Dimensionless Mixing Time Research Articles

Experimental and computational investigation of chaotic advection mixing in laminar rectangular stirred tanks

The phenomenon of chaotic advection mixing in laminar stirred tanks, particularly when handling high-viscosity fluids, represents a common and challenging issue in various chemical and biochemical industrial processes. The effectiveness of these mixing processes is often constrained by the stretching, folding, and squeezing of fluid particles. Previous research efforts have predominantly concentrated on the design and/or optimization of impellers and operation modes to increase the stretching and folding of fluid particles. However, the mechanism of triggering chaos through the squeezing of fluid particles remains comparatively less explored. This study endeavors to address the intricate problem of laminar mixing by proposing the utilization of unbaffled rectangular stirred tanks. Via a combined approach of experimental and computational investigations, we illustrate that the implementation of rectangular stirred tanks yields significant improvements in chaotic mixing within laminar flow regimes. This type of tank not only enhances the convective transport of fluids but also distorts or completely eliminates the segregation regions by squeezing. Remarkably, as the tank L/W ratio increases from 1 to 2.5, the observed asymptotic area coverage from a frontal perspective escalates from approximately 55 % to about 85 %. Concurrently, the dimensionless mixing time decreased significantly from 1950 to 350. Of particular note, macroscopic homogeneous mixing is observed in stirred tanks with L/W ratios of 2 and 2.5 at Re = 29, with dimensionless mixing times of 550 and 350, respectively. This work highlights the potential of rectangular stirred tanks as a simple and cost-effective system for laminar mixing applications. Furthermore, it also hints at the broader applicability of the approach in various industrial mixing contexts, such as the suspension of floating granules, entrainment of air, and others.

Investigation of mixing miscible liquids with high viscosity contrasts in turbulently stirred vessels using electrical resistance tomography

The time required to attain a sufficient degree of homogeneity i.e., mixing time, is an important parameter in mixing processes. This paper presents results from a study employing an experimental approach to estimate mixing times for a miscible Newtonian liquid mixture system with high viscosity contrasts in a turbulent stirred vessel. An Electrical Resistance Tomography (ERT) based technique has been adopted to monitor dimensionless mixing time across a range of additive viscosities, impeller designs, sizes, and speed. Dimensional analysis has been used to interpret these mixing time results in terms of the magnitude of the bulk inertia forces relative to the initial viscous forces within the added fluid. Critical non-dimensional numbers, uniting the properties of the two liquids, have been proposed as the criterion for avoiding undesirable operating conditions under which the mixing time is much longer than that required for mixing fluids with similar properties. The work proposes novel correlations for mixing time and incorporates a new dimensionless group, thereby enabling a more nuanced and accurate characterisation of mixing behaviours. This research stands to contribute to energy saving and waste minimisation efforts in the industry. It provides insights for process designers and simulation engineers, propelling a leap forward in the design and operation of mixing processes when dealing with liquid systems that have significant viscosity differences.

Power Consumption and Fluid Mixing in a Scale-Down Geometry of a Stirred Digester for Biogas Production

A unconventional stirred tank of geometry typically adopted for the production of biogas is experimentally investigated with pseudo-plastic model fluids. The apparent viscosities of the fluids, based on the Metzner–Otto method, are in the range of 39–264 mPa·s, resulting in a range of rotational Reynolds number equal to 17–648. The power consumption of the three top-entering agitators is measured by a strain gauge technique, and the power number curve is obtained in the full range of flow regimes, going from laminar to fully turbulent conditions. The flow field measured by particle image velocimetry allows us to observe the fluid circulation patterns and their variations in different operative conditions. The measurements reveal relatively low axial and radial velocities, especially toward the bottom of the tank, that may hinder solid feedstock suspension and subsequent biogas production. Significant changes in the flow patterns are observed with small variations in the impeller speed and the mixture viscosity. The homogenization dynamics of a tracer obtained by planar laser-induced fluorescence leads us to estimate the dimensionless mixing time, a trend similar to that observed for conventional stirred vessel geometries. The detailed fluid dynamics information collected by a combination of different techniques can contribute to optimize the energy requirement and to avoid failure of the biogas production due to poor fluid mixing.

