In-line Rotor-stator Mixer Research Articles

CFD simulation of an axial discharge rotor-stator mixer: LES versus RANS predictions

The large eddy simulation (LES) technique is used to model the turbulent flow of water in a two-stage, axial discharge, in-line rotor-stator mixer. The WALE sub-grid scale model is employed, and the resulting filtered velocity field is ensemble averaged to predict the mean velocity, turbulent kinetic energy, energy dissipation rate, and energy production rate. The results of these 3-D sliding mesh simulations are compared to analogous RANS predictions on similar meshes using the realizable k-ε turbulence model. Stator slot flow rate and rotor torque/power draw are also monitored. RANS and LES predict similar mean velocity profiles, flow rate and rotor torque. LES predicts higher turbulent kinetic energy, but lower dissipation rate compared to RANS. Results from a coarse and refined computational mesh are compared to discuss the significance of resolving smaller scales for LES. The effect of operating conditions on throughput, power draw, and other quantities of practical utility are also discussed. It was found that prediction of macroscopic quantities such as flow rate and power draw can be done efficiently using either RANS or LES on a relatively course mesh while capturing turbulence quantities requires a well refined LES simulation.

A hybrid approach based on Lagrangian particles and immersed-boundary method to characterize rotor–stator mixing systems for high viscous mixtures

In-line multi-stage rotor–stator mixing systems are the recent industrial solution for mixing highly viscous liquids in a short period of time while minimizing temperature increase throughout the mixing process. Unlike their predecessors, namely batch mixers, in-line rotor–stator mixers facilitate a continuous mode of operation. However, there is a lack of detailed insight into their flow patterns, power consumption, and mixing behavior, as these mixers, particularly the multi-stage variants, are rarely studied in the scientific community. In this work, we propose a computational framework for modeling rotor–stator mixers using Lagrangian particle tracking and the immersed-boundary method. The tracer particles present an alternative to the commonly used Eulerian approach, which is susceptible to numerical diffusion. The use of the immersed-boundary method for modeling the motion of the rotor not only significantly reduces pre-processing time but also facilitates the modeling of various rotor–stator shapes with different motion patterns, making it possible to complete the modeling in a short time. The proposed method is used to investigate an industrial in-line multi-stage rotor–stator mixer, and the accuracy of the numerical results is verified by comparing them with experimental data. The simulations unveiled that at a rotational Reynolds number of up to 4000, significant back-mixing occurs, whereas for lower Reynolds numbers, the flow maintains a smooth forward motion without any back-mixing. The study also examines the residence time of the additive in the mixer, revealing that, particularly when dealing with high-viscosity mixtures, the additive has the potential to persist in the mixer for up to 3.5 times the theoretical residence time. Additionally, the obtained results are utilized to derive empirical equations that enable predicting the mixer’s performance for different Reynolds numbers.

Residence time distribution and micromixing efficiency of a dynamic inline rotor–stator mixer

An industrially available dynamic inline–mixer which operates on the rotor–stator principle was investigated for aqueous solutions with a total volume flow rate of up to 40 L/h to gain valid insight into the mixing behavior. In residence time distribution (RTD) experiments, mean residence times ranging between 29 and 305 s and Bodenstein numbers ranging between 1.4 and 5.1 were measured. Micromixing efficiency was investigated with the Villermaux–Dushman reaction at varying rotational speeds, total volume flow rates and injection inlets. The results suggest that micromixing processes are especially complex in a continuous rotor–stator mixer. As expected, the injection inlet had a decisive influence on micromixing efficiency. Surprisingly, even at higher volume flow rates backmixing was identified as a factor which significantly extends the micromixing time. A new method is proposed for estimating the degree of backmixing based on micromixing experiments. Micromixing times range between 3 · 10–4 and 4 · 10–3 s depending on the operating point.

Continuous Production of Water-Based UV-Curable Polyurethane Dispersions Using Static Mixers and a Rotor-Stator Mixer.

