Search

The impact of orbitally shaking bioreactors (OSRs) on the biopharmaceutical industry is becoming increasingly important. In the preliminary exploration of the orbitally shaking bioreactor performance, the vessel wall shape has a crucial influence on the mixing and mass transfer in the bioreactor. However, the shape of OSRs still maintains a cylindrical structure, significantly limiting the advantages of the orbital shaking mixing. Therefore, in order to further improve the mixing and mass transfer performance of OSRs, a novel wall shape is proposed in this paper. This novel wall shape consists of cylindrical and square parts and looks like a square tank with a large circular chamfer (STCC), which was found could effectively enhance the efficiency of material mixing and mass transfer theoretically. Based on the same specific volumetric power consumption, a comparative analysis was conducted on the mixing time and oxygen transfer efficiency of OSRs with different shape walls using simulation and experimental methods. The results showed that the OSR with STCC was expected to perform higher mixing and oxygen transfer efficiency than the OSR with cylindrical wall. These findings suggested a promising prospect for the future application of the OSRs with STCC. • Developing a novel wall structure (STCC) improving the mixing performance of OSRs. • Both oxygen mass transfer and mixing efficiency were increased with the STCC effect. • Improving the bioreactor performance with low calculated shear stress. • Mixing speed was found significantly lower in the vortex center than other regions. • Promising prospect for the future application of the OSRs with STCC. [ABSTRACT FROM AUTHOR]

The measurement of mixing time in a water model of soft-stirring steelmaking ladles is practically facing a problem of bad repeatability. This uncertainty severely affects both the understandings of transport phenomenon in ladles and the measurement accuracy. Scaled down by a ratio of 1:4, a water model based on an industrial 260-ton ladle is used. This paper studies the transport process paths and mixing time of salt solution tracers in the water model of eccentric gas-stirred ladles with a low gas flow rate. After a large number of repeated experiments, the different transport paths of the tracer and the error of the mixing time in each transport path are discussed and compared with the numerical simulation results. The results of a large number of repeated experiments on the water model show that there are five transport paths for the tracer in the ladle. The tracer of the first path is mainly transported by the left-side main circulation flow, which is identical to the numerical simulation results. The tracer of the second and third paths are also mainly transported by the left-side circulation flow, but bifurcations occur when the tracer in the middle area is transported downward. In the third path, the portion and intensity of the tracer transferring to the right side from the central region is higher than in the second path. The fourth path is that the tracer is transported downward from the left, middle, and right sides with a similar intensity at the same time. While the tracer in the fifth path is mainly transported on the right side, and the tracer forms a clockwise circulation flow on the right side. The mixing times from the first transport path to the fifth transport path are 158.3 s, 149.7 s, 171.7 s, 134 s and 95.7 s, respectively, among which the third transport path and the fifth transport path are the maximum and minimum values among all transport paths. The error between the mixing time and the averaged mixing time at each monitoring point in the five transport paths of the tracer is between −34.7% and 40.9%. Furthermore, the error of the averaged mixing time of each path and the path-based average value is between 5.5% and 32.6%. [ABSTRACT FROM AUTHOR]

We analyze the convergence rates for a family of auto‐regressive Markov chains on Euclidean space depending on a parameter n$$ n $$, where at each step a randomly chosen coordinate is replaced by a noisy damped weighted average of the others. The interest in the model comes from the connection with a certain Bayesian scheme introduced by de Finetti in the analysis of partially exchangeable data. Our main result shows that, when n gets large (corresponding to a vanishing noise), a cutoff phenomenon occurs. [ABSTRACT FROM AUTHOR]

We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate μ between open and closed, following a Glauber dynamics for the random cluster model with parameters p, q. At the same time, the walker jumps at rate 1 as a simple random walk on the torus, but is only allowed to traverse open edges. We show that for small enough p the mixing time of the random walker is of order n 2 / μ . In our proof we construct a non-Markovian coupling through a multi-scale analysis of the environment, which we believe could be more widely applicable. [ABSTRACT FROM AUTHOR]

This study aims to investigate the effect of the temperature of the self-consolidating concrete (SCC) mixture during casting on fresh and hardened properties for two types of SCC. Also, the rheological properties of the mixtures were assessed at specific time intervals (0, 20 and 40 min after mixing) to determine their sensitivity to changes in mixtures' properties and temperature over time. For this purpose, two categories of SCC were prepared: Powder type and Viscosity-Agent type. Silica fume, metakaolin (MK) and slag were utilised as substitutes for cement in these samples. The mixtures were tested at low and high temperatures of 5 °C and 34 °C, respectively, with an average temperature of 21 °C. Results indicated that as the mixture temperature decreased, the yield stress decreased by 30% and the plastic viscosity increased by 25% on average. Conversely, as the temperature increased, the yield stress increased by 20% and the plastic viscosity decreased by 40% on average. Moreover, increasing the mixture temperature resulted in a 10% increase in the 7-d compressive strength but a 15% decrease in the 28-d compressive strength of the specimens. Additionally, increasing the rest time after mixing increased the yield stress, while the plastic viscosity remained relatively stable with occasional increases. [ABSTRACT FROM AUTHOR]

We show that the total variation mixing time is not quasi-isometry invariant, even for Cayley graphs. Namely, we construct a sequence of pairs of Cayley graphs with maps between them that twist the metric in a bounded way, while the ratio of the two mixing times goes to infinity. The Cayley graphs serving as an example have unbounded degrees. For non-transitive graphs, we construct bounded degree graphs for which the mixing time from the worst starting point for one graph is asymptotically smaller than the mixing time from the best starting point of the random walk on a network obtained by increasing some of the edge weights from 1 to $1+o(1)$. [ABSTRACT FROM AUTHOR]