Impingement and mixing dynamics of micro-droplets on a solid surface

• Impingement on sessile micro-droplet with different impinging angles was simulated. • Convective time, diffusion time and total mixing time were determined quantitatively. • Influence factors on the dimensionless droplet mixing time were discussed. • Mixing time can be shortened by reducing the impinging angle. The hydrodynamics and mixing during the nonaxisymmetry impingement of a micro-droplet and a sessile droplet of the same fluid are investigated by many-body dissipative particle dynamics (MDPD) simulation. In this work, the range of the impingement angle ( θ i ) between the impinging droplet and the sessile droplet is 0°–60° and the contact angle is set as 45° or 124°. The droplets impingement and mixing behavior is analyzed based on the droplet internal flow field, the concentration distribution and the time scale of the decay of the kinetic energy of the impinging droplet. The dimensionless total mixing time ( τ m ) is calculated by a modified mixing function. With the Weber number ( We ) ranging from 5.65 to 22.7 and the Ohnesorge number ( Oh ) ranging from 0.136 to 0.214, we find τ m hardly changes with We and Oh . Whereas, θ i and surface wettability are found to have a significant effect on τ m . We find that θ i has no clear effect on τ m on a hydrophobic surface, while on the hydrophilic surface, τ m increase with the θ i . Thus, reducing the impinging angle is a valid method to shorten the τ m .

Study on cavern evolution and performance of three mixers in agitation of yield-pseudoplastic fluids

The hydrodynamic performance of three mixers (single shaft central mixer (SSC), single shaft off-centred mixer (SSO), dual shaft off-centred mixer (DSO), was investigated in the mixing of yield-pseudoplastic fluids (xanthan gum solutions) in the laminar regime. To explore and determine the efficiency of three mixers, both numerical and experimental approaches were adopted. The fluid rheology was described by the Herschel–Bulkley rheological model. Computational fluid dynamics was employed to simulate the apparent viscosity distribution, mixing time, and the flow pattern inside the stirred tank. The developed model was validated through experimentally measured torque. The influence mechanism of the rotational speed and fluid rheology on the cavern evolution was explored deeply. The performances of three mixers in this work were compared at the constant power input and fluid rheology with respect to the flow pattern, mixing time, and mixing efficiency. The results verify that the faster the rotating speed, the greater influence of the fluid rheology on the cavern evolution, and the more uniform apparent viscosity distribution. Moreover, the mixing time decreases continuously as the increasing power consumption per unit volume, and the dimensionless mixing time of DSO mixer was nearly 42.8% and 6.1% shorter than that of SSC and SCO mixer at the same Reynolds number, respectively. According to the mixing efficiency criteria, these data also revealed that DSO was more efficient than SSC and SSO.

Enhanced production of Bacopa saponins by repeated batch strategy in bioreactor.

Cultivation of cell suspension culture of Bacopa monnieri targeting the production of bacosides was explored in a 5-l stirred tank reactor using statistically optimized conditions. The bioreactor cultivation conditions were modified and this led to profuse biomass growth (2.81 ± 0.20g/l) and total bacosides (1.26 ± 0.23mg/g in cells and 0.60 ± 0.11mg/l in fermenter broth) production in 9days. The values of static volumetric mass transfer coefficient (kLa), dimensionless mixing time (Nm) were measured in the bioreactor. The culture grew efficiently and produced enhanced amount of bacoside A (5.59 ± 0.41mg/g total bacosides in cells and 3.12 ± 0.13mg/l in the fermenter broth) using one cycle of repeated batch strategy adopted in the bioreactor for 15days. The intracellular concentration of bacoside A3 (1.18 ± 0.11mg/g), bacopaside II (2.09 ± 0.35mg/g), bacopaside X (0.79 ± 0.17mg/g) and bacopasaponin C (2.24 ± 0.23mg/g) were significantly higher in repeated batch as compared to batch bioreactor cultivation. The yield of total bacosides in the fermenter broth was 5-times higher in repeated batch as compared to batch cultivation. This strategy can be helpful for the enhanced production of other valuable triterpenoid saponins.