UV-curable polyurethane dispersions (UV-PUDs) have applications in coatings for a variety of materials. Historically, the neutralization and dispersion steps of the UV-PUD production process have been performed in batch. However, continuous processing might reduce capital and operating costs, improve the dispersion characteristics, and facilitate scale-up. Static mixers and inline high-shear mixers are able to provide the necessary shear forces to obtain miniemulsions. The production of a UV-PUD is therefore studied in a continuous setup, whereby the neutralization step is performed in static mixers and the dispersion step is performed either in static mixers or in a high-shear mixer. The influence of the prepolymer temperature, mixing energy, and feed flow rate on the particle size and stability of the UV-PUD particles in water is explored. The results show that the neutralization step is mixing-sensitive, and the temperature of the neutralized prepolymer influences the particle size in the dispersion process. The amount of shear force applied during the dispersion step has a limited effect on the particle size. UV-PU dispersions with an average particle size below 80 nm and PDI below 0.1 are obtained with static mixers or in an inline rotor-stator mixer, at flow rates of 5.2 and 7.2 L/h, respectively. This research demonstrates that continuous processing using static mixers and high-shear mixing is a viable option for the neutralization and dispersion of UV-PUDs.

Residence Time Distribution and Micromixing Efficiency of a Dynamic Inline Rotor–Stator Mixer

Residence Time Distribution and Micromixing Efficiency of a Dynamic Inline Rotor–Stator Mixer

Analysis of Power Input of an In-Line Rotor-Stator Mixer for Viscoplastic Fluids

In this work, the power draw and shear profile of a novel in-line rotor-stator mixer were studied experimentally and the laminar flow regime was simulated. The power draw of the rotor-stator mixer was investigated experimentally using viscoplastic shear-thinning fluid and the results of the obtained power consumptions were verified through simulations. The power draw constant and Otto-Metzner coefficient were determined from the result of experimental data and through simulations. A new method is suggested for the determination of the Otto-Metzner coefficient for the Herschel–Bulkley model and the term efficiency is introduced. It was shown that the proposed method can be applied successfully for the prediction of the Otto-Metzner coefficient for the mixing of viscoplastic shear-thinning fluids. The effect of geometry and rotor speed on power consumption and shear rate profile in the investigated mixer is discussed from the results of the simulations. It was found that numerical methods are a convenient tool and can predict the power draw of the in-line rotor-stator mixer successfully.

Scale-up of continuous microcapsule production

The objective of this work is to establish an experimental approach to scale-up the production of melamine formaldehyde (MF) microcapsules from a batch lab-scale to a pilot-scale inline rotor stator mixer (RSM). The inline RSM is operated in a continuous recycle mode, allowing multiple passes of the emulsion through the intensive mixing zone during continuous production. The liquid is continuously recirculated directly to the RSM, without a holding vessel, as is the case in conventional batch recirculation emulsification. The setup is operated at feed flow rates of 0.24 kg/h - 20 kg/h. Parameters including the Weber number, tip speed and energy density are investigated to correlate the mean capsule size of the batch and flow process. Rotational speeds range from 3000 to 26,000 rpm. The dimensionless maximum diameter correlated well with the Weber number to the power -0.4, for both devices operated at the same residence time. Volume and number based mean diameters showed little influence of the feed flow rate in the continuous recycle mode of operation. This inline RSM setup is therefore an ideal tool to optimize emulsification processes at lab scale and increase production by increasing the feed flow rate, while maintaining rotor-stator geometry.

A comparison of power and flow characteristics between batch and in-line rotor-stator mixers

Rotor-stator mixers are used in many industries to perform emulsification and de-agglomeration processes. Despite previous research, different modes of operation have not been compared in terms of flow and power characteristics. The aim of this study was to use CFD to investigate power and flow characteristics of a Silverson L5M mixer operating in batch and in-line mode. MRF was used along with the standard k-∊ turbulence model for the simulations. Results suggest that batch mixers can be characterised in the same was as in-line mixers, and for a given mixing head design, the characterisation is independent of the mode of operation. A new way of the calculating flow number is proposed, which explains some discrepant results from previous studies. Overall, this work enhances our understanding of rotor-stator mixers and allows for better design choices of mixer.

