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The article discusses a study on how dispersion can be suppressed through a properly designed mixer element and how the effect on the resulting chemical reactions occurring in the flow can be controlled. It presents the Taylor dispersion or residence time distribution (RTD) phenomena where a viscous liquid spends more time in a microfluidic device and describes the effect of the dispersion on the outcome of chemical reactions. It suggests that a pressure driven micromixer design with characteristics similar to the ideal plug-flow reactor can be achieved.

Abstract: We consider the stirring of an inviscid fluid caused by the locomotion of bodies through it. The swimmers are approximated by non-interacting cylinders or spheres moving steadily along straight lines. We find the displacement of fluid particles caused by the nearby passage of a swimmer as a function of an impact parameter. We use this to compute the effective diffusion coefficient from the random walk of a fluid particle under the influence of a distribution of swimming bodies. We compare with the results of simulations. For typical sizes, densities and swimming velocities of schools of krill, the effective diffusivity in this model is five times the thermal diffusivity. However, we estimate that viscosity increases this value by two orders of magnitude. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the enhancement of both mixing and heat transfer in a two-rod mixer for highly viscous non-Newtonian fluids. The mixer is composed of two vertical circular rods in a cylindrical tank. Chaotic flows are obtained by imposing the temporal modulations of the rotational velocities of the walls. We study the effects of different stirring protocols, which lead to non-chaotic and chaotic flows, on the efficiency of both mixing and heat transfer for three different rheological fluid behaviors: shear-thinning, Newtonian and shear-thickening. For this purpose, we use statistical indicators that characterize the mean value of the fluid temperature and its homogenization. We find that chaotic mixing is suitable for shear-thickening fluids for which we observe a clear enhancement of the thermal mixing (heat extraction and homogenization). This is due to the increase in the apparent fluid viscosity in the vicinity of the rotating walls. This aspect confirms the relevance of chaotic mixing for highly viscous fluids. [Copyright &y& Elsevier]

The variation of chemical element compositions in two pyroclastic sequences (Astroni 6 and Averno 2, Phlegrean Fields, Italy) is studied. Both sequences are compositionally zoned indicating a variability of melt compositions in the magma chamber prior to eruption. A clear dichotomy between the behaviour of major vs. trace elements is also observed in both sequences, with major elements displaying nearly linear inter-elemental trends and trace elements showing a variable scattered behaviour. Together with previous petrological investigations these observations are consistent with the hypothesis that magma mixing processes played a key role in the evolution of these two magmatic systems. Recently it has been suggested that mixing processes in igneous systems may strongly influence the mobility of trace elements inducing a ‘diffusive fractionation’ phenomenon, whose extent depends on the mixing time-scale. Here we merge information from 1) numerical simulations of magma mixing, and 2) magma mixing experiments (using as end-members natural compositions from Phlegrean Fields) to derive a relationship relating the degree of ‘diffusive fractionation’ to the mixing time-scales. Application of the ‘diffusive fractionation’ model to the two studied pyroclastic sequences allowed us to apply the relationship derived by numerical simulations and experiments to estimate the mixing time-scales for these two magmatic systems. Results indicate that mixing processes in Astroni 6 and Averno 2 systems lasted for approximately 2 and 9 days, respectively, prior to eruption. [ABSTRACT FROM AUTHOR]

Abstract: In this study, we numerically investigate the evolution of two-dimensional mixing and heat transfer enhancement within a two-rod stirring device. The fluid is heated by the walls, which are maintained at a constant temperature. We show by analysis of different stirring protocols that the use of discontinuous wall rotations is necessary to promote heat transfer by chaotic mixing. This condition is also required to avoid hot spots in the vicinity of the walls. The statistics of temperature scalars (mean and standard deviation of dimensionless temperature fields) allow us to determine the influence of geometrical and physical parameters on mixing and heating performance. Thermal strange eigenmodes are revealed during the mixing process by the development of complex recurrent patterns, and the self-similar character of temperature evolutions is confirmed by the probability distribution functions of the rescaled non-dimensional temperature. [Copyright &y& Elsevier]

Abstract: The chaotic mixing of miscible liquids in gas-segmented serpentine channels is studied computationally in a two-dimensional setting. Passive tracer particles are used to visualize and quantify the mixing. The molecular diffusion is ignored and only the mixing due to chaotic stirring is considered. Mixing is quantified using the entropy and intensity of segregation measures. The effects of various non-dimensional parameters on the quality of mixing are investigated and it is found that the relative bubble size, the capillary number and the non-dimensional channel corrugation length are the most important parameters influencing the mixing. The mixing is found to be weakly dependent on Reynolds number and nearly independent of viscosity ratio. [Copyright &y& Elsevier]

