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The mixing mechanism in an oscillatory baffled reactor (OBR) at the low oscillatory Reynolds number was analyzed using numerical simulation. OBR is a tubular reactor in which baffles are placed at equal intervals, and the interaction between the baffles and oscillatory flow mixes the fluid. At the low oscillatory Reynolds number, mixing induced by the folding and stretching of the fluid was observed at each baffle section. This was caused by the radial flow in the vicinity of the baffles when the direction of the oscillatory flow was reversed. The mixing performance was quantified by applying virtual particle tracing, setting up a virtual boundary surface, and following the changes in its area over time. The area increased exponentially, confirming the chaotic mixing characteristics. [ABSTRACT FROM AUTHOR]

In response to the observed phenomenon of poor fluid mixing within the reactor, this study proposes a novel mixing method to enhance fluid mixing efficiency. In this study, numerical simulation and purification tests were carried out for the purification of zinc sulfate solution. Numerical simulations were conducted to compare the effects of variable-speed stirring and uniform-speed stirring on mixing efficiency, considering both momentum transfer process and mass transfer process. The purification test further demonstrated a significant improvement in the reaction rate under variable-speed stirring, as evidenced by the analysis of purification efficiency and microscopic morphology. It was elaborated that the enhancement mechanism of variable-speed stirring involved disrupting the periodic order structure in the tank, leading to the generation of a multi-scale vortex that increased stirring kinetic energy to form a shear force. This force contributed to reducing the velocity slip between the impurity ions and zinc particles, consequently decreasing reaction time and enhancing purification rate. The results indicated that sinusoidal stirring yielded the most effective mixing. When implemented in practical production settings, it enhanced dimensionless mixing efficiency by 24.83 % compared to the homogeneous stirring system. Additionally, it reduced reaction time by 15.47 % and decreased mixing energy per unit volume by 32.38 %, while simultaneously lowering energy consumption by 24.77 %. [ABSTRACT FROM AUTHOR]

The direct ink writing (DIW) process, used for creating components with functionally graded materials, holds significant promise for advancement in various advanced fields. However, challenges persist in achieving complex gradient variations in small-sized parts. In this study, we have developed a customized pin shape for an active screw mixer using a combination of quadratic B-Spline, the response surface method, and global optimization. This tailored pin design was implemented in a two-material extrusion-based printing system. The primary objective is to facilitate the transformation of material components with shorter transition distances, overcoming size constraints and enhancing both printing flexibility and resolution. Moreover, we characterized the transition delay time for material component changes and the mixing uniformity of the extruded material by constructing a finite element simulation model based on computational fluid dynamics. Additionally, we employed a particle tracking method to obtain the Lyapunov exponent and Poincaré map of the mixing process. We employed these metrics to represent and compare the degree of chaotic mixing and dispersive mixing ability with two other structurally similar mixers. It was found that the optimized pin-type mixer can reduce the transition delay distance by approximately 30% compared to similar structures. Finally, comparative experiments were carried out to verify the printing performance of the optimized pin-type active mixer and the accuracy of the finite element model. [ABSTRACT FROM AUTHOR]

Purpose of this article is to study the transport of passive particles in the velocity field of a vortex tripole with a change in the parameter that determines the speed of the configuration movement. A structure consisting of a central vortex and satellite vortices rotating around it with the opposite vorticity is understood as a tripole. We employ a system of three point vortices, the most simple mathematical representation of a vortex tripole, which may be expressed as a system of nonlinear ordinary differential equations with a parameter. Consideration is limited to a particular case of a tripole with zero total vorticity. The influence of the speed values of vortex configuration movement on the processes of passive particle transport has been studied. Methods. The study was carried out numerically using algorithms based on the dynamical systems approaches including the construction of the Poincare map and the analysis of the dynamics of marker particles. Were carried out long ´ times calculations, corresponding to hundreds and thousands of turns around the tripole center. Integrators of high orders of accuracy were used to solve the Cauchy problems, which made it possible to adequacy of the calculation result control. Results. We found that transferring passive particles is fundamentally different depending on the speed of the tripole. A vast zone of chaotic dynamics forms in the neighborhood of the vortices when the velocity is low. This zone slowly shifts along with the tripole. There are subregions of active and slow mixing inside the chaos region. The possible stages of particle dynamics are: transfer from the region to the right of the tripole to the area to the left, vigorous mixing near the vortices, and slowly drifting to the region to the left of the tripole. At a high speed of vortex configuration in the entire chaotic region, the particles are strongly mixed. The vortex tripole removes particles from the vicinity of its initial position over long distances and practically does not capture new particles along its path. In intermediate situations, both processes can be realized at varying degrees. Conclusion. Non-trivial scenarios for the transport of passive particles by a vortex tripole, which can also occur in real vortex configurations of fluids, have been discovered and described.

