Power Requirement for Mixing Shear‐Thinning Fluids with a Planetary Mixer

The optimal control of processes dealing with non‐Newtonian liquids requires the knowledge and control of the power demand of the mixing equipment. In this context, an extension of the Metzner and Otto concept to planetary mixers is proposed to adapt this concept to planetary mixers. The theoretical part of this work defines modified expressions of Reynolds and power numbers. These definitions introduce a characteristic velocity u_ch that is used to define the parameter K_s. A planetary mixer is employed to experimentally ascertain this guideline. Power consumption measurements carried out by mixing shear‐thinning fluids permit to determine the K_s factor. This factor varies only slightly with the flow behavior index and may be regarded as a defined constant for this geometry. Finally, experiments with an additional shear‐thickening fluid confirm the validity of this approach.     

Determination of Mixing Times with Helical Ribbon Impeller for Non‐Newtonian Viscous Fluids Using an Advanced Imaging Method

New results on mixing times for viscous Newtonian and non‐Newtonian fluids being homogenized with a helical ribbon impeller are presented. In particular, a recently developed technique to determine the macromixing kinetics of an impeller in a transparent vessel was applied to investigate the effects of rheological properties on mixing times. Significant differences were observed in the mixing times for viscous Newtonian and non‐Newtonian fluids. Based on the new data obtained in this work, a correlation incorporating the elastic effects is proposed in terms of a Weissenberg number for predicting the mixing time as a function of the Reynolds number and the system geometry.     

Power Consumption in Agitated Vessels with Dual Rushton Turbines: Baffle Length and Impeller Spacing Effects

The dependence of power consumption on baffle length, L, in vessels agitated by a dual Rushton turbine system was studied within the turbulent regime, and also in relation to the impeller spacing, ΔH. A dependence of varying strength could be observed. The presence of baffles in the agitated systems provided a stabilizing effect with regard to the dependence of the Newton number Ne on the Reynolds number Re. A sharp decrease in power consumption could be detected for baffle lengths L < 0.3 H, with H the liquid height in the vessel. The Newton number was not significantly affected by L in the range 0.3 H < L< 0.5 H. For L > 0.5 H a sharp increase in Ne with increasing L could be observed. The two Rushton turbines act independently at ΔH > 1.65 d, with d being the impeller diameter. As the baffle length decreased, an increased mutual interaction between the two impellers could be observed for a broad regime of ΔH/d values. Ne was not affected by ΔH for the unbaffled agitated systems studied.     

特型螺带桨叶在高粘弹性和非弹性流体中的搅拌功率

本文研究了层流区域有较大叶片截面积的特型双螺带──锚桨叶在高粘弹性和非弹性流体中的搅拌功率，测定了Ｋ_ｐ和Ｋ_ｓ，采用广义二阶流体本构方程导出搅拌功率计算式参数ｆ_ｓ和Ｆ_（１ａｃ）由实验数据确定。该式适用于牛顿型流体、假塑性和粘弹性流体的功率消耗计算。     

Power Consumption in Dual Impeller Gas‐Liquid Contactors: Impeller Spacing,Gas Flow Rate,and Viscosity Effects

The dependence of power consumption on impeller spacing, and also in relation to gas flow rate and viscosity, in unaerated and aerated gas‐liquid contactors agitated by dual Rushton‐ and by dual pitched blade turbines was comparatively studied. In tap water the two Rushton impellers acted independently for spacings greater than ΔH = 1.65d, while in glycerol solutions the impellers acted independently on reaching an impeller spacing equal to 1.20d; the corresponding values for the two pitched blade impellers were 1.50d for tap water, 1.07d for relatively high viscosities, and 0.53d for very high viscosity values. The Newton number Ne decreases with increasing viscosity for the dual Rushton turbine systems, while an increase of Ne can be observed with increasing viscosity for the corresponding pitched blade systems. For the dual Rushton turbines, gas flow number Q has no effect on Ne, at very high values of viscosity, while at low and relatively high viscosity values a small effect of Q on Ne can be detected. As observed for the dual Rushton turbine systems, Ne is also not affected by Q for the corresponding pitched blade systems at very high viscosity values. Flow number Q does not significantly affect the Newton number for the water‐glycerol solutions with a relatively high viscosity agitated by dual pitched blade turbines, while for the aerated water systems a decrease of Ne can be observed at relatively small gas flow numbers; high values of Q do not affect the Newton number.     