Fluid mixing is a common topic in contemporary industry. The search for more efficient processes and reliable equipment is a constant challenge. In this work, numerical and experimental tests analyzed a 45° pitched blade turbine in a contra‐rotating coaxial impeller system (CRCIS) configuration mounted on baffles‐free reactors and compared it with conventional systems with one (CS1I) and two (CS2I) impellers mounted on tanks with baffles. Experimental tests were carried out using a pilot reactor with reduced scales of 1.0 m in diameter and 1.0 m in height (square batch). The behaviour of the physical variables was analyzed for mixing operations, solid particle suspension, and formation of vortices, and the power consumption was recorded through a torque transducer for different rotations. The acquired results helped in the validation of models and numerical simulations. The numerical simulation was carried out using the OpenFOAM® open‐source field operation and manipulation software. In addition, the velocity profile along with the height of the reactor, flow lines, pumping number, power consumption variations, and mixing time were compared. The conclusion of this study showed that CRCIS can be used in tanks without baffles. It also showed promising results for applications involving the suspension of solids, developing axial velocities at the bottom of the reactor higher than those of the CS1I and CS2I arrangements for the same rotation, with less energy consumption, proving to be a technically promising option for application on an industrial scale. [ABSTRACT FROM AUTHOR]

This study explores the impact of carbon fiber length and content on the rheological properties and performance of coatings used in lost foam casting. The investigation encompassed fiber lengths of 1 mm, 3 mm, and 6 mm and fiber contents of 0.2%, 0.5%, and 0.8%. The effects on coating viscosity, shear stress, coating weight, and surface morphology were meticulously evaluated. The results demonstrate that incorporating carbon fibers significantly enhances coating viscosity and shear stress compared to fiber-free coatings, with more pronounced effects observed at higher fiber contents and longer fiber lengths. Nevertheless, excessive fiber contents and lengths can lead to agglomeration, negatively impacting coating uniformity. The optimal fiber length and content were identified, striking a balance between improved rheological properties and coating performance. These findings provide critical insights for the development and industrial application of high-performance coatings in lost foam casting. [ABSTRACT FROM AUTHOR]

This study investigates the rheological properties and performance of coatings used in lost foam shell casting, focusing on the influence of mixing and standing times. The experimental procedure involved systematically preparing coatings by varying the mixing times (10, 20, 30, 40, 50, and 60 min) to assess the dispersion of particles and the subsequent standing times (1, 7, 11, 24, 40, and 48 h) to evaluate the stability of the mixture. A rotational viscometer was utilized to measure the viscosity and shear stress of the coatings under different conditions. The results indicate a significant decrease in viscosity with increasing mixing time, stabilizing after 50 min due to the uniform dispersion of solid particles and shear-thinning behavior. Conversely, the viscosity initially increases with prolonged standing time as the binder's molecular chains reform, reaching a peak before gradually decreasing. The optimal performance of the coatings, characterized by stable viscosity and consistent rheological properties, was achieved with a mixing time of at least 50 min and a standing time not exceeding 40 h. These findings provide critical insights into optimizing the preparation and application processes of coatings, ensuring enhanced efficiency and quality in lost foam shell casting. [ABSTRACT FROM AUTHOR]

Stirred mixers are ubiquitous in industrial applications, operating optimally to achieve homogeneous mixing of liquids, gases, and solids. Improving mixer performance is critical for attaining high efficiency, low production costs, and high product quality. This review examines three key aspects of mixer optimization: power consumption, mixing time, and impeller geometry. The research aims to summarize a comprehensive review on mixing time and the experimental devices used to measure it. The effect of using impellers and changing their geometry on the power consumption, mixing efficiency, and mixing time. Power usage is a vital metric for evaluating mixer efficiency. Complex interplay between impeller design, operating conditions, and fluid properties governs energy consumption. Understanding and minimizing power requirements are essential for efficient, sustainable mixing operations. Mixing time also significantly impacts efficiency, relating directly to impeller geometry and fluid rheology. Reviewing research on mixing time highlights opportunities to reduce durations, boosting productivity. Impeller geometry, governing mixer design for target applications, represents another major optimization variable. Impeller selection plays a major role in stirred tanks, especially in chemical processing. Elucidating relationships between fluid dynamics and impeller configurations is thus necessary for developing effective, economical mixing solutions. [ABSTRACT FROM AUTHOR]

We address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on contraction with respect to total variation. Specifically, we estimate the contraction coefficient introduced in Wolfer (2020), inspired from Dobrushin's. This quantity, unlike the spectral gap, controls the mixing time up to strong universal constants and remains applicable to nonreversible chains. We improve existing fully data‐dependent confidence intervals around this contraction coefficient, which are both easier to compute and thinner than spectral counterparts. Furthermore, we introduce a novel analysis beyond the worst‐case scenario by leveraging additional information about the transition matrix. This allows us to derive instance‐dependent rates for estimating the matrix with respect to the induced uniform norm, and some of its mixing properties. [ABSTRACT FROM AUTHOR]

The importance of a single-use bioreactor (SUB) is continuously increasing in research and industrial fields for biopharmaceutical production. In this study, a newly developed SUB system, the CELBIC® system, applied with the unique agitation method is introduced, and its physical properties and biological applications are evaluated. The mixing time was in the range of 11.0–129.0 s, and the volumetric mass transfer coefficient, kLa, measured through surface aeration, was in the range of 2.7–15.5 h−1 at a working volume of 1–10 L. Biological evaluations using two Chinese hamster ovary (CHO) cell lines, CHO-DG44 and CHO-S cell, were carried out in the CELBIC® systems in 1 and 50 L scales, showing similar cell culture performance as that from stirred tank-type bioreactors. These results support the CELBIC® system as a new SUB system applicable to cell cultures for biopharmaceutical production. [ABSTRACT FROM AUTHOR]

