Determination of the just-suspended speed,Njs, in stirred tanks using electrical resistance tomography (ERT)

N_js, the minimum agitation speed to just-suspend dispersed solids in liquids in stirred tanks, is a critical parameter to operate industrial processes. The focus of this work was to develop a novel observer-independent method to experimentally obtain N_js in tanks that cannot be visually inspected internally using electrical resistance tomography (ERT). The mean bulk resistivity was measured across electrodes mounted on an ERT linear sensing probe placed inside a stirred tank containing water and glass beads. As the agitation speed increased, more solids became suspended and the resistivity measured by the probe changed. Plots of resistivity variation vs. agitation speed resulted in an S-shaped curve that could be analyzed to determine N_js. The N_js values obtained with this novel approach compared very favorably with those obtained using other methods requiring transparent tanks. It is expected that the ERT method proposed here could find applications in many industrial solid–liquid mixing processes.     

Design rules for suspending concentrated mixtures of solids in stirred tanks

This study examines complete off-bottom suspension conditions for slurries containing mixtures of solids at a wide range of concentrations. Binary combinations of five different particles; bronze, two sizes of glass beads, ion exchange resin, and nickel were tested with two impellers: the Lightnin A310 and the down pumping 45° PBT. The effect of particle size ratio and density ratio of the two solid phases on N_js was investigated. Solids loadings were varied from 3 to 56 wt% (weight percent) with water as the liquid phase. The results showed that the highest particle N_js in a mixture of solids is not a sufficient design specification to ensure suspension of the mixture. For one of the cases studied, the particle–particle interactions became significant at high loadings and resulted in a decrease in N_js. Different behaviours were observed for the other mixtures. The performance of the two impellers was also compared. The A310 impeller consumes significantly less power at N_js than the PBT. Both impellers showed an effect of off-bottom clearance on N_js, but the effect of off-bottom clearance depended on both the solids concentration and on the solids used.     

Mechanisms of solids drawdown in stirred tanks

Agitated tanks are used in several industrial processes to achieve complete drawdown of floating solids in liquids. The design requirements for this process are not completely defined, and are currently limited to heuristics regarding the use of a surface vortex and the effect of wettability on the difficulty of mixing, along with several initial studies in the literature. In this study, the effect of the type of impeller, particle size and shape, solids concentration, impeller submergence, and baffle configuration on the minimum drawdown speed (N_jd) are investigated. It was found that the formation of a large surface vortex acts to hold particles close to the surface. Suppression of the surface vortex is recommended. In baffled tanks where the formation of a large surface vortex is suppressed, the intensity of turbulence and mean circulation velocity of the liquid are responsible for solids drawdown and distribution in the tank. The submergence of the impeller relative to the liquid surface and the pumping mode of the pitched blade turbine (PBT) were found to be the controlling parameters. CFD simulations were carried out to obtain a better understanding and interpretation of the flow patterns and drawdown mechanisms for the different baffle configurations.     

Unsuspended mass of solid particles in stirred tanks

An original technique for the determination of the fraction of unsuspended solid particles at agitation speeds smaller than N_js, is proposed. The technique is based on the “twin-systems” concept and is completed by a suitable tracing and detection technique for the solid phase. Results obtained with a fully baffled tank stirred by a Rushton turbine impeller show that the fraction of solids never leaving the tank bottom can be simply correlated to the ratio between agitation speed and Zwietering's complete suspension speed. It is shown that at agitator speeds of about 80% of Zwietering's complete suspension speed, practically all particles but a few, are already suspended. This finding implies that large energy and installation cost savings can be achieved, with respect to current design practices, without significantly affecting the solid-liquid mixing performance.     

Suspension pattern and rising height of sedimentary particles with low concentration in a mechanically stirred vessel

In this study, the effects of impeller rotation speed, off‐bottom clearance, blade angle, types of solid and liquid, etc., on the suspension pattern of sedimentary particles and particle rise height in liquid were investigated with a hemispherical vessel without baffles under low particle concentration. The transition conditions of suspension pattern between regimes I and II, and regimes II and III, were observed visually, and their non‐dimensional equations were expressed with an acceptable correlation by varying the above operation factors a great deal. Here, regime I is stagnation of particles on a vessel bottom, II is partial suspension, and III is complete suspension in liquid. The non‐dimensional equation of the maximum particle rise height was also successfully obtained. The combination of the non‐dimensional equations of transition and maximum particle rise height permitted us to determine the adequate solid/liquid mixing operation conditions without collision of particles with device parts.     