Particle de-agglomeration with an in-line rotor-stator mixer at different solids loadings and viscosities

Rotor-stator mixers are commonly used in energy intensive processes but there is relatively little published information on which to base process design. This study investigated the de-agglomeration of nanoparticle clusters in a liquid to determine the effects of solids loading (up to 15%wt) and continuous phase viscosity (up to 100mPas) on the mechanisms and kinetics of breakup and dispersion fineness in an in-line rotor-stator. A Silverson 150/250MS rotor-stator was used in the recirculation loop of a stirred tank. It was shown that the power number values previously obtained at Reynolds numbers greater than 200,000 are constant at Reynolds numbers as low as 2400.It was found that the breakup kinetics were not significantly affected by the solids loading, within the range covered in this study. On the other hand, when the viscosity of the continuous phase was increased, the de-agglomeration became slower even though the solids concentration was low (1%wt) and the flow through the rotor-stator was still turbulent. This indicates that it is the flow conditions around the particle and not the bulk rheology of the dispersion that determines the kinetics of the de-agglomeration process. Breakup mechanism was found to be erosion and the dispersion fineness was determined by the size of aggregates.

Energetic efficiency of mass transfer accompanied by chemical reactions in liquid-liquid systems

Abstract Energetic efficiency depicting the fraction of energy dissipation rate used to perform processes of drop breakup and mass transfer in two-phase, liquid-liquid systems is considered. Results of experiments carried out earlier in two types of high-shear mixers: an in-line rotor-stator mixer and a batch rotor-stator mixer, have been applied to identify and compare the efficiency of drop breakage and mass transfer in both types of mixers. The applied method is based on experimental determination of both: the product distribution of chemical test reactions and the drop size distributions. Experimental data are interpreted using a multifractal model of turbulence for drop breakage and the model by Favelukis and Lavrenteva for mass transfer. Results show that the energetic efficiency of the in-line mixer is higher than that of the batch mixer; two stator geometries were considered in the case of the batch mixer and the energetic efficiency of the device equipped with a standard emulsor screen (SES) was higher than the efficiency of the mixer equipped with a general purpose disintegrating head (GPDH) for drop breakup but smaller for mass transfer.

Continuous, recycle and batch emulsification kinetics using a high-shear mixer

In-line rotor-stator mixers are widely used to emulsify immiscible liquids, but there is little understanding on the size reduction kinetics and on their performance if used in a continuous or in a recycle arrangement. In this study, a systematic series of experiments were performed to study the droplet size reduction of a 10cSt silicon oil coarse emulsion using different flow rates and number of passes for a continuous and a recycle configuration using a L5M-A Silverson Laboratory mixer.The droplets size distributions obtained were bimodal. It was found that the mode of the larger daughter droplets is a better parameter to follow the emulsification kinetics than the Sauter mean diameter; the volume fraction of the small daughter droplets was estimated to be ≈6% using two generalized gamma functions. For the continuous arrangement it was found that impeller speed and mean residence time inside the rotor-stator correlated with an average error of 3.2%. It was also found that a Poisson chain can link the results of both operation arrangements. This stochastic model allowed following the disappearance rate of the coarse droplets and the evolution of the daughter droplets’ mode with an average error of 2.3%. The model developed allowed the comparison of both arrangements using an in-line rotor-stator.A simplification of the Poisson chain model for long times was used to analyse batch emulsification kinetics. The droplet size reduction rate and batch volume could be explained in terms of the in-line results.