We study the mixing time of a random walk on the torus, alternated with a Lebesgue measure preserving Bernoulli map. Without the Bernoulli map, the mixing time of the random walk alone is O(1/\varepsilon ^2), where \varepsilon is the step size. Our main results show that for a class of Bernoulli maps, when the random walk is alternated with the Bernoulli map \varphi the mixing time becomes O(\lvert \ln \varepsilon \rvert). We also study the dissipation time of this process, and obtain O(\lvert \ln \varepsilon \rvert) upper and lower bounds with explicit constants. [ABSTRACT FROM AUTHOR]

We study the simple random walk on trees and give estimates on the mixing and relaxation times. Relying on a seminal result by Basu, Hermon and Peres characterizing cutoff on trees, we give geometric criteria that are easy to verify and allow to determine whether the cutoff phenomenon occurs. We provide a general characterization of families of trees with cutoff, and show how our criteria can be used to prove the absence of cutoff for several classes of trees, including spherically symmetric trees, Galton–Watson trees of a fixed height, and sequences of random trees converging to the Brownian continuum random tree. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a finite, combinatorial graph. We define a notion of curvature on the vertex set V via the inverse of the resistance distance matrix. We prove that this notion of curvature has a number of desirable properties. Graphs with curvature bounded from below by K > 0 have diameter bounded from above. The Laplacian L = D − A satisfies a Lichnerowicz estimate, there is a spectral gap λ 2 ≥ 2 K. We obtain matching two-sided bounds on the maximal commute time between any two vertices in terms of | E | ⋅ | V | − 1 ⋅ K − 1 . Moreover, we derive quantitative rates for the mixing time of the corresponding Markov chain and prove a general equilibrium result. [ABSTRACT FROM AUTHOR]

In previous research simulating steelmaking ladles using cold water models, the dosage/volume of the salt tracer solution is one of the factors that has been overlooked by researchers to a certain extent. Previous studies have demonstrated that salt tracers may influence the flow and measured mixing time of fluids in water models. Based on a water model scaled down from an industrial 130-ton ladle by a ratio of 1:3, this study investigates the impact of salt tracer dosage on the transport and mixing of tracers in the water model of gas-stirred ladle with a moderate gas flow rate. A preliminary uncertainty analysis of the experimental mixing time is performed, and the standard deviations were found to be less than 15%. It was observed in the experiments that the transport paths of tracers in the ladle can be classified into two trends. A common trend is that the injected salt solution tracer is asymmetrically transported towards the left sidewall of the ladle by the main circulation. In another trend, the injected salt solution tracer is transported both by the main circulation to the left side wall and by downward flow towards the gas column. The downward flow may be accelerated and become a major flow pattern when the tracer volume increases. For the dimensionless concentration curve, the sinusoidal type, which represents a rapid mixing, is observed at the top surface monitoring points, while the parabolic type is observed at the bottom monitoring points. An exception is the monitoring point at the right-side bottom (close to the asymmetric gas nozzle area), where both sinusoidal-type and parabolic-type curves are observed. Regarding the effect of tracer volume on the curve and mixing time, the curves at the top surface monitoring points are less influenced but curves at the bottom monitoring points are noticeably influenced by the tracer volume. A trend of decreasing and then increasing as the tracer volume increases was found at the top surface monitoring points, while the mixing times at the bottom monitoring points decrease with the increase in the tracer volume. [ABSTRACT FROM AUTHOR]

The reliable transfer of bioprocesses from single-use bioreactors (SUBs) of different scales to conventional stainless steel stirred-tank bioreactors is of steadily growing interest. In this publication, a scale-up study for SUBs with volumes of 200 L and 2000 L and the transfer to an industrial-scale conventional stainless steel stirred-tank bioreactor with a volume of 15,000 L is presented. The scale-up and transfer are based on a comparison of mixing times and the modeling of volumetric mass transfer coefficients kLa, measured in all three reactors in aqueous PBS/Kolliphor solution. The mass transfer coefficients are compared with the widely used correlation of van't Riet at constant stirrer tip speeds. It can be shown that a van't Riet correlation enables a robust and reliable prediction of mass transfer coefficients on each scale for a wide range of stirrer tip speeds and aeration rates. The process transfer from single-use bioreactors to conventional stainless steel stirred-tank bioreactors is proven to be uncritical concerning mass transfer performance. This provides higher flexibility with respect to bioreactor equipment considered for specific processes. [ABSTRACT FROM AUTHOR]

We show that for every integer m≥2$$ m\ge 2 $$ and large n$$ n $$, every properly edge‐colored graph on n$$ n $$ vertices with at least n(logn)53$$ n{\left(\log n\right)}^{53} $$ edges contains a rainbow subdivision of Km$$ {K}_m $$. This is sharp up to a polylogarithmic factor. Our proof method exploits the connection between the mixing time of random walks and expansion in graphs. [ABSTRACT FROM AUTHOR]

