Chaotic Advection Research Articles

Geochemistry and geochronology of mafic rocks from the Jinghe ophiolitic mélange, northwest China: Implications for plume-related magmatism and accretionary processes within the North Tianshan Ocean

We present geological, whole-rock geochemical and Sr–Nd isotopic, and zircon U–Pb geochronological data for mafic rocks found as angular fragments in the Jinghe ophiolitic mélange of the Northern Tianshan orogenic belt, northwest China. The investigated exotic blocks comprise layered and massive gabbros and pillow basalts that are embedded in a serpentinite-rich matrix. The 380.5 ± 4.9 Ma layered gabbros have chondrite-normalized rare earth element (REE) patterns characterized by significant depletions in the light rare earth elements (LREE) and positive Eu anomalies, suggesting that the petrogenesis of these rocks was controlled by cumulus processes. The 381.5 ± 3.7 Ma massive gabbros have near-flat normal-type mid-ocean ridge basalt (MORB)-normalized multi-element patterns with moderate to strong negative Nb–Ti anomalies. These rocks have initial 87Sr/86Sr ratios (87Sr/86Sr(i)) of 0.703825–0.704758 and high εNd(t) values (+6.7 to +9.0). Two compositional groups of basalts can be recognized: ocean island basalt (OIB)- and enriched MORB-type rocks. Both groups display variable enrichments in large-ion lithophile elements (LILE) in N-MORB-normalized trace element diagrams. Semi-quantitative modelling demonstrates that the parental magmas of the massive gabbros were derived by 5%–10% partial melting of a spinel-bearing lherzolite source influenced by minor inputs of subducted crustal components. The parental magmas of the subalkaline and alkaline basalts were derived by 10%–20% and 1%–5% polybaric melting, respectively, of a lherzolite source containing spinel and garnet in equal amounts. The petrogenesis of the Jinghe basalts can be linked to continental rifting followed by seafloor spreading caused by upwelling of a mantle plume. The petrogenesis of the gabbros is linked to plate re-organization that provided the geodynamic impetus for southwestward subduction in the North Tianshan Ocean, and the onset of incorporation of oceanic materials with different origins into a growing accretionary prism during the Late Devonian. Accretion resulted in chaotic mixing of dismembered pieces of variably deformed oceanic rocks, which are now preserved as an extensive block-in-matrix ophiolitic mélange.

Fouling mitigation in crossflow filtration using chaotic advection: A numerical study

AbstractFouling mitigation in a crossflow filtration system using chaotic advection is numerically studied. A barrier‐embedded partitioned pipe mixer (BPPM) is selected as a static mixer, creating chaotic advection in a laminar flow regime. Mixing characteristics are controlled via two design parameters, the mixing protocol and the dimensionless barrier height (β). The average dimensionless concentration boundary layer thickness () and the surface‐averaged dimensionless wall concentration () dramatically decrease with the introduction of the BPPM, incorporating a chaotic flow system. and decrease as β increases, and the largest reduction of is observed in the counter‐rotational protocol. A semi‐ring configuration is revealed to be the most appropriate configuration to characterize mixing near the membrane surface. It is found that a filtration system with a globally chaotic flow shows the best mixing performance and the largest reduction of fouling.

On the computational analysis of short mixing length planar split and recombine micromixers for microfluidic applications

ABSTRACT Micromixers are one of the prominent devices in applications like Lab-On-A-Chip (LOC), micro-total analysis system (µTAS), etc. The performance of micromixer is governed by geometry of micromixer, type of obstructions like baffles, obstacles introduced in the fluid flow. In this paper, the mixing performance for three types of baffle-based split and recombination planar passive micromixers is analysed using numerical simulation. The three design configurations, namely, square baffle-based split and recombination (SB-SAR), circular baffle-based split and recombination (CB-SAR) and triangular baffle-based split and recombination (TB-SAR) micromixers are considered. In-depth flow physics analysis was carried out to assess and affirm the quantitative results of the mixing quality at Reynolds number in the range of 0.1–60. The mixing index is found to be 1.0 at Re = 0.1 for SB-SAR micromixer and 0.80 at Re ≥ 10 for all the micromixer design configurations. Micromixers showed diffusion-dominated mixing mechanism at Re = 0.1, and chaotic advection dominated mixing mechanism at Re ≥ 30. The advantages of rapid mixing, simple geometry and shortest mixing length make these micromixers more encouraging in chemical, biochemical and medical applications.