Motivated by the three-dimensional serpentine channel (Liu et al. in J Microelectromech Syst 9:190–197, 2000), we introduce a chaotic serpentine mixer (CSM) and demonstrate a systematic way of utilizing a mapping method to find out an optimal set of design variables for the CSM. One periodic unit of the mixer has been designed to create two streamlines portraits crossing each other. As a preliminary study, flow characteristics and mixing in the original serpentine channel has been reinvestigated. The working principle of the CSM is demonstrated via a particle-tracking method. From the design principle and the flow characteristics of the CSM, we choose three key design variables with an influence on mixing. Then, simulations for all possible combinations of the variables are carried out. At proper combinations of the variables, almost global chaotic mixing is observed in the Stokes flow regime. The design windows obtained can be used to determine an optimal set of the variables to fit with a specific application. [ABSTRACT FROM AUTHOR]

Continuous chaotic and shear mixing-induced morphology development of 60/40 w/w polypropylene/polyamide 6 (PP/PA6) blend and its nanocomposite with 5 wt% clay was investigated. PP and PP nanocomposite were mixed with PA6 in a single-screw extruder, respectively. Two screw geometries were used to induce chaotic and shear mixing, respectively. It was demonstrated that for PP/PA6 blend, the PA6 domains were transformed from large particles to short striations and to small droplets finally in shear mixing, whereas morphology of PA6 phase developed from lamellar layers to a partial continuous structure finally in chaotic mixing. For (PP/clay)/PA6 blend nanocomposite, the PA6 domains were deformed gradually from droplets to irregular fibrils in shear mixing and from short layers to thin fibrils in chaotic mixing. The PA6 fibrils formed finally in the latter were much thinner and uniform than those in the former. The dynamic storage moduli of samples prepared in both shear and chaotic mixing with these PA6 fibrils presented a solid-like response at lower frequencies. Moreover, the clay platelets dispersed initially in the PP phase migrated into PA6 phase finally in both shear and chaotic mixing and the exfoliation of clay platelets in PA6 phase was obviously improved in the latter. [ABSTRACT FROM AUTHOR]

The article presents a study which analyzed various designs of Low-Pressure Drop (LPD) static mixer for their mixing performance using the mapping method. It describes the different mixing patterns of the two types of LPD designs, the RR and RL type. The key design parameter to decide the performance of various designs is found to be the crossing angle between the elliptical plates of the LPD. To optimize the designs, a tradeoff between pressure drop and the mixing through improved stretching is required.

Procalcitonin (PCT) is an important biomarker of bacterial infections. Detection of serum PCT is of great significance in diagnosis and therapy of a variety of diseases. In this work it is measured through immunoassay using antibody-conjugated fluorescent microspheres. To improve the binding efficiency of PCT antigen and antibody, an aeroelastic agitator is designed. Through alternate perturbations, it produces chaotic advection to enhance the fluid mixing. The influences of key design and operating factors are analyzed, including the geometrical parameters, the driving pressure, and the alternating period. Then the agitator is applied for PCT detection and its performance is compared with an ultrasonic mixer. Results show that the chaotic mixing significantly improves the capturing efficiency of PCT antigen, leading to a better detection consistency and reliability. The fluorescence intensity correlates fairly well with the serum PCT concentration in the range of 0.02 ng/ml–49.56 ng/ml. [Display omitted] • A cost-effective aeroelastic agitator is designed to produce chaotic mixing. • The agitator improves the capturing efficiency of antigen in the immunoassay for PCT detection. • In the range of 0.02–49.56 ng/ml, the fluorescence correlates well with the PCT concentration. [ABSTRACT FROM AUTHOR]

• The novel active inline RAW mixer using chaotic advection is proposed. • It is studied experimentally in the case of highly viscous Newtonian fluids. • PIV and LIF techniques were used to obtain velocity and concentration fields. • Mixing quality was characterized by statistical indicators and FSLE. • High mixing efficiency has been achieved and optimal flow conditions were identified. [Display omitted] In order to mix highly viscous fluids with minimal energetic input, a new active in-line mixer has been developed in our previous study (El Omari et al. , Phys. Rev. Fluids, 2021 [18]). Based on the principle of mixing by chaotic advection, we present in this paper an experimental characterisation of chaotic mixing of Newtonian fluid flows, at low Reynolds number. First, the flow is characterized using velocity field measurements. Distinct flow topologies are detected in the flow. The trajectories of the fluid particles are computed and show the generation of complex structures in the flow. Residence time distributions reveal that the fluid particles spend more time in the mixer under favorable controlling conditions. Finite size Lyapunov exponents are calculated and indicate that the flow is more chaotic for these conditions. Next, the mixing patterns are visualized and showed that the mixing is more homogeneous under the same favorable conditions for which the fluid particles are sufficiently subjected to the stretching and folding mechanism. [ABSTRACT FROM AUTHOR]

