Fast Mixing Research Articles

An asymmetric flow-focusing droplet generator promotes rapid mixing of reagents

Nowadays droplet microfluidics is widely used to perform high throughput assays and for the synthesis of micro- and nanoparticles. These applications usually require packaging several reagents into droplets and their mixing to start a biochemical reaction. For rapid mixing microfluidic devices usually require additional functional elements that make their designs more complex. Here we perform a series of 2D numerical simulations, followed by experimental studies, and introduce a novel asymmetric flow-focusing droplet generator, which enhances mixing during droplet formation due to a 2D or 3D asymmetric vortex, located in the droplet formation area of the microfluidic device. Our results suggest that 2D numerical simulations can be used for qualitative analysis of two-phase flows and droplet generation process in quasi-two-dimensional devices, while the relative simplicity of such simulations allows them to be easily applied to fairly complicated microfluidic geometries. Mixing inside droplets formed in the asymmetric generator occurs up to six times faster than in a conventional symmetric one. The best mixing efficiency is achieved in a specific range of droplet volumes, which can be changed by scaling the geometry of the device. Thus, the droplet generator suggested here can significantly simplify designs of microfluidic devices because it enables both the droplet formation and fast mixing of the reagents within droplets. Moreover, it can be used to precisely estimate reaction kinetics.

An Investigation of Flow Patterns and Mixing Characteristics in a Cross-Shaped Micromixer within the Laminar Regime.

A fast mixing is critical for subsequent practical development of microfluidic devices, which are often used for assays in the detection of reagents and samples. The present work sets up computational fluid dynamics simulations to explore the flow characteristic and mixing mechanism of fluids in cross-shaped mixers within the laminar regime. First, the effects of increasing an operating parameter on local mixing quality along the microchannels are investigated. It is found that sufficient diffusion cannot occur even though the concentration gradient is large at a high Reynolds number. Meanwhile, a method for calculating local mixing efficiency is also characterized. The mixing efficiency varies exponentially with the flow distance. Second, in order to optimize the cross-shaped mixer, the effects of design parameters, namely aspect ratio, mixing angle and blockage, on mixing quality are captured and the visualization of velocity and concentration distribution are demonstrated. The results show that the aspect ratio and the blockage play an important role in accelerating the mixing process. They can improve the mixing efficiency by increasing the mass transfer area and enhancing the chaotic advection, respectively. In contrast, the inflow angle that affects dispersion length is not an effective parameter. Besides, the surface roughness, which makes the disturbance of fluid flow by roughness more obvious, is considered. Three types of rough elements bring benefits for enhancing mixing quality due to the convection induced by the lateral velocity.

Random-Cluster Dynamics on Random Regular Graphs in Tree Uniqueness

We establish rapid mixing of the random-cluster Glauber dynamics on random varDelta -regular graphs for all qge 1 and p<p_u(q,varDelta ), where the threshold p_u(q,varDelta ) corresponds to a uniqueness/non-uniqueness phase transition for the random-cluster model on the (infinite) varDelta -regular tree. It is expected that this threshold is sharp, and for q>2 the Glauber dynamics on random varDelta -regular graphs undergoes an exponential slowdown at p_u(q,varDelta ). More precisely, we show that for every qge 1, varDelta ge 3, and p<p_u(q,varDelta ), with probability 1-o(1) over the choice of a random varDelta -regular graph on n vertices, the Glauber dynamics for the random-cluster model has varTheta (n log n) mixing time. As a corollary, we deduce fast mixing of the Swendsen–Wang dynamics for the Potts model on random varDelta -regular graphs for every qge 2, in the tree uniqueness region. Our proof relies on a sharp bound on the “shattering time”, i.e., the number of steps required to break up any configuration into O(log n) sized clusters. This is established by analyzing a delicate and novel iterative scheme to simultaneously reveal the underlying random graph with clusters of the Glauber dynamics configuration on it, at a given time.