Effects of the Stirred Tank's Design on Power Consumption and Mixing Time in Liquid Phase

The influence of the stirrer type and of the geometrical parameters of both tank and agitator (clearance of an impeller from tank bottom, impeller diameter, draft tube and geometry of the tank bottom) on power consumption and mixing time in liquid phase under turbulent regime conditions (Re > 10⁴) have been studied. Different types of agitators have been used, namely Rushton turbine, 45° pitched‐blade turbine, MIXEL TT and TTP propellers and 1‐stage or 2‐stage EKATO‐INTERMIG propellers. All these stirrers were tested with the same power consumption per unit mass of liquid. On the basis of measured power consumption per unit mass, which is required to achieve the same degree of mixing, the results obtained in the present work show that the TTP propeller is the most efficient in liquid phase. Recommendations on the optimum geometric configuration have been made for each type of stirrer.     

Using CFD and Ultrasonic velocimetry to Study the Mixing of Pseudoplastic Fluids with a Helical Ribbon Impeller

A commercial CFD package was used to simulate the 3D flow field generated in a cylindrical tank by a helical ribbon impeller. The study was carried out using a pseudoplastic fluid with yield stress in the laminar mixing region. Ultrasonic Doppler velocimetry (UDV), a noninvasive fluid flow measurement technique for opaque systems, was used to measure xanthan gum velocity. From flow field calculations and tracer homogenization simulations, power consumption and mixing time results were obtained. The torque and power characteristics remain the same for upward and downward pumping of the impeller, but the mixing times are considerably longer for the downward pumping mode. Overall, the numerical results showed good agreement with experimental results and correlations developed by other researchers. From the power and mixing time results, two efficiency criteria were utilized to determine the best pumping mode of the impeller.     

Unsteady Mixing Characteristics in a Vessel with Forward‐Reverse Rotating Impeller

Usually, mixing is carried out in a vessel with four baffles and a single impeller. In some applications, however, the use of a baffled vessel is not recommended. One of the stirring methods used instead is unsteady agitation with forward‐reverse rotating impellers. The aim of this work was to characterize the agitation characteristics in a baffled and an unbaffled vessel with a turbine impeller. Mixing time and mixing power were evaluated in relation to the presence of baffles and the frequency of forward‐reverse rotation. It was found that the frequency of oscillation does not affect either the mixing time and mixing power values or the drag and added mass coefficients. Power requirements and mixing time were higher compared to the steady mixing conditions in a baffled vessel. The results showed that it is not recommended to use baffles because they have no influence on unsteady mixing.     

Power Consumption in Gas‐Liquid Contactors Agitated by Double‐Stage Rushton Turbines

The dependence of power consumption on impeller spacing in unaerated and aerated gas‐liquid contactors agitated by dual Rushton turbine systems was studied, and the gas flow rate and viscosity effects were measured in relation to these parameters. The experiments were carried out in a 0.19 m i.d. vessel stirred by two Rushton turbines with a diameter d = 0.10 m; with blade length and blade height 0.25 d and 0.2 d, respectively. In tap water the impellers acted independently for spacings greater than 1.65 d, while in glycerol solutions the two impellers already acted independently at an impeller spacing equal to 1.2 d. In aerated systems, a notable increase in the power consumption with increasing impeller spacing could be detected for small gas flow rates and low viscosities, while a decrease in the Newton number with increasing Froude number could be observed at constant impeller spacing. The Newton number was not affected by flow number at high viscosity values.     