Although a number of definitions of mixing have been proposed in the literature, no single definition accurately and clearly describes the full range of problems in the field of industrial mixing. An alternate approach is proposed which defines segregation as being composed of three separate dimensions. The first dimension is the intensity of segregation quantified by the normalized concentration variance (CoV); the second dimension is the scale of segregation or clustering; and the last dimension is the exposure or the potential to reduce segregation. The first dimension focuses on the instantaneous concentration variance; the second on the instantaneous length scales in the mixing field; and the third on the driving force for change, i.e. the mixing time scale, or the instantaneous rate of reduction in segregation. With these three dimensions in hand, it is possible to speak more clearly about what is meant by the control of segregation in industrial mixing processes. In this paper, the three dimensions of segregation are presented and defined in the context of previous definitions of mixing, and then applied to a range of industrial mixing problems to test their accuracy and robustness. [ABSTRACT FROM AUTHOR]

Abstract: The design of strategies to generate efficient mixing is crucial for a variety of applications, particularly digital microfluidic devices that use small “discrete” fluid volumes (droplets) as fluid carriers and microreactors. In recent work, we have presented an approach for the generation and control of mixing inside a translating spherical droplet. This was accomplished by considering Stokes’ flow within a droplet proceeding downstream which is also subjected to time dependent (sinusoidal) rotation. The mixing obtained is the result of the stretching and folding of material lines which increase exponentially the surface contact between reagents. The mixing strategy relies on the generation of resonances between the steady and the unsteady part of the flow, which is achieved by tuning the parameters of the periodic rotation. Such resonances, in this system, offer the possibility of controlling both the location and the size of the mixing region within the droplet, which may be useful to manufacture inhomogeneous particles (such as Janus particles). While the period and amplitude of the periodic rotation play a major role, it is shown here by using a triangular function that the particular shape of the rotation (as a function of time) has a minor influence. This finding demonstrates the robustness of the proposed mixing strategy, a crucial point for its experimental realization. [Copyright &y& Elsevier]

Abstract: This review is concerned with mixing and transport in the human pulmonary acinus. We first examine the current understanding of the anatomy of the acinus and introduce elements of fluid mechanics used to characterize the transport of momentum, gas and aerosol particles. We then review gas transport in more detail and highlight some areas of current research. Next we turn our attention to aerosol transport and in particular to mixing within the alveoli. We examine the factors influencing the level of mixing, review the concept of chaotic convective mixing, and make some brief comments on how mixing affects particle deposition. We end with a few comments on some issues unique to the neonatal and developing lung. [Copyright &y& Elsevier]

The mapping method is employed as an efficient toolbox to analyze, design, and optimize micromixers. A new and simplified formulation of this technique is introduced here and applied to three micromixers: the staggered herringbone micromixer (SHM), the barrier-embedded micromixer (BEM), and the three-dimensional serpentine channel (3D-SC). The mapping method computes a distribution matrix that maps the color concentration distribution from inlet to outlet of a micromixer to characterize mixing in a quantitative way. Once the necessary distribution matrices are obtained, computations are fast and numerous layouts of the mixer are easily evaluated, resulting in an optimal design. This approach is demonstrated using the SHM and the BEM as typical examples. Mixing analysis in the 3D-SC illustrates that also complex flows, for example in the presence of back-flows, can be efficiently dealt with by using the new formulation of the mapping method. [ABSTRACT FROM AUTHOR]

An electrokinetic mixer driven by oscillatory cross flow has been studied numerically as a means for generating chaotic mixing in microfluidic devices for both confined and throughput mixing configurations. The flow is analyzed using numerical simulation of the unsteady Navier–Stokes equations combined with the tracking of single and multi-species passive tracer particles. First, the case of confined flow mixing is studied in which flow in the perpendicular channels of the oscillatory mixing element is driven sinusoidally, and 90° out of phase. The flow is shown to be chaotic by means of positive effective (finite time) Lyapunov exponents, and the stretching and folding of material lines leading to Lagrangian tracer particle dispersion. The transition to chaotic flow in this case depends strongly on the Strouhal number ( St), and weakly on the ratio of the cross flow channel length to width ( L/ W). For L/ W = 2, the flow becomes appreciably chaotic as evidenced by visual particle dispersion at approximately St = 0.32, and the transitional value of St increases slightly with increasing aspect ratio. A peak degree of mixing on the order of 85% is obtained for the range of parameter values explored here. In the second phase of the analysis, the effect of combining a fixed throughput flow with the oscillatory cross channel motion for use in a continuous mixing operation is examined in a star cell geometry. Chaotic mixing is again observed, and the characteristics of the downstream dispersion patterns depend mainly on the Strouhal number and the (dimensionless) throughput rate. In the star cell, the flow becomes appreciably chaotic as evidenced by visual particle dispersion at approximately St = 1, slightly higher than for the case of cross cell. The star cell mixing behavior is marked by the convergence of the degree of mixing to a plateau level as the Strouhal number is increased at fixed flow rate. Degree of mixing values from 70 to 80% are obtained indicating that the continuous flow is bounded by the maximum degree of mixing obtained from the confined flow configuration. [ABSTRACT FROM AUTHOR]