To address the need for enhanced biochemical reactions and overcome the shortcomings associated with passive and active mixer fabrication, reactor designs must utilize the coupled mixing concept to address the lack of insufficient heat and mass transfer through notable alterations of the physical properties. This study introduces a tubular microwave reactor based on chaotic flow dynamics, attempting to combine the concept of active and passive mixing to stimulate the development of eddy and secondary flows through electromagnetic fields and geometric disturbance enhance heat and mass transfer. Experiments and simulation analysis validate the validity of the prediction model, and reveal the fluid flow, mixing, electromagnetic and thermal characteristics and their synergistic mechanism, and shows the potential to enhance the mass and heat transfer performance at low Reynolds number, which provides a new idea for the design of chemical reactors and biological analysis. • Using the coupled concept of active and passive mixing, the fluid flow is driven. • Chaotic channel coupled with microwave technology enhance mass and heat transfer. • The 3D C-shape geometry has a prominent impact in improving reactor performance. [ABSTRACT FROM AUTHOR]

The direct ink writing (DIW) process, used for creating components with functionally graded materials, holds significant promise for advancement in various advanced fields. However, challenges persist in achieving complex gradient variations in small-sized parts. In this study, we have developed a customized pin shape for an active screw mixer using a combination of quadratic B-Spline, the response surface method, and global optimization. This tailored pin design was implemented in a two-material extrusion-based printing system. The primary objective is to facilitate the transformation of material components with shorter transition distances, overcoming size constraints and enhancing both printing flexibility and resolution. Moreover, we characterized the transition delay time for material component changes and the mixing uniformity of the extruded material by constructing a finite element simulation model based on computational fluid dynamics. Additionally, we employed a particle tracking method to obtain the Lyapunov exponent and Poincaré map of the mixing process. We employed these metrics to represent and compare the degree of chaotic mixing and dispersive mixing ability with two other structurally similar mixers. It was found that the optimized pin-type mixer can reduce the transition delay distance by approximately 30% compared to similar structures. Finally, comparative experiments were carried out to verify the printing performance of the optimized pin-type active mixer and the accuracy of the finite element model.

Inverse design of complex flows is notoriously challenging because of the high cost of high dimensional optimization. Usually, optimization problems are either restricted to few control parameters, or adjoint-based approaches are used to convert the optimization problem into a boundary value problem. Here, we show that the recent advances in automatic differentiation (AD) provide a generic platform for solving inverse problems in complex fluids. To demonstrate the versatility of the approach, we solve an array of optimization problems related to active matter motion in Newtonian fluids, dispersion in structured porous media, and mixing in journal bearing. Each of these problems highlights the advantages of AD in ease of implementation and computational efficiency to solve high-dimensional optimization problems involving particle-laden flows., Competing Interests: Competing interests statement:The authors declare no competing interest.

The polymer/hexagonal boron nitride (h-BN) thermal conductive composite an excellent candidate for thermal management materials due to its insulation properties. However, it is a challenge to achieve efficient large-scale exfoliation of h-BN through melt blending to balance thermal conductivity and mechanical properties. In this work, an innovative melt mixing strategy using the co-rotating non-twin screw extruder (NTSE) was developed to prepare the high-density polyethylene (HDPE)/h-BN composites with excellent overall performance. The results were well compared with those of conventional twin screw extruder (TSE). The NTSE triggers chaotic mixing and provides a strong elongation flow field capable of h -BN efficiently exfoliating into a few layers, while simultaneously ensuring uniform dispersion and distribution within HDPE. The in-plane thermal conductivity and elongation at break of the NTSE composite with 10 wt% h-BN addition were 7.63 W∙m−1 K−1 and 653.1 %, which were 74.7 % and 70.3 % higher than those prepared by TSE, while the enhancement rates rose to 174.6 % and 74.4 % when 30 wt% h-BN was added, respectively. The in-plane thermal conductivity enhancement ratio of NTSE was more than 3000 % when the h-BN content was higher than 10 wt%. Besides, the thermal stability, crystallinity, and thermal diffusion of the NTSE composites were also enhanced to different degrees. This strategy is efficient to coordinating the conflicting between the comprehensive performance and large-scale preparation of thermally conductive polymer composites. [Display omitted] • Efficient exfoliation of h-BN has been achieved by non-twin screw extruder. • Compared with twin screw, non-twin screw leads to higher orientation of BN. • The in-plane thermal conductivity increased 3076.3 % only with 10 wt% BN addition. • Non-twin screw can prepare polymer/BN with high comprehensive properties efficiently. [ABSTRACT FROM AUTHOR]