Assessment of Mixing Performance and Power Consumption of a Novel Polymerization Reactor System

A melt‐phase polymerization reactor with the novel geometry of two helical solid‐tube impellers rotating within a tank, consisting of two intersecting cylinders, was designed and constructed. In order to evaluate the performance of the system, mixing times and power consumption were measured using a viscous Newtonian model fluid (glucose syrup) in place of the polymer melt. The mixing regime was laminar in all runs. The mixing time at various impeller speeds was estimated by injection of a tracer dye (crystal violet), followed by fluid sampling and visible spectrophotometric analysis. A dimensionless mixing time of k_m = 104 ± 36 was obtained. The power draw required to move each impeller through the fluid at various impeller speeds was measured, and a power constant of k_p = 1156 ± 70 was obtained. The system appeared to outperform the conventional single helical ribbon impeller in terms of mixing time, but was less energy‐efficient, as indicated by the larger power constant. The power constant value lies between values previously reported in the literature for conventional helical impellers and values reported for other types of polymerization reactors with different geometries.     

Gas‐Liquid Floating Particle Mixing in an Agitated Vessel

The influence of impellers and baffles on the mixing of gas‐liquid floating particles in agitated vessels was investigated. Fifty‐two kinds of impeller combinations and twelve types of baffle arrangements were used. The associated power, gas holdup and solids concentration at the vessel bottom were measured. It is concluded that the mixing characteristics of three‐stage impellers were superior to those of two‐stage impellers for aspect ratios larger than 1.6. The optimal combination of impellers and baffles was proposed. The correlations of the relative power and the gas holdup for the optimal combination of impellers under all types of baffles were obtained.     

螺带型搅拌槽内异物性液体的混合性能

针对高固含量木质纤维素同步糖化与发酵生产燃料乙醇过程,研究了螺带型搅拌槽内层流流动条件下少量低粘低密度液体(a)加入大量高粘高密度主体液体(b)中的混合性能,考察了转速、两种液体体积比(Va/Vb)、粘度比(mb/ma)、密度差等影响因素. 结果表明,当Va/Vb>1%时,异物性物系混合时间远高于相同物性液体混合时间,可延长2~5倍;Va/Vb对混合时间影响最显著,Va/Vb=0.2%~3.7%范围内,无量纲混合时间Ntm随体积比增大先降低后升高存在一最小值;当Va/Vb≥2%,单位主体液体密度之差Dr/rb>0.2时,Ntm随着Va/Vb, Dr/rb增加线性增大;Ntm随着mb/ma增大而减小;加入相加在主体液体内所得混合时间比加在液体表面时短;Va/Vb>2%时,混合工况可分为Re数控制区(桨叶控制)及Ri数控制区(重力控制).     

Influence of Shear‐Thinning Rheology on the Mixing Dynamics in Taylor‐Couette Flow

Non‐Newtonian rheology can have a significant effect on mixing efficiency, which remains poorly understood. The effect of shear‐thinning rheology in a Taylor‐Couette reactor is studied using a combination of particle image velocimetry and flow visualization. Shear‐thinning is found to alter the critical Reynolds numbers for the formation of Taylor vortices and the higher‐order wavy instability, and is associated with an increase in the axial wavelength. Strong shear‐thinning and weak viscoelasticity can also lead to sudden transitions in wavelength as the Reynolds number is varied. Finally, it is shown that shear‐thinning causes an increase in the mixing time within vortices, due to a reduction in their circulation, but enhances the axial dispersion of fluid in the reactor.     