Mixing Time and Scale‐up Investigation of a Moving‐Baffle Oscillatory Baffled Column

AbstractMixing time and scale‐up behavior were investigated for a moving‐baffle oscillatory baffled column (MB‐OBC). Computational fluid dynamics software was used to investigate the effects of the oscillation conditions and changes in the column scale on the dimensionless mixing time. The results indicate that small amplitudes combined with high frequencies are detrimental to the mixing efficiency and that the scale‐up of an MB‐OBC is linearly dependent on the column diameter. This work, in combination with previous studies, proves that the predictability of the hydrodynamic behavior during scale‐up is inherent to oscillatory baffled columns. This trait is desirable for adapting these columns for industrial‐scale applications.

New Insight on Liquid Steel Microalloying by Pulse-Step Method in Two-Strand Slab Tundish by Numerical Simulations

Developing a technology for introducing alloy addition to liquid steel during the course of continuous casting process seems to be an interesting approach to enhancing the steelmaking process, especially as the effective introduction of micro-additives or non-metallic inclusion modifiers to the liquid steel is the key to the production of the highest-quality steel. This paper presents the results of investigation describing the process of liquid steel chemical homogenisation in the two-strand slab tundish. The alloy was fed to liquid steel by pulse-step method. Five tundish equipment variants with different flow control devices and alloy addition feeding positions were considered. The paper includes fields of liquid steel flow, alloy concentration vs. time curves, dimensionless mixing time, minimum time values and alloy concentration deviations at tundish outlets. The results pointed much more effectively with liquid steel mixing nickel than aluminium. For aluminium obtaining a 95% chemical homogenisation level requires three-fold more time. Moreover, it is definitely beneficial for chemical homogenisation to initiate the alloying process simultaneously in two sites. This procedure generates, among others, the least alloy deviation of concentration at tundish outlets.

Novel evaluation method to determine the local mixing time distribution in stirred tank reactors

Stirred tank reactors are frequently used for mixing as well as heat- and mass transfer processes in chemical and biochemical engineering due to their robust operation and extensive experiences in the past. However, for cell culture processes like mammalian cell expression systems, special requirements have to be met to ensure optimal cell growth and product quality. One of the most important requirements to ensure ideal transport processes is a proper mixing performance, characterized typically by the global mixing time tmix,global or the dimensionless global mixing time tmix,global·n. As an evaluation method for mixing time determination, the time is usually determined until a tracer signal (e.g. conductivity) has reached a constant value after a peak has been introduced (e.g. by adding a salt). A disadvantage of this method is, that the position of tracer feeding as well as the position of the probe significantly influences the detected mixing time. Further on, the global mixing time does not provide any information about the spatial and temporal ”history” of the mixing process to identify areas that are mixed poorly or areas that form stable compartments. To overcome this disadvantage, a novel image analysis will be presented in this study for the detailed characterization of mixing processes by taking into account the history of mixing. The method is based on the experimental determination of the local mixing time distribution by using a multi-color change caused by a pH-change in a bromothymol blue solution. A 3L transparent stirred tank reactor is used for the benchmark experiment. To demonstrate the suitability of the new characterization method for the validation of numerical simulations, a calculation with a commercial Lattice-Boltzmann approach (M-Star CFD) has been performed additionally and evaluated regarding mixing time distributions. The exemplary application of image analysis to a numerical mixing time simulation shows good agreement with the corresponding experiment. On the one hand, this shows that the method can also be interesting for numerical work, especially for experimental validation, and on the other hand, this allows much deeper insights into the mixing behavior compared to conventional mixing criteria. For example the new method enables the characterization of mixing on different scales as well as the identification of micro- and macroscopic flow structures. The strong influence of the acid to base ratio on mixing time experiments becomes clearly visible with the new method.

