Acoustically induced bubbles in a microfluidic channel for mixing enhancement

Due to small dimensions and low fluid velocity, mixing in microfluidic systems is usually poor. In this study, we report a method of enhancing microfluidic mixing using acoustically induced gas bubbles. The effect of applied frequency on mixing was investigated over the range 0.5–10 kHz. Under either low frequency 0.5 kHz or high frequency 10 kHz, no noticeable improvement in the present mixer was observed. However, a significant increase in the mixing efficiency was achieved within a window of the frequencies between 1.0 and 5.0 kHz. It was found in our present microfluidic structure, single (or multi-) bubble(s) could be acoustically generated under the frequency ranging from 1.0 to 5.0 kHz by a piezoelectric disc. The interaction between bubble and acoustic field causes bubble oscillation which in turn could disturb local flow field to result in mixing enhancement.     

An Eulerian–Lagrangian approach for simulating explosions of energetic devices

An approach for the simulation of explosions of “energetic devices” is described. In this context, an energetic device is a metal container filled with a high explosive (HE). Examples include bombs, mines, rocket motors or containers used in storage and transport of HE material. Explosions may occur due to detonation or deflagration of the HE material, with initiation resulting from either mechanical or thermal input. This approach is applicable to a wide range of fluid–structure interaction scenarios, the application to energetic devices is chosen because it demonstrates the full capability of this methodology.Simulations of this type are characterized by a number of interesting and challenging behaviors. These include the transformation of the solid HE into highly pressurized gaseous products that initially occupy regions which formerly contained only solid material. This rapid pressurization of the container leads to large deformations at high strain rates and eventual case rupture. Once the container breaks apart, the highly pressurized product gas that escapes the failing container generates shock waves that propagate through the initially quiescent surrounding fluid.The approach, which uses a finite-volume, multi-material compressible CFD formulation, within which solid materials are represented using a particle method known as the Material Point Method, is described, including certain of the sub-grid models required to close the governing equations. Results are first presented for “rate stick” and “cylinder test” scenarios, each of which involves detonating unconfined and confined HE material, respectively. Experimental data are available for these configurations and as such they serve as validation tests. Finally, results from an unvalidated “fast cookoff” simulation in which the HE is initiated by thermal input, which causes deflagration, are shown.     

Vortex and strain skeletons in Eulerian and Lagrangian frames

We present an approach to analyze mixing in flow fields by extracting vortex and strain features as extremal structures of derived scalar quantities that satisfy a duality property: they indicate vortical as well as high-strain (saddletype) regions. Specifically, we consider the Okubo-Weiss criterion and the recently introduced MZ-criterion. While the first is derived from a purely Eulerian framework, the latter is based on Lagrangian considerations. In both cases high values indicate vortex activity whereas low values indicate regions of high strain. By considering the extremal features of those quantities, we define the notions of a vortex and a strain skeleton in a hierarchical manner: the collection of maximal 0D, 1D and 2D structures assemble the vortex skeleton; the minimal structures identify the strain skeleton. We extract those features using scalar field topology and apply our method to a number of steady and unsteady 3D flow fields.     

Evolution of mixing in a microfluidic reverse-staggered herringbone micromixer

Microfluidic platforms offer a variety of advantages including improved heat transfer, low working volumes, ease of scale-up, and stronger user control on operating parameters. However, flow within microfluidic channels occurs at low Reynolds number (Re), which makes mixing difficult to accomplish. Adding V-shaped ridges to channel walls, a pattern called the staggered herringbone design (SHB), alleviates this problem by introducing transverse flow patterns that enable enhanced mixing. Building on our prior work, we here developed a microfluidic mixer utilizing the SHB geometry and characterized using CFD simulations and complimentary experiments. Specifically, we investigated the performance of this type of mixer for unequal species diffusivities and inlet flows. A channel design with SHB ridges was simulated in COMSOL Multiphysics® software under a variety of operating conditions to evaluate its mixing capabilities. The device was fabricated using soft-lithography techniques to experimentally visualize the mixing process. Mixing within the device was enabled by injecting fluorescent dyes through the device and imaging using a confocal microscope. The device was found to efficiently mix fluids rapidly, based on both simulations and experiments. Varying Re or species diffusion coefficients had a weak effect on the mixing profile, due to the laminar flow regime and insufficient residence time, respectively. Mixing effectiveness increased as the species flow rate ratio increased. Fluid flow patterns visualized in confocal microscope images for selective cases were strikingly similar to CFD results, suggesting that the simulations serve as good predictors of device performance. This SHB mixer design would be a good candidate for further implementation as a microfluidic reactor.     