In this study, a numerical investigation based on the CFD method is carried out to study the unsteady laminar flow of Newtonian fluid with a high viscosity in a three-dimensional simulation of a twisted double planetary mixer, which is composed of two agitating rods inside a moving tank. The considered stirring protocol is a "Continuous sine squared motion" by using the dynamic mesh model and user-defined functions (UDFs)to define the velocity profiles. The chaotic advection is obtained in our active mixers by the temporal modulation of rotational velocities of the moving walls in order to enhance the mixing of the fluid for a low Reynolds number and a high Peclet number. For this goal, we applied the Poincaré section and Lyapunov exponent as reliable mathematic tools for checking mixing quality by tracking a number of massless particles inside the fluid domain. Additionally, we investigated the development of fluid kinematics proprieties, such as vorticity, helicity, strain rate and elongation rate, at various time periods in order to view the impact of temporal modulation on the flow properties. The results of the mentioned simulation showed that it is possible to obtain a chaotic advection after a relatively short time, which can deeply enhance mixing fluid efficiency. [ABSTRACT FROM AUTHOR]

We study finite-time mixing in time-periodic open flow systems. We describe the transport of densities in terms of a transfer operator, which is represented by the transition matrix of a finite-state Markov chain. The transport processes in the open system are organized by the chaotic saddle and its stable and unstable manifolds. We extract these structures directly from leading eigenvectors of the transition matrix. We use different measures to quantify the degree of mixing and show that they give consistent results in parameter studies of two model systems. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'. [ABSTRACT FROM AUTHOR]

A recently published approach for modeling the cross flow in an extruder channel using a new solution to the biharmonic equation is utilized in a study of chaotic mixing in a free‐helix single‐screw extruder. This novel extruder was designed and constructed with the screw flight, also referred to as the helix, detached from the screw core. The flight‐helix had straight sides that more closely emulated rectangular channel theory than the nominal sloped sides of a conventional single screw channel. Each of the screw elements could be rotated independently to obtain chaotic motion in the screw channel. Using the new extruder, experimental evidence for the increased mixing of a dye, for both a Dirac and droplet input, with a chaotic flow field relative to the traditional residence time distribution is presented. These experimental results are compared using the new biharmonic equation‐based model. Comparing the experimental chaotic mixing with theoretical calculations was facilitated by a recently published technique for accurately placing the dye in the extruder channel. Because of the ability to periodically rotate only the flight/helix, the chaotic mixing results are minimally confounded by the existence of Moffatt eddies. [ABSTRACT FROM AUTHOR]

A microreaction system, which combines chaotic mixing with liquid-segmented flow for the synthesis of hazardous ionic materials, was established. Previous single micro-segmented flow achieved good mixing by increasing the length of the tube via the slow diffusion of the reactants; however, it consumed a long residence time and achieved a low efficiency. Consequently, optimized chaotic micromixing was applied to achieve rapid and excellent initial mixing of the reactants. Thereafter, the optimized chaotic micromixing was combined with the liquid-segmented flow to ensure the homogeneity of particle nucleation/growth while overcoming encrustation challenges. Two tubing coils were employed for the crystal nucleation and growth; they extensively reduced the size of the microreaction system. Additionally, a separation column was designed to achieve on-line recovery of the carrier fluid, followed by on-line separation of the products and waste. Furthermore, the initial performance and design evaluation of the microreaction system were performed. Furthermore, we utilized typical ionic primary explosives, barium-2,4,6-trinitroresorcinate (BaTNR) and lead-2,4,6-trinitroresorcinate styphnate (LTNR), to verify the applicability of the microreaction system. Further, BaTNR and LTNR particles with better crystal morphologies, narrower size distributions, and higher heat release than those of the single micro-segmented flow were prepared to illustrate the advantages of the system. The particle size of BaTNR synthesized by the microreaction system ranged from 5 to 13 ​μm, while the heat release was 168.7 ​J·g−1 greater than that of BaTNR prepared by the micro-segmented flow platform. The particle size of LTNR ranged from 30 to 90 ​μm, while the heat release was 230.1 ​J·g−1 greater than that of LTNR prepared by the micro-segmented flow platform. Conclusively, this study demonstrated the feasibility of an efficient and safe microreaction system for synthesizing hazardous ionic materials.

Understanding mixing and transport of passive scalars in active fluids is important to many natural (e.g., algal blooms) and industrial (e.g., biofuel, vaccine production) processes. Here, we study the mixing of a passive scalar (dye) in dilute suspensions of swimming Escherichia coli in experiments using a two-dimensional (2D) time-periodic flow and in a simple simulation. Results show that the presence of bacteria hinders large-scale transport and reduces overall mixing rate. Stretching fields, calculated from experimentally measured velocity fields, show that bacterial activity attenuates fluid stretching and lowers flow chaoticity. Simulations suggest that this attenuation may be attributed to a transient accumulation of bacteria along regions of high stretching. Spatial power spectra and correlation functions of dye-concentration fields show that the transport of scalar variance across scales is also hindered by bacterial activity, resulting in an increase in average size and lifetime of structures. On the other hand, at small scales, activity seems to enhance local mixing. One piece of evidence is that the probability distribution of the spatial concentration gradients is nearly symmetric with a vanishing skewness. Overall, our results show that the coupling between activity and flow can lead to nontrivial effects on mixing and transport. [ABSTRACT FROM AUTHOR]