Mixing efficiency studies in an airlift bioreactor with helical flow promoters for improved reactor performance

Cultivation of aerobic microorganisms typically requires rapid, but gentle and simultaneously energy efficient mixing in bioreactors to prevent high gradients between local concentrations. The mixing efficiency in a pilot scale airlift bioreactor with helical flow promoters was investigated with varying air inputs. Helical flow promoters were helical tubes attached to riser or downcomer, or both and besides acting as flow promoter they were used as additional gas spargers. Mixing time, circulation time, dimensionless mixing time and Bodenstein number were used as assessment parameters to analyze the mixing efficiency of different airlift setups with helical flow promoters. Introducing air through the helical flow promoter in the downcomer zone prolonged the circulation time, but shortened the mixing time and decreased the Bodenstein number. Low Bodenstein number indicated an improved axial dispersion. Mixing was more related to dispersion in the airlift reactor with helical flow promoter in the downcomer zone whereas in a regular airlift reactor mixing was related to liquid circulation speed.

Investigation of mixing time in liquid under influence of rotating magnetic field

Abstract The aim of the study was to present an experimental investigation of the influence of the RMF on mixing time. The obtained results suggest that the homogenization time for the tested experimental set-up depending on the frequency of the RMF can be worked out by means of the relationship between the dimensionless mixing time number and the Reynolds number. It was shown that the magnetic field can be applied successfully to mixing liquids.

Intensification of chaotic mixing in a stirred tank with a punched rigid-flexible impeller and a chaotic motor

Laminar mixing of non-Newtonian CMC solution was investigated experimentally in a stirred tank with a rigid impeller, a rigid impeller coupled with a chaotic motor, a rigid-flexible impeller, a rigid-flexible impeller coupled with a chaotic motor, a punched rigid-flexible impeller, and a punched rigid-flexible impeller coupled with a chaotic motor. Visualization experiment was used to reveal the presence of segregated regions, and observe the structure changes of segregated regions. The mixing performance was characterized by the largest Lyapunov exponent (LLE) and dimensionless mixing time (NTm). Results showed that punched rigid-flexible impeller could further enhance the value of LLE, namely, the chaotic extent of mixing system compared with rigid impeller and rigid-flexible impeller, and the NTm for punched rigid-flexible impeller was shorter than that for rigid impeller and rigid-flexible impeller at the same consumption per unit volume (Pv). The chaotic motor could further increase LLE value, and reduce the NTm on the basis of the normal motor. Moreover, the optimum aperture diameter and aperture ratio of punched rigid-flexible impeller were 8mm and 12%, respectively, and the variable speed period of 10s and constant speed period of 5s of chaotic motor were particularly suitable for the laminar mixing process.

CFD simulation of local and global mixing time in an agitated tank

The Issue of mixing efficiency in agitated tanks has drawn serious concern in many industrial processes. The turbulence model is very critical to predicting mixing process in agitated tanks. On the basis of computational fluid dynamics(CFD) software package Fluent 6.2, the mixing characteristics in a tank agitated by dual six-blade-Rushton-turbines(6-DT) are predicted using the detached eddy simulation(DES) method. A sliding mesh(SM) approach is adopted to solve the rotation of the impeller. The simulated flow patterns and liquid velocities in the agitated tank are verified by experimental data in the literature. The simulation results indicate that the DES method can obtain more flow details than Reynolds-averaged Navier-Stokes(RANS) model. Local and global mixing time in the agitated tank is predicted by solving a tracer concentration scalar transport equation. The simulated results show that feeding points have great influence on mixing process and mixing time. Mixing efficiency is the highest for the feeding point at location of midway of the two impellers. Two methods are used to determine global mixing time and get close result. Dimensionless global mixing time remains unchanged with increasing of impeller speed. Parallel, merging and diverging flow pattern form in the agitated tank, respectively, by changing the impeller spacing and clearance of lower impeller from the bottom of the tank. The global mixing time is the shortest for the merging flow, followed by diverging flow, and the longest for parallel flow. The research presents helpful references for design, optimization and scale-up of agitated tanks with multi-impeller.