An alternative mixed Eulerian Lagrangian approach to high speed collision between solid structures on parallel clusters

The conventional approach to the analysis of collision problems, where a projectile penetrates a structure, involves a Lagrangian–Lagrangian contact driven methodology. Over the years there has been an enduring interest in collision type problems. However, since the events of 11th September 2001 (9/11) there has emerged a particular interest in projectile–structure collision events which simultaneously involve combustion, significant heat transfer and melting. These latter aspects are conventionally modelled using an Eulerian approach with computational fluid dynamics (CFD) software technology. Thus to model high speed collision in a comprehensive manner, it is necessary to take full advantage of the wide range of physics represented by CFD codes and explicit dynamic structural FE codes, which is not a trivial matter.The strain rates are so high in the neighbourhood of the collision that in representing the material behaviour as plastic one can formulate a model in an Eulerian manner. Thus, if the projectile–structure interaction can be captured adequately by an Eulerian approach, then one could use conventional CFD technology to model the whole spectrum of physics where combustion is simultaneously involved. As such, the prime objective of this paper is to implement and evaluate the use of conventional Eulerian CFD technology using well established free surface algorithms to capture the multi-material behaviour in a fixed grid environment and to evaluate the performance and whether the parallel scalability can be preserved. The paper is completed by a preliminary evaluation of whether compatible Eulerian and Lagrangian code modules can be coupled to capture the elastic behaviour of the structure far from the collision site.     

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle-based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid-based advection in other regions of the flow. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C¹ continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.     

Efficient batch-mode mixing and flow patterns in a microfluidic centrifugal platform: a numerical and experimental study

During recent years centrifugal-based microfluidic devices known as Lab-on-a-CD have attracted a lot of attentions. Applications of these CD-based platforms are ubiquitous in numerous biological analyses and chemical syntheses. Mixing of different species in microscale is one of the essential operations in biochemical applications where this seemingly simple task remains a major obstruction. Application of centrifugal force, however, may significantly improve the flow agitation and mixing, especially when it is combined with the Coriolis force which acts perpendicular to centrifugal force. In this study, mixing process in minichambers located on a rotating platform under a periodic acceleration and deceleration angular velocity profile is investigated both numerically and experimentally. We have incorporated various arrangements of obstacles and baffles, which are usually used in stationary mixers, within a batch-mode rotating mixing chamber. Subsequently, the effect of these obstacles on flow field and mixing process has been studied, and among these arrangements four cases have been selected for further experimental analysis. Experimental studies have been performed on a multi-layer CD platform fabricated in polycarbonate plates, and subsequently mixing has been investigated in these minichambers. The quantitative mixing data were obtained after a set of image analyses on the captured images of mixing chamber during the process and the results were compared with the simulation. The results indicate a good resemblance between the two studies both qualitatively and quantitatively. Furthermore, it has been shown that the application of obstacles and baffles together in chamber results in reducing the mixing time more than 50 % as compared to a chamber without any obstacle and/or baffle configuration. Obtaining mixing times less than 10 s in both studies, makes these CD-based platforms an appropriate device for many applications in which a cost-effective device as well as low mixing time is required.

     

Effective mixing in a microfluidic oscillator using an impinging jet on a concave surface

In this study, we present a microfluidic oscillator design that employs an impinging jet on a concave surface to enhance the microscale mixing process. The Coand? effect along with the G?rtler instability proves to incite sustainable flapping motion beyond the obstacle and mixing is profoundly improved. From the flow visualization results, four different regimes are identified and we find that the primary enhancement of mixing performance is always linked to the transition of flow regime. Moreover, incorporating a sudden-expansion confluence provokes flow three dimensionality and elevates the mixing level significantly at low Reynolds numbers. For a Reynolds number as low as 70, the tail flow behind the concave obstacle successfully exhibits a periodic oscillation and Hopf bifurcation is induced, leading to a drastic augmentation in the time-average mixing efficiency. By utilizing the spectrum analysis, the characteristic frequency of flapping motion is found to vary linearly with the throat velocity, resulting in a constant Strouhal number of 3.8?×?10^?5.     