[Display omitted] • Combined with RGB brightness and quantitative area analysis, the mixing performance of the stirred reactor was evaluated. • There is an inherent axial mixing limit in traditional stirred reactors under laminar flow conditions. • The DSO mixing system exhibits enhanced mass transfer efficiency and overall mixing performance. • The flow pattern from radial flow to axial flow is adjusted by changing the interface evolution. Efficiently realizing laminar flow mixing of non-Newtonian fluids is a key challenge faced by conventional stirred reactors. In this study, an innovative strategy is proposed to regulate the flow pattern from radial to axial flow by changing the interface evolution of the flow field, so as to solve the problem of uneven mixing materials in laminar flow. An innovative combination of the RGB (Red, Green, Blue) brightness analysis and quantitative analysis area method was used to quantitatively describe the mixing performance of the three stirred reactor in the laminar flow. We found that the coloring area ratio of the dual shaft off-centred mixer (DSO) mixer was approximately 165.7 % and 93.8 % higher than that of the single shaft central (SSC) and single shaft off-centred mixer (SSO), respectively. Results showed that the DSO mixer can directionally adjust the stable interface of the flow field, and then obtain the ideal velocity distribution and flow pattern. Importantly, it is found that the mixer has an inherent axial mixing limit in the laminar flow. Increasing the Reynolds number can only shorten the time for the mixing system to reach the steady state, and cannot further improve the axial transport capacity of the system. Compared to the SSC and SSO systems, the DSO mixer demonstrated a reduction of nearly 20 % in overall mixing time and power consumption. Through comparative analysis of pressure distribution and Poincaré cross section, the DSO mixing system can switch chaos oscillation and realize the "globally chaotic mixing" from "locally chaotic mixing". Remarkably, this work highlights the potential of DSO mixer as a simple and efficient system for laminar flow mixing applications, such as polymerization processes, biological fermentation. [ABSTRACT FROM AUTHOR]

In this study, a numerical investigation based on the CFD method is carried out to study the unsteady laminar flow of Newtonian fluid with a high viscosity in a three-dimensional simulation of a twisted double planetary mixer, which is composed of two agitating rods inside a moving tank. The considered stirring protocol is a “Continuous sine squared motion” by using the dynamic mesh model and user-defined functions (UDFs)to define the velocity profiles. The chaotic advection is obtained in our active mixers by the temporal modulation of rotational velocities of the moving walls in order to enhance the mixing of the fluid for a low Reynolds number and a high Peclet number. For this goal, we applied the Poincaré section and Lyapunov exponent as reliable mathematic tools for checking mixing quality by tracking a number of massless particles inside the fluid domain. Additionally, we investigated the development of fluid kinematics proprieties, such as vorticity, helicity, strain rate and elongation rate, at various time periods in order to view the impact of temporal modulation on the flow properties. The results of the mentioned simulation showed that it is possible to obtain a chaotic advection after a relatively short time, which can deeply enhance mixing fluid efficiency.

• Multi-scale entropy was used to characterize gas-liquid chaotic mixing characteristic. • Relative power demand (P g / P 0) in gas-liquid mixing system can be enhanced by fractal impeller. • Mass transfer coefficient can be improved by fractal impeller. • Dispersion coefficient (σ) in gas-liquid mixing system can be reduced by fractal impeller. Gas-liquid mixing characteristics in fractal impeller stirred tank were experimentally investigated by measuring multi-scale entropy (MSE), relative power demand (RPD), local gas holdup, bubble size, and mass transfer coefficient (K L a). Results showed that fractal impeller could enhance 21.69% of MSE and 11.94% of RPD on the basis of pitched-blade impeller. Fractal impeller can enhance the local gas holdup, decrease the bubble size, reduce the dispersion coefficient (σ) and improve the gas-liquid dispersion performance. Meanwhile, the regression based on d 32 − for pitched-blade impeller and fractal impeller were obtained. In addition, fractal impeller can also increase 11.07% of volume mass transfer coefficient (K L a) compared with pitched-blade impeller in the gas-liquid mixing process. The results can provide theoretical guidance for the optimal design of gas-liquid stirred tank. Fractal impeller could create a longer turbulence production region and higher turbulence intensities over a wider spatial extent to reduce the impeller trailing vortex and improve the gas-liquid chaotic mixing degree. [Display omitted] [ABSTRACT FROM AUTHOR]