This paper presents a study on the effectiveness of two turbulence models, the large eddy simulation (LES) model and the k-ε turbulence model, in predicting mixing time within a ladle furnace using the computational fluid dynamics (CFD) technique. The CFD model was developed based on a downscaled water ladle from an industrial ladle. Corresponding experiments were conducted to provide insights into the flow field, which were used for the validation of CFD simulations. The correlation between the flow structure and turbulence kinetic energy in relation to mixing time was investigated. Flow field results indicated that both turbulence models aligned well with time-averaged velocity data from the experiments. However, the LES model not only offered a closer match in magnitude but also provided a more detailed representation of turbulence eddies. With respect to predicting mixing time, increased flow rates resulted in extended mixing times in both turbulence models. However, the LES model consistently projected longer mixing times due to its capability to capture a more intricate distribution of turbulence eddies. [ABSTRACT FROM AUTHOR]

We provide a general framework for computing mixing times of finite Markov chains whose semigroup's minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary distributions of finite Markov chains. Stationary distributions can be computed from the Karnofsky-Rhodes and McCammond expansion of the right Cayley graph of the finite semigroup underlying the Markov chain. Using loop graphs, which are planar graphs consisting of a straight line with attached loops, there are rational expressions for the stationary distribution in the probabilities. From these we obtain bounds on the mixing time. In addition, we provide a new Markov chain on linear extension of a poset with n vertices, inspired by but different from the promotion Markov chain of Ayyer, Klee, and the last author. The mixing time of this Markov chain is O(n log n).

In the Fastest Mixing Markov Chain problem, we are given a graph G = (V , E) and desire the discrete-time Markov chain with smallest mixing time τ subject to having equilibrium distribution uniform on V and non-zero transition probabilities only across edges of the graph. It is well-known that the mixing time τ RW of the lazy random walk on G is characterised by the edge conductance Φ of G via Cheeger's inequality: Φ - 1 ≲ τ RW ≲ Φ - 2 log | V | . Analogously, we characterise the fastest mixing time τ ⋆ via a Cheeger-type inequality but for a different geometric quantity, namely the vertex conductance Ψ of G: Ψ - 1 ≲ τ ⋆ ≲ Ψ - 2 (log | V |) 2 . This characterisation forbids fast mixing for graphs with small vertex conductance. To bypass this fundamental barrier, we consider Markov chains on G with equilibrium distribution which need not be uniform, but rather only ε -close to uniform in total variation. We show that it is always possible to construct such a chain with mixing time τ ≲ ε - 1 (diam G) 2 log | V | . Finally, we discuss analogous questions for continuous-time and time-inhomogeneous chains. [ABSTRACT FROM AUTHOR]

Multi-objective optimizations are performed for single and dual-impeller systems. The steady-state mean age theory approach with a novel method developed in previous work is applied for mixing time prediction. The three-blade Pitched-blade turbines are the baseline designs. The study aims to find the optimum impellers with lower mixing time and power consumption than the benchmark designs. The blade consists of two parts characterized by 10 to 12 design parameters, and 120 designs are investigated during optimization. The parameter analysis study highlights that the angle formed by the line connecting the two parts is the most critical parameter affecting mixing performance and power input in both systems. Compared to the baseline design, experimental results show that the optimum designs from single and dual impeller optimization reduce the power consumption 10% and 35%, respectively. However, the reduction in mixing time is not significant. Designs that have lower power numbers with higher power input reduce mixing times by 20%–30%. • The connection line angle affects mixing performance and power input significantly. • Pareto plots are obtained from optimization studies with SHERPA algorithm. • The reliability of the mean age theory approach in optimization study is confirmed. • Optimum designs decrease power by 10% and 35% with no distinct decreases on mixing. • Designs with low power numbers but high power input significantly reduce mixing time. [ABSTRACT FROM AUTHOR]

An important paradigm in the understanding of mixing times of Glauber dynamics for spin systems is the correspondence between spatial mixing properties of the models and bounds on the mixing time of the dynamics. This includes, in particular, the classical notions of weak and strong spatial mixing, which have been used to show the best known mixing time bounds in the high‐temperature regime for the Glauber dynamics for the Ising and Potts models. Glauber dynamics for the random‐cluster model does not naturally fit into this spin systems framework because its transition rules are not local. In this article, we present various implications between weak spatial mixing, strong spatial mixing, and the newer notion of spatial mixing within a phase, and mixing time bounds for the random‐cluster dynamics in finite subsets of ℤd$$ {\mathbb{Z}}^d $$ for general d≥2$$ d\ge 2 $$. These imply a host of new results, including optimal O(NlogN)$$ O\left(N\log N\right) $$ mixing for the random cluster dynamics on torii and boxes on N$$ N $$ vertices in ℤd$$ {\mathbb{Z}}^d $$ at all high temperatures and at sufficiently low temperatures, and for large values of q$$ q $$ quasi‐polynomial (or quasi‐linear when d=2$$ d=2 $$) mixing time bounds from random phase initializations on torii at the critical point (where by contrast the mixing time from worst‐case initializations is exponentially large). In the same parameter regimes, these results translate to fast sampling algorithms for the Potts model on ℤd$$ {\mathbb{Z}}^d $$ for general d$$ d $$. [ABSTRACT FROM AUTHOR]