Fabrication and characteristic study on mixing enhancement of a magnetofluidic mixer

The needs for fast mixing of two miscible fluids in microfluidic device is increasing recently and has been widely used for DNA synthesis, clinic diagnostics and chemical reaction. However, the mixing at microscale relies heavily on slow molecular diffusion because of its low Reynolds number and thus laminar flow. In this work, therefore, a magnetofluidic mixer with the integration of magnetic field is presented for rapid mixing between ferrofluid and distilled water with no harmful Joule heat generated. Parametric study of experiment and simulation was performed to discuss the effect of flow rate, placement angle of magnet and width of magnet on the mixing efficiency between two fluids. It was found that the mixing performance of 0.76 was the most homogeneous when the angle α = 1/12π because of the acceleration-deceleration couples (ADC) and mass conservation law. It was also found that the mixing performance increases from 0.13 to 0.49 as the magnet width increases from wm=50μm to wm=250μm while decreases when magnet width is wider than wm=250μm due to local reduced Peclet number. The developed micromixer and mixing mechanism will be of great potentials and insight for future quick optimization of biomedical and chemical mixing devices.

Characterizing limits and opportunities in speeding up Markov chain mixing

A variety of paradigms have been proposed to speed up Markov chain mixing, ranging from non-backtracking random walks to simulated annealing and lifted Metropolis–Hastings. We provide a general characterization of the limits and opportunities of different approaches for designing fast mixing dynamics on graphs using the framework of “lifted Markov chains”. This common framework allows to prove lower and upper bounds on the mixing behavior of these approaches, depending on a limited set of assumptions on the dynamics. We find that some approaches can speed up the mixing time to diameter time, or a time inversely proportional to the graph conductance, while others allow for no speedup at all.

Design and application of a self-pumping microfluidic staggered herringbone mixer

The rapid mixing of reagents is critical to a wide range of chemical and biological reactions but is difficult to implement in microfluidic devices, particularly in capillary action/passive pumping devices or in point-of-need environments. Here, we develop a self-pumping asymmetric staggered herringbone mixer made from only laser-ablated glass and tape. This lab-on-a-chip platform is capable of rapid flow (0.14 mL min−1, 1 cm s−1) and fast mixing (< 10 s) without external forces or pumps and is amenable to the flow of non-aqueous solvents. Furthermore, the degree of mixing and flow rates are easily tunable through the length and depth of the herringbone grooves, and the thickness of the double-sided tape that defines the channel height, respectively. The device utility is demonstrated for chemical and biological assays through the reaction of Ni(II) and DMG in ethanol/water and the enzymatic reaction of o-dianisidine with peroxidase, respectively.

Detonation Re-initiation behind an Aluminum Foam Plate in Stoichiometric Methane-oxygen Mixture

ABSTRACT Porous materials can be used for accidental explosion prevention and suppression in process industries. In this study, an experimental study was conducted to study the effect of an aluminum foam plate on stoichiometric methane-oxygen detonation propagation behavior at different initial pressures (i.e., 10 kPa to 50 kPa). Experiments were carried out in a 4.4-m long, 48-mm diameter tube. Downstream of the foam plate, the detonation velocity was measured using even-spaced photodiodes, and the detonation structure evolution was recorded using the soot foil technique. The density of the aluminum foam was 1.1 g/cm3 and the thicknesses were 10 mm and 15 mm. Results demonstrate that behind the foam plate, the detonation fails first and re-initiates after a certain distance (re-initiation distance). At the end of the tube, the detonation velocity can be steady although the velocity fluctuation is significant downstream of the plate. The soot pattern indicates that the onset of detonation is achieved via the interaction between shock waves and wall, and fast turbulence mixing. For the case of the 10-mm foam plate, the single-headed mode can be observed. Generally, the re-initiation distance increases with the cell size. When the single-headed spin appears, the re-initiation distance is decreased notably.

Two Electrical Engineers, One Problem, and Evolution Produced the Same Solution: A Historical Note.

This note adds historical context into solving the problem of improving the speed of the step response of a low-order plant in two different types of control systems, a chemical mixing system and the human saccadic system. Two electrical engineers studied the above problem: one to understand and model how nature and evolution solved it and the other to design a control system to solve it in a man-made commercial system. David A. Robinson discovered that fast and accurate saccades were produced by a pulse-step of neural innervation applied to the extraocular plant. Leonidas M. Mantgiaris invented a method to achieve rapid and accurate chemical mixing by applying a large stimulus for a short period of time and then replacing it with the desired steady-state value (i.e., a “pulse-step” input). Thus, two humans used their brains to: 1) determine how the human brain produced human saccades; and 2) invent a control-system method to produce fast and accurate chemical mixing. That the second person came up with the same method by which his own brain was making saccades may shed light on the question of whether the human brain can fully understand itself.