Coaxial Mixer Hydrodynamics with Newtonian and non‐Newtonian Fluids

The performance of several combinations of a wall scraping impeller and dispersing impellers in a coaxial mixer operated in counter‐ and co‐rotating mode were assessed with Newtonian and non‐Newtonian fluids. Using the power consumption and the mixing time as the efficiency criteria, impellers in co‐rotating mode were found to be a better choice for Newtonian and non‐Newtonian fluids. The hybrid impeller‐anchor combination was found to be the most efficient for mixing in counter‐rotating or co‐rotating mode regardless of the fluid rheology. For both rotating modes, it was shown that the anchor speed does not have any effect on the power draw of the dispersing turbines. However, the impeller speed was shown to affect the anchor power consumption. The determination of the minimum agitation conditions to achieve the just suspended state of solid particles (N_js) was also determined. It was found that N_js had lower values with the impellers having the best axial pumping capabilities.     

Mixing Agglomeration in a High‐Shear Mixer with a Stirred Mixing Vessel

This paper deals with the agglomeration process in a high‐shear mixer. High‐shear mixers rotate with a very high mixing tool speed such that not only a mixing effect, but also a grinding effect is achieved. The parameter study reported here was carried out to determine the parameters influencing mixing agglomeration. The results will help the user to decide which parameters have to be considered for an optimum mixing agglomeration. This article will highlight some of the findings obtained from the comprehensive parameter study.     

Mixing of Shear‐Thinning Fluids with Dual Off‐Centred Impellers

Mixing times for inelastic shear‐thinning fluids in stirred tanks have been experimentally investigated using a combination of two off‐centred impellers operating in both co‐ and counter‐rotating modes. A colour‐discolouration technique based on fast acid‐base reaction was used for the determination of the mixing times as well as to reveal the possible presence of caverns and dead regions. A statistical plan of experiments allowed determining the effects of the impeller position, the rotational speed, the flow behaviour index, the impeller type and their mutual interactions. A stronger influence of the impeller position on mixing times was observed for both rotating modes with fluids exhibiting pronounced shear‐thinning. It was also found that segregated regions could be readily destroyed by dual off‐centred impellers as compared with the single centred impeller configuration. Mixed flow impellers were shown to be less efficient in terms of mixing times than radial flow impellers. Results obtained under the best operating conditions were compared to steady stirring experiments showing the potential and drawbacks of the proposed scenarios.     

Investigation of Fluid and Coarse‐Particle Dynamics in a Two‐Dimensional Spouted Bed

The aerodynamics of particles and gas flow in a two‐dimensional spouted bed (2DSB) with draft plates is investigated with the aid of the discrete element method. The geometry of the 2DSB with draft plates is set as close as possible to the experimental apparatus of Kudra [1] and Kalwar [2]. The physical properties of the coarse particles are similar to those of shelled corn. The calculated minimum spouting velocity and pressure drop agree well with the correlations of Kudra [1] and Kalwar [2]. In the spout region, the particle vertical velocities are found to decrease as the height increases. The fluid velocity in the downcomer region decreases as the superficial gas velocity increases. The particle circulation rate increases when the friction coefficient decreases or the separation height increases. At the minimum spouting velocity, the bed height does not affect the particle circulation rate in the 2DSB with draft plates. The draft plates not only reduce the minimum spouting velocity and pressure drop but also increase the maximum spoutable bed height. The effect of taking out the draft plates on the spouting phenomenon is investigated and the effect of putting in a deflector on the possible breakage of the particles is also estimated.     

Transitional Mixing of Shear‐Thinning Fluids in Vessels with Multiple Impellers

The mixing efficiency of shear‐thinning fluids was evaluated using carboxymethylcellulose sodium salt (Na‐CMC) aqueous solutions of varying mass concentrations and three types of impellers (Rushton turbine (RT), six‐flat‐blade turbine (FBT), six‐pitched‐down‐blade turbine (PBT)) which were mounted on a common shaft in combinations of three, four, and five impellers. The mixing time proved to be dependent on the number of impellers as well as on the distance between. The Reynolds number has a significant influence on the mixing time for all studied systems. The results of power consumption allowed to choose the impeller system with the best efficiency.