BACKGROUND: The development of processes for transforming vegetable oils into useful products has received increasing attention in the biotechnological field. The reactor used for this purpose should meet adequate mass transfer, mixing, and oil dispersion conditions. In this work, comprehensive research into the use of a jet‐loop reactor as a potential alternative to airlift and stirred tank reactors was conducted in the presence of avocado oil in a water‐air system. Additionally, the assessment of the jet‐loop for biomass growth in the presence of oil was performed. RESULTS: The increase of avocado oil from 1% to 5% v/v resulted in a reduction in the performance of the three reactors. Despite the airlift reactor having the lowest power input, it exhibited the worst performance in terms of mass transfer, mixing, and oil dispersion. The estimation of the energetic oxygen transfer efficiency (Kg O2 KW−1 h−1) allowed the determination that the jet‐loop reactor was superior to the stirred tank. This superiority was attributed to the low values of the mixing time and oil droplet diameter observed in the jet‐loop reactor. Finally, all these parameters had a positive impact on the growth of Wautersia eutropha in the jet‐loop reactor compared with the other two reactors. CONCLUSION: The results showed that the jet‐loop reactor presented superior performance in most cases compared to the stirred tank and airlift reactors. Particularly, the jet‐loop exhibits an interesting potential to reduce the size of the avocado oil droplets, which could lead to a significative increase in the growth rate of Wautersia eutropha. © 2023 Society of Chemical Industry (SCI). [ABSTRACT FROM AUTHOR]

Bioreactor scale‐up is complicated by dynamic interactions between mixing, reaction, mass transfer, and biological phenomena, the effects of which are usually predicted with simple correlations or case‐specific simulations. This two‐part study investigated whether axial diffusion equations could be used to calculate mixing times and to model and characterize large‐scale stirred bioreactors in a general and predictive manner without fitting the dispersion coefficient. In this first part, a resistances‐in‐series model analogous to basic heat transfer theory was developed to estimate the dispersion coefficient such that only available hydrodynamic numbers and literature data were needed in calculations. For model validation, over 800 previously published experimentally determined mixing times were predicted with the transient axial diffusion equation. The collected data covered reactor sizes up to 160 m3, single‐ and multi‐impeller configurations with diverse impeller types, aerated and non‐aerated operation in turbulent and transition flow regimes, and various mixing time quantification methods. The model performed excellently for typical multi‐impeller configurations as long as flooding conditions were avoided. Mixing times for single‐impeller and few nonstandard bioreactors were not predicted equally well. The transient diffusion equation together with the developed transfer resistance analogy proved to be a convenient and predictive model of mixing in typical large‐scale bioreactors. [ABSTRACT FROM AUTHOR]

Processed cheese spread (PCS) is currently experiencing rapid growth and is recognised as a prominent segment within the cheese‐based product industry worldwide. This type of cheese spread is produced by comminuting and blending natural cheese of varying ages and degrees of maturity, along with other ingredients, to achieve a homogeneous plastic mass. The high viscosity of PCS necessitates thorough mixing and blending, posing a challenge for cheese processors. In this study, a mechanical unit known as a universal disperser was utilised to prepare PCS. The study aimed to evaluate the impact of different processing parameters on the quality of the final product. Response surface methodology (RSM) was employed to design the experiment and optimise the process accordingly. The experiment involved conducting trials at three distinct melting temperatures: 50, 65 and 80 °C. The impeller speed used for blending the content was set at three levels: 10 000, 15 000 and 20 000 r.p.m. Responses, such as mixing index, mixing time, power consumption, spreadability, and overall acceptability, were recorded. Based on the findings, it was concluded that by employing the optimal parameters, a high‐quality PCS with a desirable overall acceptability score of 8.3 could be achieved while also meeting the desired mixing performance. [ABSTRACT FROM AUTHOR]

In this work, the influence of mixing conditions on aluminium recovery from alum sludge and on the recovered coagulant (RC) quality was investigated using acidic treatment. The response surface methodology with a Face Centred Design was used to evaluate the effects of velocity gradient and mixing time on aluminium recovery efficiency, and on the chemical oxygen demand (COD), total suspended solids (TSS) and total phosphorus contents of the RC. No significant effects of both mixing intensity and mixing time on aluminium recovery efficiency were observed; however, these factors significantly affected the quality of the RC in terms of COD, TSS and total phosphorus. The higher velocity gradient increased COD and TSS and the longer mixing time increased phosphorus and TSS in the RC. Operational conditions velocity gradient = 100 s−1 and mixing time = 5 minutes) for aluminium recovery were suggested on economic basis. At these conditions, the RC presented the lowest values of TSS and total phosphorus (100 mg L−1 and 7.0 mg P L−1, respectively), and the following other characteristics: 1,001 mg Al L−1; 384 mg Fe L−1; 1100 mg COD L−1. HIGHLIGHTS The influence of mixing conditions on coagulant recovery efficiency and quality was investigated.; Mixing intensity was studied in terms of the velocity gradient.; Mixing conditions did not influence the aluminium recovery from sludge.; The use of low velocity gradient and low mixing time results in better quality of the recovered coagulant.;

The measurement of mixing time in a water model of soft-stirring steelmaking ladles is practically facing a problem of bad repeatability. This uncertainty severely affects both the understandings of transport phenomenon in ladles and the measurement accuracy. Scaled down by a ratio of 1:4, a water model based on an industrial 260-ton ladle is used. This paper studies the transport process paths and mixing time of salt solution tracers in the water model of eccentric gas-stirred ladles with a low gas flow rate. After a large number of repeated experiments, the different transport paths of the tracer and the error of the mixing time in each transport path are discussed and compared with the numerical simulation results. The results of a large number of repeated experiments on the water model show that there are five transport paths for the tracer in the ladle. The tracer of the first path is mainly transported by the left-side main circulation flow, which is identical to the numerical simulation results. The tracer of the second and third paths are also mainly transported by the left-side circulation flow, but bifurcations occur when the tracer in the middle area is transported downward. In the third path, the portion and intensity of the tracer transferring to the right side from the central region is higher than in the second path. The fourth path is that the tracer is transported downward from the left, middle, and right sides with a similar intensity at the same time. While the tracer in the fifth path is mainly transported on the right side, and the tracer forms a clockwise circulation flow on the right side. The mixing times from the first transport path to the fifth transport path are 158.3 s, 149.7 s, 171.7 s, 134 s and 95.7 s, respectively, among which the third transport path and the fifth transport path are the maximum and minimum values among all transport paths. The error between the mixing time and the averaged mixing time at each monitoring point in the five transport paths of the tracer is between −34.7% and 40.9%. Furthermore, the error of the averaged mixing time of each path and the path-based average value is between 5.5% and 32.6%.