We conducted a numerical study on mixing in a barrier embedded micromixer with an emphasis on the effect of periodic and aperiodic sequences of mixing protocols on mixing performance. A mapping method was employed to investigate mixing in various sequences, enabling us to qualitatively observe the progress of mixing and also to quantify both the rate and the final state of mixing. First, we introduce the design concept of the four mixing protocols and the route to achieve chaotic mixing of the mixer. Then, several periodic sequences consisting of the four mixing protocols are used to investigate the mixing performance depending on the sequence. Chaotic mixing was observed, but with different mixing rates and different final mixing states significantly influenced by the specific sequence of mixing protocols and inertia. As for the effect of inertia, the higher the Reynolds number the larger the rotational motion of the fluid leading to faster mixing. We found that a sequence showing the best mixing performance at a certain Reynolds number is not always superior to other sequences in a different Reynolds number regime. A properly chosen aperiodic sequence results in faster and more uniform mixing than periodic sequences. [ABSTRACT FROM AUTHOR]

Abstract: We consider the residence time distribution (RTD) of a liquid flowing through a spatially periodic channel. It is shown that chaotic advection significantly reduces deviation of the RTD which then consist of two parts: the main pulse which does not depend on the Péclet number and a long tail which is formed in the near-boundary layer, where the advection is weak. Boundary layer approximation provides the dependence of the statistical moments of the RTD on Péclet number. It is shown that the length of the tail increases with Pe, while its mass decreases. The numerical results support the theoretical findings. [Copyright &y& Elsevier]

Abstract: In this Letter we report a method for enhancing mixing of a passive tracer in an electro-osmotic flow in a rectangular microchannel. A time-periodic electric field across the microchannel, filled with an electrolyte solution, is applied in order to realize a well-mixed state. A random perturbation to the time-periodic electric field is introduced in order to break the invariant tori of the system and achieve better mixing results. It is shown that under such period-modulation the enhancement effect increases with the strength of the modulation, and it is much reduced as diffusion is increased. [Copyright &y& Elsevier]

Abstract: Several studies of the chaotic motion of fluid particles by two-dimensional time-periodic flows or three-dimensional steady flows, called Lagrangian chaos, are first introduced. Secondly, some of the studies on efficient mixing caused by Lagrangian chaos, called chaotic mixing, are reviewed with discussion of several indices for the estimation of mixing efficiency. Finally, several indices to estimate the efficiency of mixing in a short time, such as those related to transport matrices, stable and unstable manifolds of hyperbolic periodic points of Poincaré maps, and lines of separation, are explained by showing examples of mixing by two-dimensional time-periodic flows between eccentric rotating cylinders and mixing by three-dimensional steady flows in a model of static mixers. [Copyright &y& Elsevier]

A two-dimensional numerical investigation into the mixing of magnetic microparticles with bio-cells in a chaotic micromixer is carried out by using a multiphysics finite element analysis package. Fluid and magnetic problems are simulated in steady-state and time-dependent modes, respectively. Intensity of segregation is utilized as the main index to examine the efficiency of the mixer. Trajectories of the particles are used in order to detect chaos in their motion and quantify its extent. Moreover, probability of the collision between particles and target bio-cells is examined as a supplemental index to study the effects of driving parameters on the mixing process. Simulation results reveal that while in some ranges of operating conditions all indices are in good agreement, there are some ranges where they appear to predict contradicting results which is discussed in details. It is found that optimum operating conditions for the system is obtained when the Strouhal number is less than 0.6, which corresponds to the efficiency of about 85% in a mixing length of 500 μm (The mixer design described here is patent pending). [ABSTRACT FROM AUTHOR]

Roughness effects on lubricant flows are investigated via 2D lattice Boltzmann simulations. At a Reynolds numbers of order 1000 a transition from laminar to unsteady flow is observed by an increase of the roughness height from about 10% to about 25% of the channel width. At lower Reynolds numbers (where the flow is laminar in both channels), the transition is observed when increasing the wall roughness further. In other words, the critical Reynolds number for the transition from laminar toward unsteady flow decreases at higher wall roughness. Wall roughness may, therefore, qualitatively change the flow properties in confined geometry. Due to the ubiquitous presence of the wall roughness, the phenomenon is relevant in all cases where relatively high Reynolds number flow occur in strongly confined channels such as lubricant flow during the deformation of solid surfaces. For a fixed Reynolds number and channel geometry, time and spatial dependence of the velocity field and fluctuating quantities obey the scaling behavior as expected from the structure of the Navier-Stokes (NS) equations. This underlines the physical significance of the observed transition. As a possible application, wall roughness may be used in order to enhance mixing efficiency at a given Reynolds number. [ABSTRACT FROM AUTHOR]