Modelling the Effects of Boundary Walls on the Fire Dynamics of Informal Settlement Dwellings

Characterising the risk of the fire spread in informal settlements relies on the ability to understand compartment fires with boundary conditions that are significantly different to normal residential compartments. Informal settlement dwellings frequently have thermally thin and leaky boundaries. Due to the unique design of these compartments, detailed experimental studies were conducted to understand their fire dynamics. This paper presents the ability of FDS to model these under-ventilated steel sheeted fire tests. Four compartment fire tests were modelled with different wall boundary conditions, namely sealed walls (no leakage), non-sealed walls (leaky), leaky walls with cardboard lining, and highly insulated walls; with wood cribs as fuel and ISO-9705 room dimensions. FDS managed to capture the main fire dynamics and trends both qualitatively and quantitatively. However, using a cell size of 6 cm, the ability of FDS to accurately model the combustion at locations with high turbulent flows (using the infinitely fast chemistry mixing controlled combustion model), and the effect of leakage, was relatively poor and both factors should be further studied with finer LES filter width. Using the validated FDS models, new flashover criteria for thermally thin compartments were defined as a combination of critical hot gas layer and wall temperatures. Additionally, a parametric study was conducted to propose an empirical correlation to estimate the onset Heat Release Rate required for flashover, as current knowledge fails to account properly for large scale compartments with thermally thin boundaries. The empirical correlation is demonstrated to have an accuracy of ≈ ± 10% compared with the FDS models.

Yeşil sentez yoluyla mikrosistemlerde çinko oksit nanopartiküllerin üretimi ve karakterizasyonu

Nanoparticles (NP), which can be produced for many different fields and purposes; are at size vary from nanometer to a micrometer. These particles can be prepared by different approaches such as chemical, physical and biological methods. However, the biological approach is the most promising approach among other methods due to its simplicity and environmentally friendly conditions. The production of the nanoparticle by means of a biological approach does not require any high temperature, acidic/basic conditions and hazardous chemicals. Therefore, this method is named “green synthesis”. Development in microtechnology has had profound effects in many areas such as drug discovery, biology, diagnosis, and tissue engineering. Microfluidics which focuses on the processing of liquids in microscale systems has attracted wide attention in the production process of nanoparticles due to precise control and fast mixing. The main purpose of this study is to produce and characterize metal nanoparticles by combining microsystems and green synthesis approaches. For this purpose, in the first step, the design of microsystems that suitable for the flow of different phases was performed. In the second step, ZnO nanoparticle synthesis was carried out using the red cabbage (Brassica oleracea var.capitata f. Rubra) extracts. The synthesis of nanoparticles achieved by optimizing different parameters such as; extract: zinc ratio, zinc solution concentration, flow rates, and flow rates ratio in the microsystem and temperature. The results showed that the herbal red cabbage components can be used for the green synthesis of ZnO nanoparticles.

A pre-expectation calculus for probabilistic sensitivity

Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When programs are probabilistic, the distance between outputs is a distance between distributions. The Kantorovich lifting provides a general way of defining a distance between distributions by lifting the distance of the underlying sample space; by choosing an appropriate distance on the base space, one can recover other usual probabilistic distances, such as the Total Variation distance. We develop a relational pre-expectation calculus to upper bound the Kantorovich distance between two executions of a probabilistic program. We illustrate our methods by proving algorithmic stability of a machine learning algorithm, convergence of a reinforcement learning algorithm, and fast mixing for card shuffling algorithms. We also consider some extensions: using our calculus to show convergence of Markov chains to the uniform distribution over states and an asynchronous extension to reason about pairs of program executions with different control flow.

The desalting/salting pathway: a route to form metastable aggregates with tuneable morphologies and lifetimes.

We investigate the formation/re-dissociation mechanisms of hybrid complexes made from negatively charged PAA2k coated γ-Fe2O3 nanoparticles (NP) and positively charged polycations (PDADMAC) in aqueous solution in the regime of very high ionic strength (I). When the building blocks are mixed at large ionic strength (1 M NH4Cl), the electrostatic interaction is screened and complexation does not occur. If the ionic strength is then lowered down to a targeted ionic strength Itarget, there is a critical threshold Ic = 0.62 M at which complexation occurs, that is independent of the charge ratio Z and the pathway used to reduce salinity (drop-by-drop mixing or fast mixing). If salt is added back up to 1 M, the transition is not reversible and persistent out-of-equilibrium aggregates are formed. The lifetimes of such aggregates depends on Itarget: the closer Itarget to Ic is, the more difficult it is to dissolve the aggregates. Such peculiar behavior is driven by the inner structure of the complexes that are formed after desalting. When Itarget is far below Ic, strong electrostatic interactions induce the formation of dense, compact and frozen aggregates. Such aggregates can only poorly reorganize further on with time, which makes their dissolution upon resalting almost reversible. Conversely, when Itarget is close to Ic more open aggregates are formed due to weaker electrostatic interactions upon desalting. The system can thus rearrange with time to lower its free energy and reach more stable out-of-equilibrium states which are very difficult to dissociate back upon resalting, even at very high ionic strength.