Mixing time is an important parameter for quantifying the mixing efficiency of a bioreactor system, essential for successful bioprocess development in various branches of the bioengineering sector (e.g., biopharma, biorefineries, food industry and bioreactor design). The colourimetric method is one of the ways of obtaining valuable quantitative data about the mixing process and the liquid flow inside a vessel. This review consists of a catalogue and a discussion of previously published data in which the colourimetric method has been utilised; a critical comparison between the colourimetric and other mixing time measurement methods; an explanation of practical considerations regarding the bioreactor setup and the choice of reagents; a practical guide for requirements for the acquisition of high-quality images of the mixing process; a thorough discussion of aspects connected to the computer image processing of the video material. This review is intended to thoroughly present the versatility of the colourimetric method for mixing time measurement in miscellaneous bioreactor systems, i.e., in classical tanks and modern single-use (disposable) plastic film-based bag-like containers, and to facilitate the implementation of the colourimetric method in new research setups by providing complete and valuable recommendations about each step of the methodology. [ABSTRACT FROM AUTHOR]

A three‐dimensional mathematical model on fluid flow, ferrochrome dissolution, and mixing phenomena in a nitrogen‐stirred gas‐oxygen refining furnace is established. The multiphase fluid flow is simulated using the standard k–ε model, the volume of fluid (VOF) model, and the Lagrangian discrete phase model. Interfaces between fluids are tracked by the VOF model, and nitrogen bubbles are treated as discrete phase particles. The melt time of ferrochrome particles and the local mixing time are calculated using the user‐defined function. Effects of gas flow rate and bottom tuyere configuration on the fluid flow and the melting and mixing of ferrochrome are investigated. The results show that the average turbulent kinetic energy and its dissipation rate first increase and then decrease with the increasing gas flow rate, while the melting time and mixing time first decrease and then increase. The shortest melting and mixing time with the condition of seven bottom tuyeres are reached when the gas flow rate is 6.5 Nm3 min−1, which are 40.5 and 94.6 s, respectively. The mixing time decreases from 190.0 to 104.5 s when the three bottom tuyeres configuration changes to the seven bottom tuyeres configuration with the gas flow rate of 3.9 Nm3 min−1. [ABSTRACT FROM AUTHOR]

The mixing performance and power consumption for four dual‐impeller configurations in a stirred tank are studied using the mean age theory (MAT) approach, the fully transient techniques (FTT), and experiments. A novel method is developed based on the scaled mean age probability distribution curve, allowing the MAT method to be applied to multi‐impeller systems for the first time. The MAT approach provides three‐dimensional tracer distribution within the vessel, which is confirmed by FTT and experiments. Compared to the experimental data, the predicted mixing time from the MAT approach shows a deviation within 20%. This is a good degree of accuracy compared to FTT and correlations. For steady‐state predicted power numbers, a 20% deviation from the experimental data is observed, while the transient approach exhibits a lower deviation at 10%. However, the computational time can be reduced significantly using the steady‐state MAT approach. [ABSTRACT FROM AUTHOR]

In this study, laser-induced fluorescence is used to investigate the homogenization in stirred vessels equipped with single- and two-stage stirrers. The acquired local mixing times across the reactor cross-section are plotted as mixing time distribution (MTD) and then compared with the previously measured flow fields of the identical systems. With the help of a novel evaluation method, the mixing times are characterized with a normal distribution fit. With mean value and standard deviation as determined parameters, the mixing results of different installation heights and stirrer combinations are quantitatively evaluated and lead to clear recommendations for installations that enable efficient mixing. [ABSTRACT FROM AUTHOR]

Bath stirring, degassing, and decarburization in steel refining are strongly related to flow behaviors. The bubble plume produced in Ruhrstahl–Heraeus (RH) up‐snorkel plays an important role during refining, since it not only acts as a bubble pump, but also provides the reaction interface. Herein, it is aimed to form a new flow pattern in the up‐snorkel by using a nonradially arranged gas‐injection nozzle to enhance the 260 ton RH refining process. The results show that an upward spiral steel flow is produced, when nonradial gas‐injection nozzles are used in the up‐snorkel. Meanwhile, some bubbles moved toward the center region of the up‐snorkel, which may be caused by the centripetal effect in a rotational steel flow. This leads to a more uniform bubble distribution on the cross section of the snorkel, compared to that of the conventional case. Specifically, the circulation flow rate is increased by about 18.0%, and the mixing time are shortened by about 26.2% (criteria of ±5%), compared to that of the conventional case. In addition, the inclusion removal rate is increased by 0.5%, 4.8%, and 11.3% for the inclusion size of 20, 50, and 100 μm, respectively, compared to the conventional radial nozzle case. [ABSTRACT FROM AUTHOR]