Measurements of power requirement and mixing time have been conducted in a cylindrical vessel installed with a disk impeller reciprocating up and down. Mixing time was measured by using the decolorization reaction of iodine with sodium thiosulphate. As the Reynolds number specially defined for this reciprocation system increases, the dimensionless mixing time, which is the product of mixing time by reciprocation frequency, decreases and approaches a constant value. Mixing was completed within several reciprocations when the flow is turbulent with vortex generation behind the moving disk. The power number, Po, was correlated with Reynolds number, Re, without showing any dependency on the ratio of impeller diameter to vessel diameter: Po=44 Re−1 for Re<20 and Po=1 for Re>200. The rate of recipro-mixing is compared with that of ordinary rotating mixing under the same power input per volume, Pv. In order to clarify the mechanism of rapid recipro-mixing, stretching and folding behaviours of a fluid interface between two miscible liquids were investigated by visualization with LIF. The fluid interface stretches exponentially with time in laminar flow with vortex generation, which indicates that reciprocation of a disk produces a chaotic mixing filed. Chaotic mixing together with strong turbulence caused by reciprocation yields rapid mixing that is not achievable by the ordinary rotating mixing. [ABSTRACT FROM AUTHOR]

Abstract: We have achieved rapid chaotic mixing of two fluids flowing in a planar serpentine convergent–divergent mini-channel, and analyzed the transient three-dimensional flow field and distribution of concentration. The degree of irregularity of trajectories is increased through experiencing a repeated configuration of turning with an amplified pressure gradient in the designed channel. The results reveal that the pattern of the alternating convergent–divergent cross sections induces corner Dean cells with much increased Dean numbers; the stretching and folding of interfaces are effectively enhanced, resulting in superior chaotic mixing of fluids. Viewed on cross sections normal to the main stream, the complicated trajectories appear to halt, swing and twist as the fluids approach the Dean cells. Along the stream, the flow trajectories become increasingly irregular. The flow trajectories of Dean cells are symmetric with respect to the central cross section; on each side of the cross section, the flow trajectories are highly unstable, spatially and temporally, around the Dean cell. In our mixing channel the Dean cells in the mixing channel are arranged across the interfaces; the interfacial area between fluids is continuously distorted and enlarged in a spiral behavior, thus effectively promoting the fluid mixing. [Copyright &y& Elsevier]

The probability distribution function (PDF) of a passive tracer, forced by a “mean gradient”, is studied. First, we take two theoretical approaches, the Lagrangian and the conditional closure formalisms, to study the PDFs of such an externally forced passive tracer. Then, we carry out numerical simulations for an idealized random flow on a sphere and for European Center for Medium-Range Weather Forecasts (ECMWF) stratospheric winds to test whether the mean-gradient model can be applied to studying stratospheric tracer mixing in midlatitude surf zones, in which a weak and poleward zonal-mean gradient is maintained by tracer leakage through polar and tropical mixing barriers, and whether the PDFs of tracer fluctuations in midlatitudes are consistent with the theoretical predictions. The numerical simulations show that when diffusive dissipation is balanced by the mean-gradient forcing, the PDF in the random flow and the Southern-Hemisphere PDFs in ECMWF winds show time-invariant exponential tails, consistent with theoretical predictions. In the Northern Hemisphere, the PDFs exhibit non-Gaussian tails. However, the PDF tails are not consistent with theoretical expectations. The long-term behavior of the PDF tails of the forced tracer is compared to that of a decaying tracer. It is found that the PDF tails of the decaying tracer are time-dependent, and evolve toward flatter than exponential. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a robust watermarking approach for hiding grayscale watermarks into digital images. Plugging the codebook concept into the singular value decomposition (SVD), the proposed method embeds the singular values (SVs) of the original image into the watermark one to attain the lossless objective. The experimental results show that the proposed scheme guarantees the extracted watermark on an average and the worst PSNR values of 24.91 and 19.96 dB, respectively. In addition to the guarantee of the quality of extracted watermark image, the security of the referenced watermark is further strengthened by applying chaos permutation on it in advance. The proposed scheme leads to satisfactory robustness to various attacks and is compared to other well-known grayscale watermarking methods to reveal its efficiency for practical applications. [Copyright &y& Elsevier]