Modeling snowflake divertors in MAST-U tokamak using UEDGE code

In a snowflake (SF) divertor, two magnetic field nulls are placed close to each other creating four strike points (SPs) cf. two in a standard single-null (SN) divertor. In preparation to MAST-U experiments, magnetic configurations with SN and SF divertors located symmetrically at the top and at the bottom of the tokamak were modeled using a two-dimensional multi-fluid code UEDGE with a full plasma transport model featuring charge-state-resolved sputtered carbon impurities. SF configurations with various relative locations of the nulls and small null separation were considered. The complex interplay of the plasma transport and magnetic configurations was comprehensively studied using a simple model for the theoretically predicted fast plasma mixing (the “churning” mode) in the two-null SF region. The modeling results show that: 1) SF-plus and SF-minus configurations with closely located nulls produce same plasma parameters and heat fluxes at same SPs; 2) SF divertors approach the outer and inner SP detachment conditions at lower upstream density w.r.t. SN divertor; 3) heat flux profiles at primary SPs are substantially broadened and peak values are reduced in SF configurations w.r.t. SN divertor; this effect becomes more pronounced with the fast plasma mixing increase; 4) with the SF mixing, secondary SPs receive up to 10% (each) of the heat flux to the primary outer SP.

Effect of conical section structure on liquid-liquid cyclone reactor for isobutane alkylation catalyzed by ionic liquid

The liquid-liquid cyclone reactor (LLCR) integrating fast mixing and quick separation is a promising device for isobutane alkylation catalyzed by ionic liquids. The conical section of LLCR is an essential part where both mixing and separation occur. To optimize the mixing and separation performance of LLCR, four designs of the conical section (single-cone structure, standard dual-cone structure, parabolic structure and hyperbolic structure) were studied in this work. The cold model experiment and numerical simulation were carried out to investigate the distribution of light phase, mixing performance and separation performance. The formation of the pseudo-steady light phase core was observed from experiments and simulations. The effective mixing zone of LLCR was proposed in this study by obtaining the boundaries of the light phase core and the bottom of the locus of zero axial velocity. The distributions of the turbulent energy dissipation rate and the mean separation efficiency were employed to evaluate the mixing and separation performance, respectively. The result showed that the LLCR with hyperbolic structure were better than the other three structures in terms of mixing performance and separation efficiency.

Real-World Networks Are Not Always Fast Mixing

Abstract The mixing time of random walks on a graph has found broad applications across both theoretical and practical aspects of computer science, with the application effects depending on the behavior of mixing time. It is extensively believed that real-world networks, especially social networks, are fast mixing with their mixing time at most $O(\log N)$ where $N$ is the number of vertices. However, the behavior of mixing time in the real-life networks has not been examined carefully, and exactly analytical research for mixing time in models mimicking real networks is still lacking. In this paper, we first experimentally evaluate the mixing time of various real-world networks with scale-free small-world properties and show that their mixing time is much higher than anticipated. To better understand the behavior of the mixing time for real-world networks, we then analytically study the mixing time of the Apollonian network, which is simultaneously scale-free and small-world. To this end, we derive the recursive relations for all eigenvalues, especially the second largest eigenvalue modulus of the transition matrix, based on which we deduce a lower bound for the mixing time of the Apollonian network, which approximately scales sublinearly with $N$. Our results indicate that real-world networks are not always fast mixing, which has potential implications in the design of algorithms related to mixing time.

Microreaction system combining chaotic micromixing with fast mixing and particle growth in liquid-segmented flow for the synthesis of hazardous ionic materials

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.