We study the dissipation enhancement by cellular flows. Previous work by Iyer, Xu, and Zlato\vs produces a family of cellular flows that can enhance dissipation by an arbitrarily large amount. We improve this result by providing quantitative bounds on the dissipation enhancement in terms of the flow amplitude, cell size, and diffusivity. Explicitly we show that the mixing time is bounded by the exit time from one cell when the flow amplitude is large enough, and by the reciprocal of the effective diffusivity when the flow amplitude is small. This agrees with the optimal heuristics. We also prove a general result relating the dissipation time of incompressible flows to the mixing time. The main idea behind the proof is to study the dynamics probabilistically and construct a successful coupling. [ABSTRACT FROM AUTHOR]

Motivated by de Finetti's representation theorem for almost exchangeable arrays, we want to sample p ∈ [ 0 , 1 ] d from a distribution with density proportional to exp (− A 2 ∑ i < j c i j (p i − p j) 2) , where A is large and c i j 's are non-negative weights. We analyze the rate of convergence of a coordinate Gibbs sampler used to simulate from these measures. We show that for every non-zero fixed matrix C = (c i j) , and large enough A , mixing happens in Θ (A 2) steps in a suitable Wasserstein distance. The upper and lower bounds are explicit and depend on the matrix C through few relevant spectral parameters. [ABSTRACT FROM AUTHOR]

Let { G n } 1 ∞ be a sequence of non-trivial finite groups. In this paper, we study the properties of a random walk on the complete monomial group G n ≀ S n generated by the elements of the form (e , ⋯ , e , g ; id) and (e , ⋯ , e , g - 1 , e , ⋯ , e , g ; (i , n)) for g ∈ G n , 1 ≤ i < n . We call this the warp-transpose top with random shuffle on G n ≀ S n . We find the spectrum of the transition probability matrix for this shuffle. We prove that the mixing time for this shuffle is O n log n + 1 2 n log (| G n | - 1) . We show that this shuffle exhibits ℓ 2 -cutoff at n log n + 1 2 n log (| G n | - 1) and total variation cutoff at n log n . [ABSTRACT FROM AUTHOR]

Fine particles are widely used as intermediate and final products in industrial processes. Because particle properties are directly linked to the function and quality of the products, synthesizing monodispersed particles is a key technology. A microreactor, which comprises microchannels typically narrower than 1 mm, is a promising reaction tool because it offers excellent mixing and heat transfer performance. We used a microreactor for the synthesis of single-component and composite nanoparticles. This review introduces our synthetic results for functional nanoparticles including nickel, platinum–cobalt alloys, gold and silver nanoshells, patchy particles, core–shell clusters, and metal–organic frameworks. The microreactor we used is of the central-collision type and exhibits a characteristic mixing time 100~1,000 times shorter than that of the conventional batch mixing. The excellent mixing ability of the microreactor enables the synthesis of monodisperse particles in size and shape as well as core–shell particles with uniform shell thickness through instantaneous nucleation. More importantly, the microreactor realizes syntheses, which are not possible with batch reactors, by trapping reaction intermediates in a sequential reaction process and by rapidly changing the reaction temperature. These results demonstrate great advantages of using the microreactor for nanoparticle synthesis.

A statistical approach was conducted to investigate effect of independent factors of the mixing time compactability and bentonite percentage on dependent variables of permeability, compression and tensile strength of sand mould properties. Using statistical method save time in estimating the dependent variables that affect the moulding properties of green sand and the optimal levels of each factor that produce the desired results. The results yielded indicate that there are variations in the effects of these factors and their interactions on different properties of green sand. The outcomes obtained a range of permeability values, with the highest and lowest numbers being 125 and 84. The sand exhibited high values of tensile and compressive strength measuring at 0.33N/cm2 and 17.67N/cm2. Conversely it demonstrated low levels of tensile and compressive strength reaching 0.14N/cm2 and 9.32N/cm2. These results suggest that the moulding factors and their interactions have an important role in determining properties of the green sand. ANOVA was used to assess effect of various factors on different properties of the green sand. The results obtained suggest that compactability factor play a significant effect on permeability, the mixing time or bentonite factor has a significant effect on the compressive strength and mixing time or compactability factor has a significant impact on the tensile strength with a significance level lower than 5%. It is found that neither the mixing time nor the amount of bentonite used in the green sand mix has a significant impact on its permeability. Compactability of the green sand does not has a significant effect on the compressive strength. Bentonite used in green sand mix does not have a significant impact on its tensile strength.

The current trend in the preparation of green sand mixtures emphasizes the acceleration of the mixing process while maintaining the quality of the mixture. This requirement results in the necessity of determining the optimal conditions for mixing the mixture with a given mixer. This work aims to determine the optimal mixing conditions for the newly introduced eddy mixer LM-3e from the company Multiserw-Morek in the sand laboratory at the Department of Metallurgical Technologies, Faculty of Materials and Technology, VŠB - Technical University of Ostrava. The main monitored properties of mixtures will be green compressive strength and moisture of the mixture. The measured properties of the mixture mixed on the eddy mixer will be compared with the properties of the mixture mixed on the existing LM-2e wheel mixer. The result of the experiment confirmed that the eddy mixer is suitable for the preparation of a mixture of the same quality as the wheel mixer but with a significantly reduced mixing time.

The reliable transfer of bioprocesses from single-use bioreactors (SUBs) of different scales to conventional stainless steel stirred-tank bioreactors is of steadily growing interest. In this publication, a scale-up study for SUBs with volumes of 200 L and 2000 L and the transfer to an industrial-scale conventional stainless steel stirred-tank bioreactor with a volume of 15,000 L is presented. The scale-up and transfer are based on a comparison of mixing times and the modeling of volumetric mass transfer coefficients kLa, measured in all three reactors in aqueous PBS/Kolliphor solution. The mass transfer coefficients are compared with the widely used correlation of van’t Riet at constant stirrer tip speeds. It can be shown that a van’t Riet correlation enables a robust and reliable prediction of mass transfer coefficients on each scale for a wide range of stirrer tip speeds and aeration rates. The process transfer from single-use bioreactors to conventional stainless steel stirred-tank bioreactors is proven to be uncritical concerning mass transfer performance. This provides higher flexibility with respect to bioreactor equipment considered for specific processes.