The study evaluated if excellent mixing conditions prevailing in chaotic mixers also promote droplet coalescence in the mixing of immiscible polymers. A combined approach of experiments and simplified modeling was used to understand the effects of the degree of chaotic mixing, shear rate, and viscosity ratio on coalescence rates. It was found experimentally that the extent of coalescence was substantially reduced when the bulk of the fluid in the mixer experienced chaotic mixing. In addition, coalescence was subdued at higher rates of shear and for higher viscosity ratio droplets. Pseudo-steady state droplet size distributions were reached faster with higher droplet volume fractions and for higher viscosity ratio droplets. [ABSTRACT FROM AUTHOR]

Abstract: Aerosols too large for significant Brownian transport, and too small for significant inertial transport, are nonetheless known to deposit deep in the lung, and are associated with increased risk of pulmonary disease. Classical models fail to explain such transport. We hypothesized that kinematic irreversibility in ventilation, arising from velocity saddle-points or from flow asynchrony at airway bifurcations, may be the fundamental transport mechanism. Our experimental evidence shows striking trajectory irreversibility in rat lungs ventilated with 2-color polymerizable silicones, representing resident and tidal gas. The striated patterns in small airways, even after one ventilatory cycle, support our hypothesis. Here we analyze bifurcating flow asynchrony in a simplified one-dimensional model. We find: unexpected richness and chaos in particle trajectories; almost all trajectories visit all spatial positions; surprisingly, there is complete mixing—the limiting concentration is spatially uniform. This is a new finding supporting the idea that kinematic irreversibility is a potent mixing and transport mechanism for aerosols deep in the lung. [Copyright &y& Elsevier]

Abstract: An industrially relevant continuous flow blending process has been developed that controllably forms in the melt various structured distributions of carbon black particles to impart uniform or directional conductivities to extrusions such as film, sheet, or tubing. A range of electrical properties was selectable on line via process parameter specification. Process control also made possible production of extrusions with graduated or periodic properties such that functional materials and devices can be extracted from extrusions. The process was enabled by chaotic advection, a recent sub-field of fluid mechanics, and was previously demonstrated in part for particulate additives with batch devices. Unlike conventional mixing where the focus is on attaining uniform particle dispersions, chaotic advection inherently promoted structure formation in melts at increasingly smaller length scales such that percolation thresholds can be reduced. Because conducting conditions are attained at low solid additive loadings, a reverse percolation effect was also induced via controlled structure breakdown. Progressive structure formation is related to electrical properties and processing conditions. Methods are applicable to other melt-processable materials and additives. [Copyright &y& Elsevier]

Abstract: This paper presents functional three-dimensional microchannels whose top and side walls have slanted microgrooves. These microchannels can generate short pitch spiral flow for efficient chaotic mixing. We proposed a novel fabrication method for 3-D SU-8 molds using two-step inclined backside exposures and additional two-step top side exposures. The width and depth of the SU-8 microchannel are 100μm. Slanted grooves of 50μm in width and 30μm in depth were patterned on the top and the side walls of the microchannel. Their orientation angle was 63.5° with the microchannel axis. It was demonstrated that the microchannel with slanted grooves on three walls achieved short pitch spiral flow compared to the microchannel with slanted grooves on one wall. Since liquid in the channel flows along the grooves on the walls, optimum design of the pitch and placement of the slanted grooves enables efficient spiral flows in the channel. [Copyright &y& Elsevier]

Abstract: This article addresses the application of pulsed system models (in which the advection operator is decoupled from the diffusion operator) for investigating the physics of dispersion/homogenization in deterministic chaotic flows. The analysis is organized along to main directions: (i) the development of a simplified time-continuous model which can be viewed as a generalization in a time-continuous frame of the baker''s transformation, and which is amenable to analytical investigation, and (ii) the comparison of the results deriving from several typical pulsed-system models with the direct numerical simulation of the advection-diffusion equation. Both these approaches reveal the intrinsic ambiguity of the pulsed system approach in describing advection-diffusion problems. [Copyright &y& Elsevier]

Abstract: When immiscible polymer melts are combined by chaotic advection, melt domains are recursively stretched and folded. A multi-layer blend morphology results that has a hierarchical structure and intrinsic mechanical interlocking. Novel derivative morphologies can be obtained via the formation and interactive growth of holes among melt layers. In this study, a unique continuous chaotic advection blender (CCAB) was used to investigate influences of these morphologies on tensile and impact toughness properties of polypropylene (PP)-low density polyethylene (LDPE) blends. Although prior related work has focused on batch processing, this study also demonstrated the viability of chaotic advection in continuous flow modes suited for extruding blends with target morphologies. Extrusions were producible with morphologies giving an overall combination of improved properties relative to properties associated with droplet morphologies typically obtained with conventional compounding equipment. Applicability to injection molding is also discussed. Novel processing control features of the CCAB-type devices are briefly described. [Copyright &y& Elsevier]

