not at all. The present paper pursues the question to what extent is the gas-liquid mass transfer in stirred, highly non-Newtonian liquids influenced by the mixing behaviour of the reactor. The results show that, below certain Reynolds numbers, three relatively distinct regions exist, with different mixing intensities. Between an almost ideally mixed region in the vicinity of the stirrer and a completely stagnant and dead one, there is a zone of very slight motion. This finding demonstrates that the usual determination of integral or volume-based data in the literature is neither logical nor adequate for the case under consideration. Thus, the gas-liquid mass transfer takes place mainly in the relatively well mixed region. Therefore, use of a k_La value also requires the volume of this region to be declared. Only the knowledge of this volume enables us to correlate the k_La values in such a way that the sorption characteristics thus obtained appear suitable for scale-up. This procedure, which is illustrated by numerous examples of measured results for different stirrers, is important whenever design data for highly viscous liquids are to be worked out on the basis of laboratory measurements. Only when larger equipment is used, in which turbulent flow can be achieved, this problem does not arise because of the relatively uniform mixing of reactor contents.     

Mass transfer to newtonian and non-newtonian fluids from rotating cylinders

Mass transfer from rotating cylinders to Newtonian and non-Newtonian fluids is investigated. Present and previous data are analysed and correlations are presented. Free convection mass transfer correlations for vertical cylinders are found to differ from those for horizontal cylinders available in previous literature. Modified Prandtl analogy is applied, by considering the eddy penetration of the diffusion sublayer, to obtain the following expression for forced convection mass transferSh Sc^{?$\text{1}\text{3}$} = 0.62fRe which is found to correlate the present and previous data in the range of Sc, 2.6–32000, Pr, 0.72–676 and Re, 10²–10⁵ with a standard deviation of 14.6%. Differential viscosity is used to correlate mass transfer data to non-Newtonian fluids. Experimental results are seen to be lower than those predicted by the Newtonian correlation.