A spectral approach of suspending solid particles in a turbulent stirred vessel

The 2015 Grenville-Mak-Brown (GMB) correlation for predicting the just suspended condition assumes that the length scale of the suspending eddy is equivalent to the particle diameter. This article investigates the role of the time scale of the relevant eddies with respect to the particle response time. The local turbulence just above the tank bottom is gauged by means of single-phase LESs at the just suspended conditions determined in new experiments in dilute suspensions. By means of a novel nondimensional Suspension number we found that the relevant suspending eddies in the inertial subrange are 1.2–1.5 times larger than the particle size while the required eddy time scale is of the order of two times the particle response time. Further, we concluded that the mean energy dissipation rate is a suitable approximation of the local energy responsible for suspension. These results do not impact the effectiveness of the GMB correlation.     

Impeller power draw during turbulent operation in solid‐liquid suspensions

Experimental measurements with six impeller types in solid‐liquid suspensions indicate that impeller power draw in the turbulent regime is approximately proportional to the solid‐liquid suspension density when the solids are distributed throughout the liquid; however, the accuracy of this approach is limited and there are clear differences in the behaviours of the various impellers. In general, power draw increases are less than suspension density increases for impellers with large blade‐trailing vortices, while power draw increases are equal to or greater than suspension density increases for impellers with smaller blade‐trailing vortices. The power draw data is well‐described using linear relations between the impeller power number and the density difference correlating parameter proposed by Micheletti et al.,^[9] with the slope of the relation being dependent on impeller type. More extensive testing with a pitched‐blade turbine, using a greater variety of solids, found that the relation between the impeller power number and the density difference correlating parameter is independent of particle size for particles as large as 1 mm (1000 microns). For particles larger than 1.7 mm (1700 microns), in addition to suspension density, the solid volume fraction affects the pitched‐blade turbine power number; however, it is difficult to determine if this effect exists at all scales or if it is a result of the large particle size relative to the impeller dimensions in the experimental system. For large particles, the power draw is increased by the addition of neutrally‐buoyant particles that do not change the suspension density, with the magnitude of the increase being dependent on impeller type.     

Analysis of particle cloud height dynamics in a stirred tank

Local and temporal variations of the particle cloud formed in a cylindrical mixing vessel were investigated experimentally. Different particle sizes (0.5, 1, and 2 mm) and volumetric concentration up to 20 vol % were evaluated at different impeller speeds. The time‐averaged cloud height was linear with impeller frequency and with volume concentration. Suspensions with larger particles had a lower average cloud height, while the standard deviation for the temporal cloud height variation was larger. Two strong periodic phenomena were identified to be dominating the particle cloud height variations. The frequencies were linear with impeller speed, resulting in dimensionless frequencies of S₁=0.02–0.03 and S₂=0.05–0.06. The frequencies were affected by neither the particle size nor the volumetric concentration. The amplitude showed no dependency on the particle size, but the S₂ amplitude significantly decreases and S₁ increases with increasing solid concentration. The results were compared to LES/discrete element method simulations and showed a fair agreement. © 2015 American Institute of Chemical Engineers AIChE J, 62: 338–348, 2016     

Investigation of the mechanism of low‐density particle and liquid mixing process in a stirred vessel

In order to investigate the mechanism of the low‐density solid particle and liquid mixing process, a specialised agitator structure was used. Both computational fluid dynamics simulation and experiments were carried out to study the two‐phase mixing characteristics in the stirred vessel. The mixing process was captured by snapshots. The flow field and solid phase volume fraction evolution were analysed. Experimental and numerical results agreed well with each other. Solid particles floating on the liquid surface were gradually transported to the bottom through the centre of the vessel and the mixing time was predicted and tested. Results indicate that the agitator structure used in this study is able to form an obvious axial circulation in the vessel and then achieve a good performance in low‐density solid and liquid mixing operations. The study provides a valuable reference for the design and optimisation of solid–liquid mixing equipment. © 2011 Canadian Society for Chemical Engineering     

Effect of dispersed phase feed time on the droplet size of Pickering emulsions produced in a stirred tank

The aim of this study was to investigate the effect of feed time of the oil phase on the average droplet size of Pickering emulsions produced in stirred tanks. Three types of impellers were tested: RT, up-pumping PBT (PBTU), and down-pumping PBT (PBTD). All the impellers were tested at two sizes, T/3 and T/2. All configurations were compared at constant tip speed, power per mass, and impeller Reynolds number. The droplet diameters were measured in Mastersizer® 3,000 (Malvern). The results showed that an increase in feed time causes a reduction in the average droplet size. At lower impeller speeds and higher feed times, the effect is more pronounced. It was found that some other geometric parameters also have an impact on the average droplet size.     