An efficient magnetic force driven mixer with simple configuration is designed, fabricated, and tested. It is designed to facilitate the mixing of magnetic beads and biomolecules in a microchannel, where mixing is unavoidably inefficient due to its low Reynolds number. With appropriate temporal variations of the force field, chaotic mixing is achieved, hence the mixing becomes effective. The mixing device consists of embedded microconductors as a magnetic field source and a microchannel that guides the streams of working fluid. It is demonstrated that a pair of integrated micro conductors provides a local magnetic field strong enough to attract nearby magnetic beads. Mixing of magnetic beads is accomplished by applying a time-dependent control signal to a row of conductors, at the Reynolds number of as low as 1O_2. Two-dimensional numerical simulation has been performed to design the configuration of the channel and electrodes, which creates chaotic motion of beads. It is found that a simple two-dimensional serpentine channel geometry with the transverse electrodes is able to create the stretching and folding of material lines, which is a manifestation of chaos. The mixing pattern predicted by the simulation has been confirmed by both flow visualization and PTV (Particle Tracking Velocimetry) in the chaotic mixer fabricated, which should greatly increase the attachment of beads onto the target biomolecules. The optimum frequency of applied control signal is searched by evaluating the Lyapunov exponent in both numerical and experimental particle tracking. It is found that the range of optimum Strouhal number is 5 < St < 12, which is defined by the channel width and the mean velocity. [ABSTRACT FROM AUTHOR]

The effect of waveforms of rotor motion in a chaotic mixing device on the development of morphology in the blending of polypropylene (PP) and polyamide 6 (PA6) was investigated. The rotor motion was delivered in a steady and time-periodic manner and the mixing effectiveness was evaluated in terms of Poincaré maps and stretching distribution, the speed of conversion of PP-phase into droplets, and droplet size distribution. The pathway of morphology development, such as deformation of the PP-phase into lamella, fibrils, and droplets, was found not to depend on the nature of the waveform. However, the makeup of each morphological form depended strongly on the particular waveform used. The best results were obtained when the rotor motion was delivered using a sine waveform. In this case, the PP-phase turned most rapidly into fibrils and droplets and the droplets were of more uniform size. The square waveform, although produced higher mean stretching and showed more uniform mixing in Poincaré maps, yielded large-size droplets, purportedly through premature breakup of the fibrils in the zones of weak flow, such as in the vicinity of the stationary rotors. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate the dynamics of flows occurring in the wakes of rising bubbles of different shapes and sizes. Different wake dynamics can result in qualitatively different mixing characteristics. In the case of fast gas–liquid reaction networks, reactions occur almost exclusively in the bubble wake. Thus, wake mixing can have a strong impact on the reaction yield and selectivity. Dynamic numerical simulations were performed to study the flow of liquid around bubbles of different shapes. The obtained velocity and pressure fields were used to investigate the liquid-phase mixing in the flow for each case. As a strong connection between mixing and chaos is known to exist, Lagrangian tracking of passive tracer particles was used to identify chaotic fluid transport in the flows. Chaotic dynamics lead to folding and stretching of fluid elements, which results in very effective mixing. To quantify mixing, stretching fields were computed for each flow case. Finally, different liquid-phase chemical reaction networks were tested to illustrate the effects of mixing on chemical reaction yields and selectivities. [Copyright &y& Elsevier]

The chaotic mixing of a fluid due to a steady creeping flow in a partitioned-pipe mixer, composed of axially periodic pairs of plane plates within an infinitely long cylinder, is studied. This flow, caused by both the rotation of the cylinder and the axial pressure gradient, has reverse-flow regions unless the rotation is sufficiently small, unlike the approximate flows used in preceding studies. The dependences of the location and size of the islands in the Poincaré section based on the flow of the present study on the parameters of the system are similar to those based on the approximate flows, in spite of the differences between these flows. Moreover, we find that the stretching of fluid elements after their separation by the leading edges of the plates mainly contributes to the mixing, and that fluid elements that are stretched strongly move more slowly in the axial direction than those stretched weakly. [Copyright &y& Elsevier]

The mixing due to helical flows in curved micro channels is investigated. A new chaotic mixing mechanism is presented relying on alternately switching between different flow patterns exhibiting four Dean vortices. Flow patterns and interfacial stretching factors are numerically computed for various Dean numbers. For experimental studies a prototype of a chaotic mixer with curved channels was fabricated. The experimental evaluation of the mixing performance corroborates the numerical prediction: the mixing performance found for Dean numbers above 140 is qualitatively different from that at lower Dean numbers; the periodic switching between different vortex patterns leads to efficient mixing, manifesting itself in an exponential growth of interfacial area. In addition to the studies on mixing, residence-time distributions in the mixing channel are computed numerically. These investigations indicate that due to mass-transfer enhancement originating from the transversal redistribution of matter in the chaotic flow, hydrodynamic dispersion is substantially reduced relative to a straight channel. [ABSTRACT FROM AUTHOR]