Numerical Investigation on Multiphase Flows in Various Configurations of Microchannels Using Computational Fluid Dynamics

A two-dimensional domain of multiphase flow analyses in this study using the Volume of Fluid (VOF) model was carried out in order to simulate and predict the fluid flows and mixing performance of two miscible liquids in various microchannel configurations. The various microchannels configurations were designed accordingly and the simulation was carried out based on the justified conditions, assumptions and considerations by using the commercial computational fluid dynamics (CFD) software, FLUENT. The grid type and size of the computational domain were verified in terms of stability by performing the grid independence analysis. The result showed that static mixing would be possible to achieve in various configurations of microchannels, however, the simulation results predicted that it appeared to be more efficient in complex and retrofitted microchannels. It showed the potential to promote and enhance chaotic advection, compositions distribution, and diffusivity as compared to basic microchannels that are mostly dependent only on the injection focus. Furthermore, the Reynolds number appeared to be a significant factor to enhance the mixing performance in microchannel beside the configurations.

Analysis of straight and wavy miniature heat sinks equipped with straight and wavy pin-fins

The use of pin-fins is an effective technique for improving the performance of miniature heat sinks. Generally, this improvement is due to the larger heat transfer area as well as the chaotic advection of fluid and thermal boundary layer interruption, which are produced by pin-fins. In this analysis, the performance of straight miniature heat sink (SMHS) and wavy miniature heat sink (WMHS) is investigated in the presence of straight and wavy pin-fins and the obtained results are compared with the smooth cases. Results show us that noticeable differences of velocity and temperature fields between the enhanced cases and the smooth cases exist, and they differ from shape to shape of channel and pin-fin. It is also found that both the heat transfer coefficient and the pressure drop of SMHSs and WMHSs equipped with pin-fins are always higher than those of without pin-fins. At the studied range of Reynolds number (i.e. 100 to 1000), the enhanced cases show 0.05 to 2.3 times enhancement in the heat transfer coefficient and 2.6 to 13.6 times augmentation in the pressure drop compared with the smooth cases. The highest values are recorded for the WMHS equipped with wavy pin-fins having an opposite spin. However, it is shown that for the same pumping power the heat removal of all enhanced cases is higher than that in the smooth cases. Overall analysis using the ratio of heat transfer rate to pumping power is done to detect the best configuration: a better performance is observed for the SMHS with straight pin-fins and the WMHS with wavy pin-fins having an identical spin.

Dynamics of Synthetic Membraneless Organelles in Microfluidic Droplets.

Cells can form membraneless organelles by liquid-liquid phase separation. As these organelles are highly dynamic, it is crucial to understand the kinetics of these phase transitions. Here, we use droplet-based microfluidics to mix reagents by chaotic advection and observe nucleation, growth, and coarsening in volumes comparable to cells (pL) and on timescales of seconds. We apply this platform to analyze the dynamics of synthetic organelles formed by the DEAD-box ATPase Dhh1 and RNA, which are associated with the formation of processing bodies in yeast. We show that the timescale of phase separation decreases linearly as the volume of the compartment increases. Moreover, the synthetic organelles coarsen into one single droplet via gravity-induced coalescence, which can be arrested by introducing a hydrogel matrix that mimics the cytoskeleton. This approach is an attractive platform to investigate the dynamics of compartmentalization in artificial cells.

Dynamics of Synthetic Membraneless Organelles in Microfluidic Droplets

AbstractCells can form membraneless organelles by liquid–liquid phase separation. As these organelles are highly dynamic, it is crucial to understand the kinetics of these phase transitions. Here, we use droplet‐based microfluidics to mix reagents by chaotic advection and observe nucleation, growth, and coarsening in volumes comparable to cells (pL) and on timescales of seconds. We apply this platform to analyze the dynamics of synthetic organelles formed by the DEAD‐box ATPase Dhh1 and RNA, which are associated with the formation of processing bodies in yeast. We show that the timescale of phase separation decreases linearly as the volume of the compartment increases. Moreover, the synthetic organelles coarsen into one single droplet via gravity‐induced coalescence, which can be arrested by introducing a hydrogel matrix that mimics the cytoskeleton. This approach is an attractive platform to investigate the dynamics of compartmentalization in artificial cells.

A Micromixer with Two-Layer Crossing Microchannels Based on PMMA Bonding Process

AbstractA micromixer with two-layer crossing microchannels based on PMMA bonding process was proposed. The micromixer consists of two-layer crossing microchannels and periodic mixing chambers. The numerical simulation and parameters optimization of the micromixer were carried out in a Reynolds number range of 0.5–100 using CFD software, and the prototype of micromixer was manufactured by PMMA bonding process under certain temperature and pressure condition. The mixing performance of the micromixer was tested and verified by the mixing experiments using red-blue dye. Both the numerical and experimental results confirmed that the micromixer achieves an excellent mixing characteristics over a wide range of Reynolds numbers through generating Dean vortices and chaotic advection. At the same time, the PMMA bonding process proposed in this paper has certain application value and reference significance for expanding the application of three-dimensional flow channels in the field of microfluidics.