Mixing times in single and multi-orifice-impinging transverse (MOIT) jet mixers with crossflow

We study the macromixing behavior of single and multi-orifice-impinging transverse (MOIT) jet mixers with crossflow, in particular, the overall mixing time and the back-splash mixing time of the injected flow with the crossflow, using the PLIF technique. It is found that for a given mixer configuration, there is a critical jet-to-crossflow velocity ratio rc at which the back-splash begins to occur. Further increase in the velocity ratio r leads to sharp increase in the back-splash mixing time, which can offset the intensification of the downstream mixing. The dimensionless overall mixing time decreases as r increases to reach either a plateau or a local minimum, and the corresponding r value represents the optimal velocity ratio ropt for the macromixing. The momentum ratio of the two liquid streams is a key factor determining rc and ropt. For a larger scale mixer, a higher momentum ratio is required to achieve the optimal macromixing with the minimum dimensionless overall mixing time.

Two-scale model for quantifying the effects of laminar and turbulent mixing on algal growth in loop photobioreactors

This paper quantifies the mixing effects on algal growth in loop photobioreactors using two-scale low-dimensional models derived through spatial averaging of the Convection–Diffusion–Reaction equation using Liapunov–Schmidt technique of the classical bifurcation theory. The local mixing in the reactor is captured in terms of the mixing time and the difference between the mixing-cup and the spatially averaged concentrations of the algae, which are representatives of the convection scale in the fluid phase and the reaction scale at the algal surface, respectively. We solve coupled unsteady-state low-dimensional partial differential equations (PDEs) to simulate the temporal dynamics of the algae (Chlorella vulgaris), carbon dioxide and oxygen along the reactor in laminar and turbulent mixing regimes. Analytical solutions are derived for the unsteady and pseudo-steady state cases in the turbulent regime. We show that while laminar mixing results in significant scale separation between the convection and reaction scales, turbulent mixing – propelled by the turbulent diffusivity – eliminates all scale separation and mass transfer limitations in the photobioreactor and maximizes algal growth. Increasing Reynolds number (Re) increases the dimensionless mixing time (and thus, the scale separation) in the laminar regime but has negligible effect on turbulent mixing. Thus, the system transitions from the mixing-limited asymptote in the laminar regime to the reaction-limited asymptote in the turbulent regime. For maximum algal growth per unit energy cost, we recommend operating loop photobioreactors at a low Re (>2300) in the turbulent flow regime so as to generate turbulent mixing for rapid mass transfer of the growth substrates and the algae between the convection (fluid) and the reaction (solid) phases, at optimal pressure drops. Our two-scale model would be an important design tool for quantifying mixing effects while scaling up photobioreactors.

Gas hold-up distribution and mixing time in gas–liquid stirred tanks

In this work, the gas–liquid dispersion in a stirred tank equipped with different impellers is investigated by Electrical Resistance Tomography (ERT). The main goal of the study is to provide detailed information on the spatial distribution of the gas phase and on the effect of bubbles on the liquid homogenisation dynamics. The analysis is carried out under variable gas flow rates and impeller speeds, thus covering different regimes of gas–impeller interaction, as obtained by Rushton Turbines, Pitched Blade Turbines pumping upwards and Lightnin A310. The experimental technique allows us to overcome the typical limitations of optical methods and to gain insight into the complex behaviour of sparged stirred tanks without restriction on the upper value of overall gas hold-up, that is of great interest for several chemical and biochemical processes. Besides, the experimental data can be adopted as a benchmark for advanced modelling techniques based on CFD methods, whose scant validation is often due to limited information on the local dispersion features.The analysis of experimental results allows us to suggest simple correlations for the prediction of the prevailing flow regime based on the dimensionless Froude and flow numbers. Finally, the definition of a modified Peclet number is also suggested, as a simple parameter for the interpretation of both the gas hold-up distribution and the dimensionless mixing time.

Improvement of mixing time, mass transfer, and power consumption in an external loop airlift photobioreactor for microalgae cultures

Longer mixing times and higher power consumption are common problems in the design of photobioreactors. In this study, a vertical triangular external airlift loop photobioreactor was designed, constructed and operated for microalgae production studies. Gas feeding was performed by two spargers: one at the bottom of the hypotenuse (downcomer) and another at the bottom of the vertical side (riser). This configuration provided more effective countercurrent liquid–gas flow in the hypotenuse. The mass transfer coefficient, gas hold-up, mixing time, circulation time, dimensionless mixing time, bubble size, and volumetric power consumption were measured and optimized using response surface methodology. Investigations were carried out on the performance of the riser (the vertical side), downcomer (the hypotenuse), and separator. The countercurrent flow in the hypotenuse provided sufficient contact between gas and liquid phases, and increased mixing and mass transfer rates, in contrast to the results of previous studies. The promising results of this geometry were shorter mixing time and a significant decrease in volumetric power consumption in comparison with other configurations for photobioreactors.