In this article dedicated to micromixing, we concentrate here on a particular micromixer – the ‘cross-channel micromixer’. This mixer exploits an oscillatory perturbation to induce chaotic trajectories, favoring mixing. We present here theory, numerical simulations and experiments performed on this system. To cite this article: A. Dodge et al., C. R. Physique 5 (2004). [Copyright &y& Elsevier]

The objective of the present work is to describe a new mapping tool using anisotropic unstructured meshes to study mixing within a spatially periodic pipe flow. Instead of tracking the boundaries of elementary cell flow domains as it was done in the original mapping method established by Kruijt et al. (A.I.Ch.E. J. 47 (5) (2001a) 1005; Int. Polym. Process. 16 (2) (2001b) 151) and Galaktionov et al. (Comput. Fluids 30 (3) (2001) 271), the deformation of elementary triangles (only three nodal points) between the inlet and exit pipe cross-sections is followed. It is however necessary to adapt the initial mesh according to criteria which takes into account the spatial stretching and folding of fluid elements. The method developed is applied to the twisted curved pipes (TCP) three-dimensional (3D) flow. We show the evolution of concentration distributions along the TCP mixer for chaotic advection flow regimes. This method allows the emphasis of isolated unmixed regions (KAM islands). The flexibility of the method allows also the possibility of studying multiple stirring protocols, thus contributing to a better comprehension of the physical phenomena involved in chaotic mixing. The method developed is also applicable to 2D temporally periodic flows. [Copyright &y& Elsevier]

This study investigated the effects of viscosity ratio (p) and composition on morphology development in an immiscible polymer system mixed under chaotic flow conditions. It was seen that morphology of the dispersed phase developed through a widely accepted route involving transitions from lamellas to fibrils and to droplets. It was found in experiments with p≥1 that the dispersed phase converted into droplets very rapidly with narrow droplet size distribution when p∼1. For higher values of p, the speed of morphological transitions slowed down, the droplet size distribution became wider, and much larger droplets were formed. Similar effects were observed at higher concentration of the dispersed phase. No self-similar scaling behavior was observed in the droplet size distribution, which can be attributed to the lack of self-similarity in the breakup of lamellas into fibrils. [Copyright &y& Elsevier]

We consider the electrohydrodynamics of a spherical drop in a nonaxisymmetric electric field, which can be approximated by the sum of a uniform field and a linear straining field. We obtain the analytic solution of the three-dimensional flow fields inside and outside a drop for the Stokes flow regime by using Lamb''s general solution and the leaky dielectric model. With the analytic solution, the dielectrophoretic migration velocity of a drop is obtained as a function of the type and the frequency of the imposed electric field. The direction of drop motion is found to be parallel to the dielectrophoretic force. The analytic solution is also used to investigate the characteristics of the interfacial flow under various nonaxisymmetric electric fields. While investigating the interfacial flow, we find a surface vortex structure under certain nonaxisymmetric electric fields, which is found to be related to the chaotic mixing inside the drop. Finally, we consider the chaotic features of three-dimensional flows inside the drop under static nonaxisymmetric electric fields. [Copyright &y& Elsevier]

The evolution of a flame in a reaction–advection–diffusion combustion system in the presence of chaotic stirring by an unsteady laminar fluid flow is considered. Two distinct regimes are found as the stirring rate is increased. When the reaction is slow (or fast stirring) localised temperature perturbations decay—the flame is quenched by the flow. If the reaction is fast (or slow stirring) a localised ignition leads to a stationary flame with complex filamental structure. The width of the filaments depends on the reaction and stirring rates. This problem is investigated numerically in 2D for an open flow system formed by two alternately opened point-vortex-sinks and the results are compared with previous results [Physica D 176 (1–2) (2003) 67–81] from a 1D ‘mean-strain’ model for the transverse profile of the flame filaments. The system is studied for different Lewis and Damko¨hler numbers, with a critical Damko¨hler number being found, dependent on the Lewis number, for the transition from trivial to combustion states. A comparison between time-periodic and steady flow regimes shows that chaotic motion of the fluid elements in the unsteady flow significantly enhances the combustion. [Copyright &y& Elsevier]

The advection–diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of dimensions, for a velocity field with chaotic trajectories, with an error proportional to the square root of the diffusivity. After some time, the one-dimensional equation becomes invalid, but by that time a large fraction of the scalar variance has decayed. [Copyright &y& Elsevier]