How thermally efficient are chaotic advection mixers? An experimental assessment

Chaotic Laminar Mixers (CLMs) are static mixers whose concept uses chaotic advection based on the baker's transformation. The present work is an attempt to study CLMs from the viewpoint of heat transfer efficiency and global energy efficiency, and to compare them with helical heat exchangers with the same exchange surface. In the present work, we propose two new CLM geometries alongside two classical geometries. The influence of the number of bends and of the orientation of curvature planes was studied to detect the role of regular and alternate Dean flow. An experimental investigation using water as the inner hot fluid was carried out. It is shown that for the studied range of Reynolds numbers (100–2000), CLMs have a heat transfer efficiency two-times better than helical heat exchangers. However taking into account pressure losses, helical exchangers have global energy efficiency comparable to CLMs. For laminar flows, CLMs might be good heat exchangers when only mixing and heat transfer are required.

Diffusiophoresis, Batchelor scale and effective Péclet numbers

We study the joint mixing of colloids and salt released together in a stagnation point or in a globally chaotic flow. In the presence of salt inhomogeneities, the mixing time is strongly modified depending on the sign of the diffusiophoretic coefficient $D_{dp}$. Mixing is delayed when $D_{dp}>0$ (salt-attracting configuration), or faster when $D_{dp}<0$ (salt-repelling configuration). In both configurations, as for molecular diffusion alone, large scales are barely affected in the dilating direction while the Batchelor scale for the colloids, $\ell _{c,diff}$, is strongly modified by diffusiophoresis. We propose here to measure a global effect of diffusiophoresis in the mixing process through an effective Péclet number built on this modified Batchelor scale. Whilst this small scale is obtained analytically for the stagnation point, in the case of chaotic advection, we derive it using the equation of gradients of concentration, following Raynal & Gence (Intl J. Heat Mass Transfer, vol. 40 (14), 1997, pp. 3267–3273). Comparing to numerical simulations, we show that the mixing time can be predicted by using the same function as in absence of salt, but as a function of the effective Péclet numbers computed for each configuration. The approach is shown to be valid when the ratio $D_{dp}^{2}/D_{s}D_{c}\gg 1$, where $D_{c}$ and $D_{s}$ are the diffusivities of the colloids and salt.

Topological chaos in active nematics

Active nematics are out-of-equilibrium fluids composed of rod-like subunits, which can generate large-scale, self-driven flows. We examine a microtubule-kinesin-based active nematic confined to two dimensions, exhibiting chaotic flows with moving topological defects. Applying tools from chaos theory, we investigate self-driven advection and mixing on different length scales. Local fluid stretching is quantified by the Lyapunov exponent. Global mixing is quantified by the topological entropy, calculated from both defect braiding and curve extension rates. We find excellent agreement between these independent measures of chaos, demonstrating that the extensile stretching between microtubules directly translates into macroscopic braiding of positive defects. Remarkably, increasing extensile activity (through ATP concentration) does not increase the dimensionless topological entropy. This study represents an application of chaotic advection to the emerging field of active nematics and quantification of the collective motion of an ensemble of defects (through topological entropy) in a liquid crystal. Braiding by topological defects in an active nematic fluid produces macroscopic chaotic advection, such that the defects themselves act as effective stirring rods. The resultant mixing is revealed to be a result of sliding on a molecular scale.

Acoustically Driven Micromixing: Effect of Transducer Geometry.

The ability to drive efficient micromixing on a microfluidic platform is crucial for a wide range of lab-on-a-chip applications. Here, we investigate the ability of acoustic waves generated on different geometric surfaces (concave and convex) to enhance the micromixing efficiency in droplet acoustomicrofluidic systems, and, concomitantly, to reduce the power consumption in these devices for a given performance requirement. Quite counterintuitively, we observe that although the acoustic streaming velocity, which scaled inversely with the droplet size, tended to be generally lower (by approximately 45%) when the flow is generated by transducers with convex surfaces compared to those with concave surfaces, the mixing efficiency is disproportionately higher: compared to pure diffusional mixing in the absence of the acoustic forcing, the mixing efficiency due to the acoustically driven convection increased by up to 25% and 43% on these respective surfaces. As such, the mixing enhancement cannot simply be attributed to an increase in the convective flow arising from the acoustic forcing. Rather, we observe the mixing enhancement to be due to the stronger chaotic advection arising in the transducer with the convex surface due to its diverging acoustic field into the droplet.