Unsaturated porous media, characterized by the combined presence of several immiscible fluid phases in the pore space, are highly relevant systems in nature, because they control the fate of contaminants and the availability of nutrients in the subsoil. However, a full understanding of the mechanisms controlling solute mixing in such systems is still missing. In particular, the role of saturation in the development of chaotic solute mixing has remained unexplored. Using three-dimensional numerical simulations of flow and transport at the pore scale, built upon X-ray tomograms of a porous medium at different degrees of liquid (wetting)-phase saturation, we show the occurrence of chaotic dynamics in both the deformation of the solute plume, as characterized by computed chaos metrics (Lyapunov exponents), and the mixing of the injected solute. Our results show an enhancement of these chaotic dynamics at lower saturation and their occurrence even under diffusion-relevant conditions over the medium's length, also being strengthened by larger flow velocities. These findings highlight the dominant role of the pore-scale spatial heterogeneity of the system, enhanced by the presence of an immiscible phase (e.g., air), on the mixing efficiency. This represents a stepping stone for the assessment of mixing and reactions in unsaturated porous media.

Fluid flow in porous media drives the transport, mixing, and reaction of molecules, particles, and microorganisms across a wide spectrum of natural and industrial processes. Current macroscopic models that average pore-scale fluctuations into an effective dispersion coefficient have shown significant limitations in the prediction of many important chemical and biological processes. Yet, it is unclear how three-dimensional flow in porous structures govern the microscale chemical gradients controlling these processes. Here, we obtain high-resolution experimental images of microscale mixing patterns in three-dimensional porous media and uncover an unexpected and general mixing mechanism that strongly enhances concentration gradients at pore-scale. Our experiments reveal that systematic stretching and folding of fluid elements are produced in the pore space by grain contacts, through a mechanism that leads to efficient microscale chaotic mixing. These insights form the basis for a general kinematic model linking chaotic-mixing rates in the fluid phase to the generic structural properties of granular matter. The model successfully predicts the resulting enhancement of pore-scale chemical gradients, which appear to be orders of magnitude larger than predicted by dispersive approaches. These findings offer perspectives for predicting and controlling the vast diversity of reactive transport processes in natural and synthetic porous materials, beyond the current dispersion paradigm. [ABSTRACT FROM AUTHOR]

To understand the physico-chemical processes associated with migmatisation is an interesting petrological problem. New developments in microfluidics and chaotic mixing experiments have helped us to better perceive these processes from the migmatic rocks of the Proterozoic Chotanagpur Granite Gneiss Complex (CGGC), eastern India. The migmatic rocks of CGGC have preserved folded leucocratic veins in amphibolites representing viscous folding. The viscous folding phenomenon occurred due to the interaction between leucosome and melanosome. Based on textural features and mineral chemical data interpretations, we infer that when granitic and pegmatitic magmas intruded the gneissic rocks and amphibolites of our study area, diffusion of heat and volatiles from the hotter felsic magmas to the colder country rocks initiated partial melting in the amphibolites, forming melanosomes. After their formation, the highly viscous felsic magmas veined into the melanosomes, by progressively melting them and then interacting, leading to chaotic mixing dynamics. The development of chaotic mixing allowed the leucosome to venture into the melanosome as veins by stretching and folding dynamics. As the leucocratic veins or leucosome traversed through the partially molten rock or melanosome due to advection, the veins underwent viscous folding owing to the exertion of compressional stress brought about by the viscosity difference between the two mediums. The occurrence of viscous folding exponentially increased the contact area between the leucosome and the melanosome, eventually leading to enhanced diffusion and augmented mixing between the two mediums. Evidence of mixing through elemental diffusion is well documented by the compositions of amphibole and biotite occurring in the leucosome and melanosome. These minerals show substitution of magnesium and ferrous ion that show linear variation between the endmember compositions. [ABSTRACT FROM AUTHOR]

• Oscillation frequency increased with the increase of Re. • Mixing index within the single oscillating micromixer can be up to 0.8. • Particles inside the micromixer can be quickly dispersed by the flow oscillation. • RTD inside the micromixer was similar to that within the plug flow reactor. • Convenient scaling-up was realized by arranging the multistage units in series. The integration of time-varying flow characteristics of the active micromixer with the passive micromixer can be a promising way to enhance the mixing through chaotic convection. The present study proposed a passive oscillating micromixer based on the instability of two impinging jets. The micromixer was characterized numerically and experimentally in terms of the internal dynamics, particle tracking, mixing performance and residence time distribution (RTD). It was revealed that the oscillation frequency increased with the increase of Re , which could significantly promote the convective mixing, and the mixing index within the single micromixer could be up to 0.8. Poincaré mapping indicated that the particles inside the micromixer can be quickly dispersed by the flow oscillation, which was beneficial to prevent the blockage of the microreactor. The RTD inside the oscillating micromixer was found to be similar to that within the plug flow reactor, indicating that the flow oscillation could have a positive impact on the RTD. Furthermore, the oscillating micromixer can be conveniently scaled up by arranging the multistage units in series, while the advantages of the single oscillating micromixer could be well retained. [ABSTRACT FROM AUTHOR]

In this research work, a numerical simulation is carried out to study the performance of coupled mixing and heating generated by chaotic advection in a mixer comprising rotating rods uphold inside a cylindrical tank. The effect of the number of the rotating rods on both the chaotic advection and the thermal efficiency of the mixer is presented. It is found that the use of noncontinuous wall rotations is necessary to ameliorate the heat transfer by chaotic mixing. The increase in the number of rod within the mixer can also promote the thermal performance of the mixer.