The dissipation rate of turbulent kinetic energy and its relation to pumping power in inline rotor-stator mixers

The theoretical understanding of inline rotor-stator mixer (RSM) efficiency, described in terms of the dissipation rate of turbulent kinetic energy as a function of mixer design and operation, is still poor. As opposed to the correlations for shaft power draw, where a substantial amount of experimental support for the suggested correlations exists, the previously suggested correlations for the dissipation rate of turbulent kinetic energy have not been experimentally validated based on primary hydrodynamic measurements. This study uses energy conservation to reformulate the previously suggested dissipation rate correlations in terms of pumping power which allows for empirical testing. The dimensionless pumping power of three investigated geometrically dissimilar inline RSMs were found to be qualitatively similar to that of centrifugal pumps and decrease linearly with the inline RSM flow number. The previously suggested models for turbulent dissipation in inline RSMs are inconsistent with this observation. Using this reformulation approach, the previously suggested correlation for power-draw is extended to a correlation for dissipation. A new model is suggested based on conservation of energy and angular momentum, and the empiric pumping power relationship. The new model compares well to CFD simulations of total dissiaption and show reasonable agreement to emulsification drop size scaling.

Mass transfer and chemical test reactions in the continuous flow rotor-stator mixer

This work is on mass transfer in liquid-liquid two-phase systems. To study mass transfer in the continuous flow in-line rotor-stator mixer, a method based on experimental determination of the product distribution of a set of complex chemical reactions has been applied together with drop breakage experiments. Experiments were carried out using the high-shear rotor-stator Silverson mixer for both drop dispersion and intensification of mass transfer. Volume fraction of organic phase was in the range between 0.01 and 0.015. The product distribution of complex reactions was determined based on high-performance liquid chromatography measurements. The drop size distribution was measured with the Malvern MasterSizer just after the process. Results of modeling of mass transfer with chemical reaction were used to characterise energetic efficiency of mass transfer.

Specific features of power characteristics of in-line rotor–stator mixers

Methodthat can be used to predict agitation power of in-line rotor–stator mixers are considered in this paper. Results of experimental investigations of power draw are presented and interpreted by using proposed phenomenological models and CFD predictions for the Silverson rotor–stator 150/250 MS device and its modifications. Results of theoretical analysis lead to extended version of previously used correlation for the agitation power. Based on new correlation and the multifractal model of turbulence the problems of energetic efficiency and scale-up of drop breakage in the rotor–stator devices are presented and discussed.

Scale-up of the power draw of inline-rotor–stator mixers with high throughput

Inline-rotor–stator mixers are widely used in diverse industrial mixing and dispersing processes. Despite their expanded presence in industrial processes, no general accepted method for the scale-up of this machine type has been established so far. This paper reports of a new developed approach to predict flow rate and power consumption within the scale-up of these machines. Based on an earlier published idea, the operating behavior of these machines is characterized by power curves. The approach is further developed, considering an often used procedure for the scale up of stirring processes with non-Newtonian fluids. Additionally, characteristic flow curves are used within the new approach, which allow the prediction of flow rate and power consumption in the scale-up of these machines. The experimental work was done with inline-rotor–stator mixers whose construction design is close to centrifugal pumps. Thus, very high throughputs are generated. Power curves and characteristic flow curves were recorded with polyglycerol–water mixtures. For the validation of the method, a shear thinning model dispersion with pyrogenic nanoparticles was processed in 4 machines of different sizes. The throughput of the machines ranged from 10 to 90m3/h. These experiments showed that the proposed model enables to predict flow rates and net power consumptions with good accuracy.

A high-solids steam injection process for the manufacture of powdered infant milk formula

Introduction of more energy efficient processing practices, such as increasing the initial solids content from which powder is manufactured, is of interest to the infant formula industry. This study evaluated the use of an inline rotor-stator mixer followed by direct steam injection to disperse and heat-treat (110 °C, 3 s) high-solids (60% w/w) formulations, for the production of powdered infant milk formula. As a control, 30% w/w infant milk formulations were subjected to a typical process, i.e. heat treatment in a tubular heat exchanger, valve-type homogenisation, evaporation (to 55% w/w solids content) and spray drying. Both formulations were dried using a three-stage dryer with two-fluid nozzle atomisation at inlet and outlet temperatures of 187 °C and 85 °C, respectively. Formulations subjected to the steam injection process had significantly (P 0.05), 2.04 ± 0.22 and 1.82 ± 0.04 μm for the control and high-solids steam injection processes, respectively. Powders produced by both processes had statistically similar (P > 0.05) surface free fat content, wettability and dispersibility. The study showed that it is possible to produce quality model infant milk formula powders from a high-solids concentrate while considerably reducing process complexity.