Determination of minimum speed required for solids suspension in stirred vessels using pressure measurements

The minimum speed required for complete suspension (N_js) is a major parameter for solids suspension in stirred tanks. Micale et al. 7th UK Conference on Mixing (2002) determined N_js by using a pressure gauge technique in a model vessel. In the present work N_js was measured by the same later technique in a more practical vessel with varying C/T ratio and the impeller direction of rotation. The results were compared to those obtained by Zwietering Chem. Eng. Sci. 8 , 244–253, (1958) correlation. Agreement was found between results from present work and predictions by Zwietering's correlation with maximum difference not exceeding 17%.     

Importance of using the correct impeller boundary conditions for CFD simulations of stirred tanks

Two experimentally determined sets of impeller boundary conditions were used to simulate the flow generated by a pitched blade turbine in a cylindrical baffled tank. Use of these two sets of boundary conditions in simulations with two different off bottom clearances led to the conclusion that the flow generated by a pitched blade impeller cannot be successfully predicted without considering the impeller location. Correct prediction of velocity fields in the tank required the correct specification of velocity boundary conditions. Successful prediction of the turbulent energy distribution required proper specification of the turbulence boundary conditions. There was almost no interaction between the velocity and turbulence fields. The turbulet kinetic energy dissipation rate was at a maximum close to the impeller in both geometries. Within this region the average dissipation rate was five and a half times greater that the average dissipation rate in the tank.     

An integrated CFD methodology for tracking fluid interfaces and solid distributions in a vortexing stirred tank

Distribution of solid phase in a solid–liquid suspension being mixed in a vortexing, unbaffled stirred tank is difficult to model numerically. The need is to be able to predict the shape of the vortex (air–water interface) and the distribution of solids in the liquid domain. Typically, the problem is approached with assumptions about the shape of the interface to capture the solid distribution through a multi-phase Eulerian model (doi: 10.1016/j.ces.2018.07.023 ). In this work, a multi-step modelling framework for multi-phase systems that have a free surface along with the dispersion of secondary phase(s) in the liquid domain is proposed. To demonstrate the method, it is applied to a laboratory-scale vortexing unbaffled system reported in the literature (doi: 10.1021/ie071225m ) and a pilot-scale tank (doi: 10.1016/j.cej.2018.10.020 ). The predictions from the computational fluid dynamics model are compared with the experimental profiles of solid volume fractions. Using the model, the effects of solid density, particle size, particle loading, and impeller speed are investigated for the laboratory-scale system. An interesting self-similar nature in the axial distribution of solid is observed when the loading is varied from 0.5 to 10 volume percent.     

Influence of drag and turbulence modelling on CFD predictions of solid liquid suspensions in stirred vessels

Suspensions of solid particles into liquids within industrial stirred tanks are frequently carried out at an impeller speed lower than the minimum required for complete suspension conditions. This choice allows power savings which usually overcome the drawback of a smaller particle-liquid interfacial area. Despite this attractive economical perspective, only limited attention has been paid so far to the modelling of the partial suspension regime.     

The effect of hydrodynamic parameters on the production of Pickering emulsions in a baffled stirred tank

Pickering emulsions are potential industrial scale alternatives to surfactant-based emulsions. The stability of Pickering emulsions depends on the physicochemical nature of the liquid–particle interface and the hydrodynamic conditions of the production process. This article investigates the effect of hydrodynamic conditions on the drop size of concentrated Pickering emulsions in baffled stirred tanks. Oil in water emulsions composed of silicon oil, water, and hydrophilic glass beads as stabilizing particles were produced. Two impellers were used at different sizes: Rushton turbine (RT) and pitched blade turbine. The effects of power per mass, Reynolds number, tip speed, and Weber number on the droplet sizes were studied. The energy dissipated around the impeller and the size of the impeller high shear zone were found to be critical to the emulsion droplet sizes. The breakup and droplet-particle contact mechanism of the RT was found to be more favorable for the production of the Pickering emulsions.     

几种框式桨搅拌槽内流动特性的比较研究

用粒子成像测速（PIV）技术对传统框式桨、传统框式组合桨和新型框式组合桨的流动特性进行研究,对比了三种框式桨在相同工况下搅拌槽内的速度、流型和湍动能。结果表明：传统框式桨搅拌槽内流体流动以水平环流为主,在框式桨上方和框式桨中间区域流体流动不充分;传统框式组合桨搅拌槽内框式桨上方由于二折叶桨的作用使得框式桨上部流体流速变大,槽内流体上下部的流动得到加强,但在框式桨中心区域依旧存在流动死区;新型框式组合桨搅拌槽内两层桨叶间的连接流得到了加强,框式桨底部和中间区域物质和能量的交换更加充分。在考察的三种框式桨中,新型框式组合桨的混合效果更好。研究结果可为新型框式组合桨应用于化工合成工业中提供参考。