In previous research simulating steelmaking ladles using cold water models, the dosage/volume of the salt tracer solution is one of the factors that has been overlooked by researchers to a certain extent. Previous studies have demonstrated that salt tracers may influence the flow and measured mixing time of fluids in water models. Based on a water model scaled down from an industrial 130-ton ladle by a ratio of 1:3, this study investigates the impact of salt tracer dosage on the transport and mixing of tracers in the water model of gas-stirred ladle with a moderate gas flow rate. A preliminary uncertainty analysis of the experimental mixing time is performed, and the standard deviations were found to be less than 15%. It was observed in the experiments that the transport paths of tracers in the ladle can be classified into two trends. A common trend is that the injected salt solution tracer is asymmetrically transported towards the left sidewall of the ladle by the main circulation. In another trend, the injected salt solution tracer is transported both by the main circulation to the left side wall and by downward flow towards the gas column. The downward flow may be accelerated and become a major flow pattern when the tracer volume increases. For the dimensionless concentration curve, the sinusoidal type, which represents a rapid mixing, is observed at the top surface monitoring points, while the parabolic type is observed at the bottom monitoring points. An exception is the monitoring point at the right-side bottom (close to the asymmetric gas nozzle area), where both sinusoidal-type and parabolic-type curves are observed. Regarding the effect of tracer volume on the curve and mixing time, the curves at the top surface monitoring points are less influenced but curves at the bottom monitoring points are noticeably influenced by the tracer volume. A trend of decreasing and then increasing as the tracer volume increases was found at the top surface monitoring points, while the mixing times at the bottom monitoring points decrease with the increase in the tracer volume.

Energy savings in industrial processes have become one of the main goals of the current society. This paper aims to propose a systematic approach for the assessment of mixing equipment energy performance for highly viscous fluids. The framework is illustrated and applied by performing a rational comparison of the homogenization efficiency of classical mixing systems (involving an agitator revolving around a vertical axis centred in the tank) with that of planetary mixers when mixing highly viscous fluids. For that purpose, the pioneering framework of Zlokarnik is first reminded and its limitations with regard to non-traditional mixing equipment are discussed. Then, the theoretical background to extend this approach to these latter is presented. Experimental data on power consumption and mixing time are provided to demonstrate the applicability of the present frame. The results illustrated that a planetary mixer can be an economic solution for performing highly viscous fluids homogenization. [Display omitted] • Framework to rank different mixing equipment in terms of power and mixing time. • Generic determination of operation conditions minimizing the work of a mixing equipment. • Complementary experimental characterization of two homogenization equipment. • One-plot performance comparison of a helical ribbon impeller and a planetary mixer. [ABSTRACT FROM AUTHOR]

A generalized Partially-Stirred Reactor (PaSR) model is presented in this work based on the inclusion of multiple chemical times. The PaSR model has shown promising results at modelling turbulence-chemistry interaction in Large-Eddy Simulations (LES) and Reynolds-Averaged Navier-Stokes (RANS), providing an extension of the well-known Eddy Dissipation Concept (EDC). PaSR model divides the computational domain into reactive and non-reactive parts. The factor defining this partition is expressed as a function of the system characteristic chemical and mixing times. However, the estimation of these factors, particularly the chemical one, is often oversimplified. The approach proposed in this study seeks to include in the PaSR model the whole set of chemical times involved in the reactive system. Besides, the concept of fine structures , first introduced in the EDC and often adopted also in the PaSR model to characterize the evolution of chemistry in the reactive part of the fluid, is here abandoned in favour of direct manipulation of species production rates. The mean source term is formulated according to the new generalized model through a modal decomposition of the Jacobian matrix. The method is validated a priori with DNS data of a syngas non-premixed jet flame, whose filtered data represent the validation benchmark. A good agreement is found between the new PaSR model and the filtered data for all species at different filter widths. Comparison with the single time scale based model clearly shows the limitations of the old standard approach and the necessity of including the whole spectrum of chemical times for a more comprehensive description of turbulence-chemistry interaction. A thorough analysis with the time scale participation index reveals the complexity of reaction rates contributions to the development of a specific time scale, underlying the importance of developing a model able to inherit all kinetic pathways in the turbulent closure. [ABSTRACT FROM AUTHOR]

In metallurgical converter processes, numerical modeling is a useful tool for understanding the complexity of the systems. In this paper, we present a practical model that couples fluid dynamics and chemical reactions to explore the impact of mixing time on decarburization. Using computational fluid dynamics (CFD), in this study, we investigate an arbitrary metallurgical reactor with continuous oxygen supply, focusing on the Fe–C–O system. The model employs local equilibrium, a turbulence limiter, and finite volume method for mass, momentum, and energy transfer. Tracer injection points in the gas plume's rising region exhibit faster mixing, and a comparison of reaction cases reveals distinct decarburization rates based on oxygen injection distribution and the influence of turbulence on reactions. Overall, while mixing time matters, the results show that this system is primarily governed by thermodynamics and oxygen supply, and a 270% increase in mixing time increase had a small impact on the end carbon content. [ABSTRACT FROM AUTHOR]

Copyright of Chemical Engineering (China) / Huaxue Gongcheng is the property of Hualu Engineering Science & Technology Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)