Field Trials of Chaotic Advection to Enhance Reagent Delivery

AbstractChaotic advection is a novel approach that has the potential to enhance contact between an injected reagent and target contaminants, and thereby improve the effectiveness of in situ treatment technologies. One configuration that is capable of generating chaotic advection is termed the rotated potential mixing (RPM) flow. A conventional RPM flow system involves periodically reoriented dipole flow driven by transient switching of pressures at a series of radial wells. To determine whether chaotic advection can be engineered using such an RPM flow system, and to assess the consequent impact on the spatial distribution of a conservative tracer, a series of field‐scale experiments were conducted. These experiments involved the injection of a tracer in the center of a circular array of wells followed by either mixing using an engineered RPM flow system to invoke chaotic advection, or by natural processes (advection and diffusion) as the control. Pressure fluctuations from the mixing tests using the RPM flow system showed consistent peak amplitudes during injection and extraction at a frequency corresponding to the switching time, suggesting that the target hydraulic behavior was achieved with the time‐dependent flow field. The tracer breakthrough responses showed oscillatory behavior at all monitoring locations during the mixing tests which indicated that the desired RPM flow was generated. The presence of chaotic advection was supported by comparisons to observations from a previous laboratory experiment using RPM flow, and the Fourier spectrum of the temporal tracer data. Results from several quantitative metrics adopted to demonstrate field‐scale evidence of chaotic advection showed that mixing led to improved lateral tracer spreading and approximately uniform concentrations across the monitoring network. The multiple lines of evidence assembled in this proof‐of‐concept study conclusively demonstrated that chaotic advection can be engineered at the field scale. This investigation is a critical step in the development of chaotic advection as a viable and efficient approach to enhance reagent delivery.

Design and production of a novel microfluidic device for the capture and isolation of circulating tumor cell clusters

The three main challenges of cancer treatment are metastases, recurrence, and acquired therapy resistance. These challenges have been closely linked to circulating cancer cell clusters. A detailed understanding of their genetic and morphological composition is essential. This will not only improve our knowledge of basic cancer biology but enable the successful development of much needed therapies preventing the three main challenges mentioned above. Extensive research effort is underway to isolate, capture, and analyze circulating tumor cells. However, few if any current efforts specifically target cancer cell clusters, and their much greater ability to initiate new tumors. Growing scientific consensus over the last five years has convincingly established the importance of targeting circulating cancer cell clusters verses individual CTCs to prevent the occurrence of metastatic disease. Based on the increased clinical importance of cancer cell clusters as the main driver of cancer metastasis, new and improved methods are much needed to access these larger multi-celled structures. Microfluidic devices offer a readily accessible platform for a customizable microenvironment for cell isolation and analysis. In this study, we show how a well-known passive micromixer design (staggered herringbone mixer - SHM) can be optimized to induce maximum chaotic advection within antibody-coated channels of dimensions appropriate for the capture of cancer cell clusters. The device’s principle design configuration is called: Single-Walled Staggered Herringbone (SWaSH). The preliminary empirical results of our work show that utilization of extensive simulation and modeling can accelerate the development of a working prototype that allows for target-specific cancer cell cluster isolation.

Performance and implementation of centrifugal serpentine micromixers with non-rectangular cross-section

The fluid flow and mixing characteristics of planar serpentine microchannels consisting of repeating S-shaped units was characterized both computationally and experimentally for Reynolds numbers Re < 100. In particular, it was found that using non-rectangular cross-sections with changing orientation for the geometrical units greatly enhances their mixing performance relative to standard rectangular profile serpentine channels. The optimization of the cross-section enables efficient mixing of two-fluid components at Reynolds numbers as low as 20, making these designs practical for chemical reaction engineering and biological assays platforms. A computational analysis of the cross-sectional flow structures present in this type of channels indicates that their enhanced performance is correlated with the formation of secondary transversal vortexes. In the optimal designs, their presence increases the mass transfer in the microchannel by both stretching the interface between the fluid components to be mixed, as well as by promoting chaotic advection.

Chaotic mixing in crystalline granular media

We study the Lagrangian kinematics of steady three-dimensional Stokes flow over simple cubic (SC) and body-centred cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing in these crystalline structures. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media, such as open pore networks, with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices posses the same symmetry point group, these differences are explained in terms of their space groups. This insight is used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation. These results point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.