Application of test reactions to study micromixing in the rotor-stator mixer (test reactions for rotor-stator mixer)

Rotor-stator devices are known from their ability to generate very high shear stresses; due to focused delivery of energy, their energetic efficiency is regarded as high. In the present work performance of the Silverson double screen 150/250MS inline rotor-stator mixer is investigated using multiple test reactions (a simultaneous diazo coupling between 1- and 2-naphtols and diazotized sulphanilic acid), power measurements and CFD.In experiments a premixture of 1- and 2-naphtols was fed into the system through the main inlet whereas second reagent was introduced through the separate feeding tube. Experiments were carried out for the total volumetric flow rate equal to 0.1 dm3 s−1, the volume ratio of reactant solutions equal to 15, and for the rotor speed from the range between 500 and 9000 rpm.The hydrodynamics, mixing and the course of chemical reactions in the rotor-stator mixer are simulated using the standard k–ε model of Ansys Fluent and the multi-reference frame approach. The presented model is able to properly predict the power input to the rotor-stator system and details of turbulence structure, which was confirmed by comparing experimental data with model predictions for power input and product distributions.

Droplet break-up by in-line Silverson rotor–stator mixer

Silverson high shear in-line rotor–stator mixers are widely applied in industry for the manufacture of emulsion-based products but the current understanding of droplet breakage and coalescence in these devices is limited. The aim of this paper is to increase the understanding of droplet break-up mechanisms and to identify appropriate literature correlations for in-line rotor–stator mixers. Silicone oils with viscosities ranging from 9.4 to 969 mPa s were emulsified with surfactant in an in-line Silverson at rotor speeds up to 11,000 rpm and flow rates up to 5 tonnes/h. The effect of rotor speed, flow rate, dispersed phase fraction up to 50 wt%, inlet drop size and viscosity ratio on droplet size was investigated. It was found that rotor speed and dispersed phase viscosity have a significant effect on the droplet size, while flow rate, inlet droplet size, viscosity ratio and dispersed phase volume have a lesser effect. The results indicate that low viscosity droplets are broken by turbulent inertial stresses, while droplets smaller than the Kolmogorov length scale are broken by a combination of inertial and viscous stresses. It also appears that the weak dependence of drop size on flow rate enables the energy efficiency of an in-line high shear Silverson to be significantly improved by operating at as high a flow rate as possible.

Expression for turbulent power draw of an in-line Silverson high shear mixer

We report the validation of an expression to accurately describe the power draw of an in-line rotor–stator mixer over a range of flow rates and rotor speeds. The expression consists of a term which reflects the power required to rotate the shaft in response to the liquid resistance and a term to reflect the power convected away from the mixing chamber. A specially commissioned high speed (12,000rpm), instrumented 150/250 MS Silverson mixer has been developed with power draw determined from both torque and calorimetric measurements. Experiments are carried out using water over a range of independently controlled flow rates and rotor speeds with losses for both techniques carefully accounted for. For the torque measurement the value of the constants for the two terms above are Poz=0.197 and k1=9.35, respectively. For the calorimetric technique the measured temperature rise was similar to some of the corrections and losses over a significant range of the experimental space but nevertheless with careful experimentation constants similar to those for the torque technique were obtained, Poz=0.229 and k1=7.46. Allowing the calibration of the temperature probes to be a fit parameter in the regression routine increased the value of k1=8.10 but did not affect the value of Poz. A simple graphical method is also proposed using a dimensionless form of the expression which yielded slightly higher value of Poz but a slightly lower value of k1. The accuracy of both measurement techniques improves with rotor speed and the differences between the constants is attributed to the better accuracy of the torque technique at higher flow rates whereas the calorimetric technique is more accurate at low flow rates where the temperature rise is larger. Several repeats of the calorimetric technique with a reduced set of experimental points show good reproducibility. Finally at low flow rates (<10% of the maximum) the power unexpectantly increases and a modification to the expression is proposed by considering the pumping efficiency.