Mixing-induced reactions play a key role in a large range of biogeochemical and contaminant transport processes in the subsurface. Fluid flow through porous media was recently shown to exhibit chaotic mixing dynamics at the pore scale, enhancing microscale concentration gradients and controlling mixing rates. While this phenomenon is likely ubiquitous in environmental systems, it is not known how it affects chemical reactions. Here, we use refractive index matching and laser-induced fluorescence imaging of a bimolecular redox reaction to investigate the consequence of pore scale chaotic mixing on the reaction rates. The overestimation of measured reaction rates by the classical macrodispersion model highlights the persistence of incomplete mixing on the pore scale. We show that the reaction product formation is controlled by microscale chaotic mixing, which induces an exponential increase of the mixing interface and of the reaction rates. We derive a reactive transport model that captures experimental results and predicts that chaotic mixing has a first order control on reaction rates across a large range of time scales and Péclet and Damköhler numbers. These findings provide a new framework for understanding, assessing, and predicting mixing-induced reactions and their role on the fate and mobility of environmental compounds in natural porous media.

After a century of quiescence, Turrialba, a Quaternary stratovolcano in the Costa Rican Volcanic Front, started a new eruptive cycle in 2010 that is ongoing to this date (July 3rd, 2019). Violent eruptions began in 2014, producing columns of ash that reached 4 km above the summit of the volcano. Here we provide new major and trace element data from fresh, glassy fragments (basaltic to rhyolitic) and mineralogical data for feldspars, olivines, and pyroxenes from ash fallout collected from 2016 and 2017 eruptions. We investigate the composition of the magma replenishing the system as well as the different juvenile components involved in the latter phase of this renewed eruption cycle. We find a range of mafic to felsic compositions in every eruptive event sampled. Our new geochemical data, coupled with Monte Carlo binary mixing simulations, indicate that magmas at Turrialba volcano are influenced by the input of a back-arc-type, strongly high field strength element-enriched (20–60 ppm) component generated by decompression melting from subduction-driven corner-flow. Thermodynamic modeling using MELTS software suggests that fractional crystallization alone fails to explain the compositional range of Turrialba's eruptive products. We instead propose that a complex, multi-stage magma mixing process produced renewed activity at Turrialba based on the trace element variability, the dominant intermediate magmatic compositions observed, and the results of our multi-element mixing simulations. This mixing process occurs upon injection of new mantle-derived melts into Turrialba's fractionated magmatic reservoirs and is governed by chaotic dynamics induced by gradients in temperature and viscosity. • We found compositionally heterogeneous fresh glass and minerals in Turrialba volcano's 2016 and 2017 ash fallout • Significant presence of a rhyolitic component and predominance of trachy-andesitic to trachy-dacitic compositions • We present evidence for the coexistence and coeval eruption of a back-arc and typical arc type geochemical signatures • Pervasiveness of mixing from source to surface is observed at Turrialba volcano suggesting a multi-stage process [ABSTRACT FROM AUTHOR]

The single-screw extruder with a perturbation baffle is a novel piece of equipment for polymer processing, in which the polymer melts undergo complex chaotic mixing. In this paper, from a new Lagrangian perspective, the fluid transporting mechanism in chaotic flow of the unwound screw channel was analyzed based on the finite element method. Firstly, two-dimensional velocity distributions in the unwound screw channel were calculated based on the mesh superposition technique. Fluid particle evolution processes in the extruder were tracked based on the fourth-order Runge-Kutta scheme. The numerical method used in this paper was validated by grid independence and experiments obtained from literature. Moreover, the finite-time Lyapunov exponent (FTLE) and Poincaré sections were adopted to discuss the chaotic mixing in the novel single-screw extruder. The effects of baffle width and height on the manifold structures in the flow dynamic system were analyzed. The results show that the homoclinic point of the manifold structure can give rise to chaotic mixing in the single-screw extruder. The height of the baffle is an important parameter to control the chaotic strength. In a way, increasing the height of the baffle can enlarge the kink scale and increase the stretching and folding actions, which results in the decrease of regular regions and an increase of the mixing efficiency in the single-screw extruder. [ABSTRACT FROM AUTHOR]