The relation between flame surface area and turbulent burning velocity in statistically planar turbulent stratified flames

The relation between turbulent burning velocity and flame surface area for turbulent stratified flames has been analyzed using a direct numerical simulation database. The simulations have been carried out for different initial turbulence intensities and initial integral length scales of equivalence ratio fluctuation for a given root-mean-square value in a globally stoichiometric mixture. Additionally, statistically similar turbulent premixed flames have been considered for comparison. The turbulent burning velocity and flame surface area for stratified flames are found to be significantly smaller than in premixed flames for slow mixing cases (large scalar integral length scale and low turbulence intensity), although this trend weakens in fast mixing cases (low scalar integral length scale and high turbulence intensity). In slow mixing cases, the increase in the burning rate occurs at a smaller proportion than the increase in the flame surface area. The contributions of the components arising from tangential diffusion of displacement speed and cross-scalar dissipation rate to the turbulent burning velocity are found to be negligible in comparison to that arising from the combined reaction and normal diffusion component for all cases. The increased probability of finding fuel-lean and fuel-rich mixture affects the contribution of turbulent burning velocity arising from the combined reaction and normal diffusion component of displacement speed for slow mixing cases. Front-supported flame elements dominate over back-supported flame elements for large scalar length scale cases, but this behavior reverses for small scalar length scale cases. These findings suggest that increases in the burning rate and flame surface area do not take place in the same proportions for turbulent stratified combustion.

Mixing process of two streams within a steam ejector from the perspectives of mass, momentum and energy transfer

There is not a specific technical proposal to be able to achieve a clear presentation of the complex mixing process between the primary and entrained flows within the steam ejector. In this study, a novel ejector model with species transport is proposed that can clearly elucidate how, when, where and to what extent the two streams mix. Systematic quantitative analysis toward the mixing of two streams is performed from the perspectives of mass, momentum and energy transfer. Further, the similarities and differences of the mixing process among three analytical perspectives are clarified. Key results revealed that the mixing mainly occurs at the nearby of the local mixing layer, and there are still some distances from the homogenous mixing state after the mixing chamber process, only up to 80.6% the mixing uniformity φ obtains. Additionally, the mixing layer follows a similar growth trajectory, and φ increases as mixing continues regardless of an analytical perspective. However, a much faster mixing is observed from the mass transfer perspective. Specifically, φM (80.6%) is significantly larger than φV (60.7%) and φE (59.6%) at the mixing chamber outlet. It can be concluded that the essential mass mixing laws of the two streams are not necessarily achieving a complete replication whether from the perspective of momentum or energy transfer. These key findings provide a more in-depth and comprehensive understanding of the mixing process inside the ejector.

Ultrafast control of fractional orbital angular momentum of microlaser emissions

On-chip integrated laser sources of structured light carrying fractional orbital angular momentum (FOAM) are highly desirable for the forefront development of optical communication and quantum information–processing technologies. While integrated vortex beam generators have been previously demonstrated in different optical settings, ultrafast control and sweep of FOAM light with low-power control, suitable for high-speed optical communication and computing, remains challenging. Here we demonstrate fast control of the FOAM from a vortex semiconductor microlaser based on fast transient mixing of integer laser vorticities induced by a control pulse. A continuous FOAM sweep between charge 0 and charge +2 is demonstrated in a 100 ps time window, with the ultimate speed limit being established by the carrier recombination time in the gain medium. Our results provide a new route to generating vortex microlasers carrying FOAM that are switchable at GHz frequencies by an ultrafast control pulse.

Micropillar based active microfluidic mixer for the detection of glucose concentration

Active microfluidic mixer has attracted remarkable interest towards the applications in the Lab on Chip (LoC) for fast and accurate fluid mixing. In this work, the standard MEMS processes have been successfully implemented to fabricate the active electromagnetic microfluidic mixer incorporating micropillar on flexible membrane for glucose measurement. Three main parts of the mixer, i.e., a planar electromagnetic coil with permanent magnet, a mechanical movable membrane with pillar and microfluidic channels that were fabricated separately and later bonded with corona discharging process to complete the construction of the microfluidic mixer. The mechanical movable membrane and microfluidic channels are made of polymer and fabricated using soft-lithography technique. Analysis results show that the fabricated microfluidic mixer operated using low electrical current of below 0.5 A produced the mixing index above 0.8 within 4 s. Mixture analysis of fluid samples tested at frequencies of 1.1 kHz, 2.3 kHz and 3.7 kHz shows much better mixing performance as compared to its passive mode condition. The functionality of the fabricated mixer was tested by mixing the DNS reagent and glucose solution. The detection of glucose concentration in the microfluidic mixer chip is indicated by comparing the correlation coefficient R2 with the conventional method. The evaluation result shows that the R2 of the mixture produced by the fabricated device shows a comparable value with that of conventional method showing a very promising approach for the diabetic patient diagnosis and food analysis.