Potential of an asymmetrical agitation in industrial mixing

Mixing is one of the most fundamental operations in chemical engineering. Stirred tanks are widely used in the manufacture of such materials as chemicals, paints, inks, electronics materials, ceramics, foods, pharmaceuticals and cosmetics. Suitable mixing is indispensable to the purpose achievement of a process. Eccentric mixing, in which an impeller installed at eccentric position in a vessel, is one of the traditional methods of promoting mixing. An asymmetrical flow which occurs in vessel is complicated, and it promotes mixing, distribution, and mass transfer. In this study, a new mixing method which eccentric mixing using a large type impeller which attracts attention in recent years is shown. The high performance of a large impeller can be combined with the advantages of an eccentric impeller by using the impeller at an eccentric position. The power consumption and mixing time for MAXBLEND, which is a type of large impeller, were investigated. The power consumption, P , and mixing time, θ M , were measured under various eccentric conditions. The relation between the power number ( N p ) and Reynolds number ( Re ) and that between the dimensionless mixing time ( nθ M ) and Re were investigated. When eccentric mixing is used industrially, we should be concerned about the horizontal load to a agitating shaft. The large oscillating horizontal load causes serious problems, such as the falling off of the impeller or the breakage of the motor, mechanical seal or gearbox. It is, therefore, important to understand the relation between these values and the impeller rotational speed when designing the mixing equipment and determining the operating conditions. In this study, the torque and horizontal load were measured in eccentric mixing under various eccentric conditions. The averages of both, the torque and the horizontal load, and their standard deviations, corresponding to the amplitude of fluctuation, were shown. Doi : 10.12777/ijse.5.2.73-80 [ How to cite this article : Nishi, K., Enya, N., Sonoda, K., Misumi, R., Kaminoyama, M. (2013). Potential of an asymmetrical agitation in industrial mixing. International Journal of Science and Engineering , 5(2),73-80. Doi: 10.12777/ijse.5.2.73-80 ]

Mixing of viscous Newtonian fluids in a vessel equipped with steady and unsteady rotating dual-turbine impellers

This paper presents investigation on the possibility to improve the efficiency of mixing of the highly viscous Newtonian fluids in a vessel with utilization of unsteady rotating dual turbine impellers. Flow visualization experiments were used to examine the size, positions and structure of the IMR (Isolated Mixing Regions) regions as a function of Reynolds number as well as mixing time. Additionally, the effect of frequency of impellers’ oscillation on mixing efficiency was examined. It was found that the use of unsteady forward–reverse mixing mode enhance the mixing efficiency in comparison to standard mixing (up to about eight times). The structure of IMR in the forward–reverse mixing is much more complicated than in standard mixing, because of liquid division into spiral-shape filaments. This had caused that dimensionless mixing time was up to about eight times shorter in comparison to standard mode.

Study of Mixing Time in a Liquid Vessel with Rotating and Reciprocating Agitator

This paper presents experimental investigations of the influence of a newly constructed agitator on mixing time. Two kinds of movement (rotating and reciprocating) of a nontypical agitator are discussed. Moreover, the influence of simultaneous rotating and reciprocating movements of the agitator on the homogenization process of a mixed liquid is analyzed. The proposed dimensional analysis of the Navier–Stokes equation is allowed to describe the analyzed process by means of a relationship based on dimensionless numbers (mixing time number, rotating or reciprocating Reynolds number). The obtained results suggest that the homogenization time for the tested experimental setup may be worked out by use of the relationship between the mentioned dimensionless mixing time number and the rotating or/and reciprocating Reynolds number. Important conclusions from the discussion of experimental studies of the mixing process are also specified.