Abstract Magma mixing is a complex phenomenon and occurs through the interplay of a number of processes. Recent developments in microfluidics and chaotic mixing experiments have enabled us to better understand the complex processes associated with magma mixing from the hybrid rocks of the Ghansura Rhyolite Dome (GRD) of Proterozoic Chotanagpur Granite Gneiss Complex (CGGC), Eastern India. The hybrid rocks of GRD have preserved amphibole-rich microzones (ARM) and microfolded mineral veins resulting from the mixing of felsic (rhyolitic) and mafic (basaltic) melts. Based on textural features and mineral chemical data interpretations, we infer that viscous folding can be an important mechanism to obtain chemical equilibrium in a magma mixing scenario. Magma mixing is a chaotic process brought about by the interplay of advection (i.e. stretching and folding) and diffusion. In our scenario, stretching and folding of the mineral veins or filaments were achieved through viscous folding, followed by chemical diffusion between the contrasting magmas to enhance magma mixing. Our findings reveal that when mafic magma carrying phenocrysts of augite came in contact with the felsic magma, there was diffusion of heat from the hotter mafic phase to the colder felsic phase followed by diffusion of elemental components. Diffusion of elements like H+, Al3+ and other cations from the felsic phase to the mafic phase converted clinopyroxene phenocrysts in the mafic system into aggregates of small amphibole crystals. The formation of abundant amphibole microcrysts greatly increased the viscosity of the mafic system, allowing the amphibole-rich magma to venture into the surrounding felsic melt as veins and undergo viscous folding to facilitate mixing. Highlights • This work demonstrates the applications of results obtained from microfluidics and chaotic mixing experiments to natural rock samples. • The results obtained from mixing experiments can significantly contribute towards solving petrological problems. • Viscous folding can play an important role in magma mixing. • Amphibole-rich zones are products of magma mixing. [ABSTRACT FROM AUTHOR]

Highlights • A new formula under the action–angle–angle framework was proposed to analyze frequency ratio distribution. • Three-dimensional geometry patterns of high-period islands were constructed in the reconstructed phase space. • Standard fourth-order Runge–Kutta schemes were used to develop the post-treatment codes to predict mixing. • Mixing was sensitive to the chosen periodic lengths for large perturbation strength. Abstract Lid-driven cavity flows have been one of the most interesting and challenging flow models. Their geometries are commonly found in polymer mixing, food processing applications, and microfluidic channels. In this study, the effect of a longitudinal periodic length on mixing in a cavity disturbed by a single discontinuous baffle mounted in the middle of its bottom was investigated numerically. The finite volume method (FVM) was used to solve the three-dimensional flow field of a purely viscous, non-Newtonian fluid obeying the Power-law model. Particle tracking was done using a self-developed fourth-order Runge–Kutta scheme. Using a cavity channel with a continuous baffle as an integral system, we proposed a new formula under the action–angle–angle framework of perturbation theory mapping schemes to analyze frequency ratio distribution along the different invariant action surfaces. The perturbation theory provided a good prediction of period tori for small perturbation cases. Three-dimensional geometry patterns of high-period islands were constructed in the reconstructed phase space to intuitively show where the regularity flow predominated mixing in the flow domain. When the perturbation strength increased to 0.5, mixing was sensitive to the chosen periodic lengths. A single discontinuous baffle succeeded in achieving excellent mixing when the periodic length was selected correctly. Poincaré sections and the stretching of fluid filaments revealed that a periodic length of 12 mm achieved the best mixing in cases where the KAM cylinders disappeared and only three tiny period-3 tori wound around the top region of the cavity. It was also found that the larger the power law index, the better the mixing. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

In this paper we investigated numerically the flow and mixing characteristics of the barrier-embedded partitioned pipe mixer (BPPM) in non-creeping flow conditions. Numerical simulations are conducted for three mixing protocols of the BPPM, co-rotational, mirrored co-rotational, and counter-rotational protocols in the range of the Reynolds number (Re), 0.1≤Re≤300, focusing on the effect of the Reynolds number, the barrier height, and the mixing protocols on the mixing in the BPPM. Each mixing protocol creates two crosssectional flow portraits with crossing streamlines. Poincaré sections were plotted to investigate the flow system affected by the Reynolds number and the barrier height. Mixing in a specific BPPM is characterized using the intensity of segregation in terms of the compactness and the energy consumption. The dependency of the barrier height and the Reynolds number on the final mixing state of the BPPMs was identified by mixing analyses. The co-rotational protocol results in an efficient mixing in the creeping flow regime. Meanwhile, mirrored co-rotational and counter-rotational protocols, which lead to poor mixing in the creeping flow regime, turned out to be efficient protocols in the higher Reynolds number regime. [ABSTRACT FROM AUTHOR]