On the application of the depth-averaged random walk method to solute transport simulations

Abstract Most numerical studies on solute mixing rely on mesh-based methods, and complicated schemes have been developed to enhance numerical stability and reduce artificial diffusion. This paper systematically studies the depth-averaged random walk scheme, which is a meshfree method with the merits of being highly robust and free of numerical diffusion. First, the model is used to solve instantaneous release problems in uniform flows. Extensive parametric studies are carried out to investigate the influences of the number of particles and the size of time steps. The predictions are shown to be independent of time steps but are sensitive to the particle numbers. Second, the model is applied to the solute transport problem along an estuary subject to extensive wetting and drying during tidal oscillations. Finally, the model is used to investigate the wind-induced chaotic mixing in a shallow basin. The effect of diffusion on the chaotic mixing is investigated. This study proposes a generic sampling method to interpret the output of the random walk method and highlights the importance of accurately taking diffusion into account in analysing the transport phenomena. The sampling technique also offers a guideline for estimating the total number of particles needed in the application.

Effect of screw configuration on the dispersion and properties of polypropylene/multiwalled carbon nanotube composite

AbstractThe effect of extruder screw configuration on the dispersion and properties of compatibilised polypropylene (PP)/multi‐walled carbon nanotube (MCNT) composite is investigated. Three principle screw designs with mainly conveying elements (medium intensity), kneading elements (high intensity), and folding elements (chaotic mixing) were used to prepare polypropylene nanocomposites containing 4wt% of maleic anhydride grafted polypropylene (MAH‐g‐PP) compatibilizer and different nanotube loadings. The effect of each screw configuration and nanotube loading on the tensile, rheological, and electrical properties of the nanocomposites were studied. The screw configurations were found to have a strong influence on the electrical resistivity while only slightly affected the tensile properties of the nanocomposites. Scanning electron microscopy examinations showed that the use of screw configuration consisting of kneading elements promoted the dispersion of nanotubes and resulted in a low electrical percolation at 2wt% of MCNT.

Competition between chaotic advection and diffusion: stirring and mixing in a 3-D eddy model

Abstract. The importance of chaotic advection relative to turbulent diffusion is investigated in an idealized model of a 3-D swirling and overturning ocean eddy. Various measures of stirring and mixing are examined in order to determine when and where chaotic advection is relevant. Turbulent diffusion is alternatively represented by (1) an explicit, observation-based, scale-dependent diffusivity, (2) stochastic noise, added to a deterministic velocity field, or (3) explicit and implicit diffusion in a spectral numerical model of the Navier–Stokes equations. Lagrangian chaos in our model occurs only within distinct regions of the eddy, including a large chaotic “sea” that fills much of the volume near the perimeter and central axis of the eddy and much smaller “resonant” bands. The size and distribution of these regions depend on factors such as the degree of axial asymmetry of the eddy and the Ekman number. The relative importance of chaotic advection and turbulent diffusion within the chaotic regions is quantified using three measures: the Lagrangian Batchelor scale, the rate of dispersal of closely spaced fluid parcels, and the Nakamura effective diffusivity. The role of chaotic advection in the stirring of a passive tracer is generally found to be most important within the larger chaotic seas, at intermediate times, with small diffusivities, and for eddies with strong asymmetry. In contrast, in thin chaotic regions, turbulent diffusion at oceanographically relevant rates is at least as important as chaotic advection. Future work should address anisotropic and spatially varying representations of turbulent diffusion for more realistic models.

Temporal Fluctuations and Poroelasticity Can Generate Chaotic Advection in Natural Groundwater Systems

AbstractAlthough steady, isotropic Darcy flows are inherently laminar and nonmixing in the absence of diffusion, it is well understood that transient forcing via engineered pumping schemes can induce rapid, chaotic mixing flows in groundwater. In this study we explore the propensity for such mixing to arise in natural groundwater systems subject to cyclical forcings, for example, tidal or seasonal influences. Using a conventional linear groundwater flow model subject to tidal forcing, we show that under certain conditions these flows generate Lagrangian transport and mixing phenomena (chaotic advection) near the tidal boundary. We show that aquifer heterogeneity, storativity, and forcing magnitude cause reversals in flow direction over the forcing cycle which, in turn, generate coherent Lagrangian structures and chaos. These features significantly augment fluid mixing and transport, leading to anomalous residence time distributions, flow segregation, and the potential for profoundly altered reaction kinetics. We define the dimensionless parameter groups which govern this phenomenon and explore these groups in connection with a set of well‐characterized tidal systems. The potential for Lagrangian chaos to be present near discharge boundaries must be recognized and assessed in field studies.