As an extension of our previous study, the flow and mixing characteristics of a serpentine mixer in non-creeping flow conditions are investigated numerically. A periodic velocity field is obtained for each spatially periodic channel with the Reynolds number (Re) ranging from 0.1 to 70 and the channel aspect ratio from 0.25 to one. The flow kinematics is visualized by plotting the manifold of the deforming interface between two fluids. The progress of mixing affected by the Reynolds number and the channel geometry is characterized by a measure of mixing, the intensity of segregation, calculated using the concentration distribution. A mixer with a lower aspect ratio, which is a poor mixer in the creeping flow regime, turns out to be an efficient one above a threshold value of the Reynolds number, Re = 50. This is due to the combined effect of the enhanced rotational motion of fluid particles and back flows near the bends of the channel driven by inertia. As for a mixer with a higher aspect ratio, the intensity of segregation has its maximum around Re = 30, implying that inertia does not always have a positive influence on mixing in this mixer.

To improve the efficiency of mixing under laminar flow with a low Reynolds number (Re), a novel three-dimensional Horseshoe Transformation (3D HT) was proposed as the basis for the design of a micromixer. Compared with the classical HT, the Lyapunov exponent of the 3D HT, which was calculated based on a symbolic dynamic system, proved the chaotic enhancement. Based on the 3D HT, a micromixer with a mixing length of 12 mm containing six mixing units was obtained by sequentially applying “squeeze”, “stretch”, “twice fold”, “inverse transformation”, and “intersection” operations. Numerical simulation and Peclet Number (Pe) calculations indicated that when the squeeze amplitude 0 < α < 1/2, 0 < β < 1/2, the stretch amplitude γ > 4, and Re ≥ 1, the mass transfer in the mixer was dominated by convective diffusion induced by chaotic flow. When Re = 10, at the outlet of the mixing chamber, the simulated mixing index was 96.4%, which was far less than the value at Re = 0.1 (σ = 0.041). Microscope images of the mixing chamber and the curve trend of pH buffer solutions obtained from a mixing experiment were both consistent with the results of the simulation. When Re = 10, the average mixing index of the pH buffer solutions was 91.75%, which proved the excellent mixing efficiency of the mixer based on the 3D HT.

Inspired by the partitioned pipe mixer (PPM), a barrier-embedded partitioned pipe mixer (BPPM) is designed and analyzed using a numerical simulation scheme. The BPPM is a static mixer, composed of orthogonally connected rectangular plates with a pair of barriers, which divide, stretch, and fold fluid elements, leading to chaotic mixing via the baker's transformation. The aspect ratio of the plate (α) and the dimensionless height of the barrier (β) are chosen as design parameters to conduct a parameter study on the mixing performance. The flow characteristics and mixing performance are analyzed using the cross-sectional velocity vectors, Poincaré section, interface tracking, and the intensity of segregation. The results indicate that several designs of the BPPM significantly enhance the PPM's mixing performance. The best BPPMs are identified with regard to compactness and energy consumption. © 2017 American Institute of Chemical Engineers AIChE J, 64: 717-729, 2018 [ABSTRACT FROM AUTHOR]

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 ( NT m ). 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 NT m for punched rigid-flexible impeller was shorter than that for rigid impeller and rigid-flexible impeller at the same consumption per unit volume ( P v ). The chaotic motor could further increase LLE value, and reduce the NT m on the basis of the normal motor. Moreover, the optimum aperture diameter and aperture ratio of punched rigid-flexible impeller were 8 mm and 12%, respectively, and the variable speed period of 10 s and constant speed period of 5 s of chaotic motor were particularly suitable for the laminar mixing process. [ABSTRACT FROM AUTHOR]

Complex rheology of non-Newtonian fluids often leads to non-homogenous mixing due to the spatial viscosity gradients. The non-intrusive electrical resistance tomography (ERT) technique was employed to study the mixing of non-Newtonian fluids in a chaotic SMX static mixer. For the first time, the effect of the rheology of the yield-pseudoplastic fluids on the quality of distributive mixing was explored in this study. The non-Newtonian fluid used in this study was the xanthan gum solution, which is a yield-pseudoplastic fluid obeying the Herschel-Bulkley model and its rheological parameters change as the solution mass concentration increases. The tomography images were utilized to investigate the efficacy of the distributive mixing of two different types of the secondary streams (Newtonian and non-Newtonian) in the primary stream of xanthan gum solutions (0.5 wt%, 1.0 wt%, and 1.5 wt%). Experiments were conducted for three different primary flow rates ranging from 3.5 L/min to 12.5 L/min while keeping the center-line injection of secondary stream fixed at 100 mL/min for all experiments. Our results revealed that the Newtonian secondary stream favored effective axial mixing over the non-Newtonian secondary stream. However, interestingly, for both types of the secondary streams, a more effective radial mixing was observed as the xanthan gum mass concentration increased at low Reynolds numbers. [ABSTRACT FROM AUTHOR]