Control of mixing in fluid flow: a maximum entropy approach

In many technological processes a fundamental stage involves the mixing of two or more fluids. As a result, the design of optimal mixing protocols is a problem of both fundamental and practical importance. In this paper, the authors formulate a prototypical mixing problem in a control framework, where the objective is to determine the sequence of fluid flows that will maximize entropy. By developing the appropriate ergodic-theoretic tools for the determination of entropy of periodic sequences, they derive the form of the protocol which maximizes entropy among all of the possible periodic sequences composed of two shear flows orthogonal to each other. The authors discuss the relevance of their results in the interpretation of previous studies of mixing protocols     

A numerical design study of chaotic mixing of magnetic particles in a microfluidic bio-separator

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).     

Magnetophoretic mixing for in situ immunochemical binding on magnetic beads in a microfluidic channel

Functionalized magnetic beads offer promising solutions to a host of micro-total analysis systems ranging from immunomagnetic biosensors to cell separators. Immunochemical binding of functional biochemical agents or target biomolecules serves as a key step in such applications. Here we show how magnetophoretic motion of magnetic microspheres in a microchannel is harnessed to promote in situ immunochemical binding of short DNA strands (probe oligonucleotide) on the bead surface via streptavidin–biotin bonds. Using a transverse magnetic field gradient, the particles are transported across a co-flowing analyte stream containing biotinylated probe oligonucleotides that are labeled with a Cy3-fluorophore. Quantification of the resulting biotin–streptavidin promoted binding has been achieved through fluorescence imaging of the magnetophoretically separated magnetic particles in a third stream of phosphate buffered saline. Both the experimental and numerical data indicate that for a given flow rate, the analyte binding per bead depends on the flow fraction of the co-flowing analyte stream through the microchannel, but not on the fluid viscosity. Parametric studies of the effects of fluid viscosity, analyte flow fraction, and total flow rate on the extent of binding and the overall analyte separation rate are also conducted numerically to identify favorable operating regimes of a flow-through immunomagnetic separator for biosensing, cell separation, or high-throughput applications.     

Quantitative analysis of microfluidic mixing using microscale schlieren technique

In this study, we discuss the employment of microscale schlieren technique to facilitate measurement of inhomogeneities in a micromixer. By mixing dilute aqueous ethanol and water in a T-microchannel, calibration procedures are carried out to obtain the relation between the concentration gradients and grayscale readouts under various incident illuminations, concentrations of aqueous ethanol solution, and knife-edge cutoffs. We find that to broaden measuring range with minimal error, the luminous exitance should be tuned to have a reference background with an average grayscale readout of 121, and dilute aqueous ethanol solution with a mass fraction of 0.05 should be used along a 50 % cutoff. For concentration gradients greater than 6.8 × 10^?3 or below ?2.5 × 10^?2 μm^?1, the calibration curves show great linearity. Correspondingly, the discernable limit of our microscale schlieren system is 2.3 × 10^?5 μm^?1 for a positive refractive index gradient and ?8.6 × 10^?5 μm^?1 for a negative refractive index gradient. Once the relation between concentration gradients and grayscale readouts is known, the concentration distribution in a microfluidic can be reconstructed by integrating its microscale schlieren image with appropriate boundary conditions. The results prove that the microscale schlieren technique is able to provide spatially resolved, noninvasive, full-field measurements. Since the microscale schlieren technique is directly linked to the measurement of a refractive index gradient, the present method can be easily extended to other scalar quantifications that are related to the variation of refractive index.     

Dual margin approach on a Lagrangian support vector machine

In this paper, we propose a new support vector machine (SVM) called dual margin Lagrangian support vectors machine (DMLSVM). Unlike other SVMs which use only support vectors to determine the separating hyperplanes, DMLSVM utilizes all the available training data for training the classifier, thus producing robust performance. The training data are weighted differently depending on whether they are in a marginal region or surplus region. For fast training, DMLSVM borrows its training algorithm from Lagrangian SVM (LSVM) and tailors the algorithm to its formulation. The convergence of our training method is rigorously proven and its validity is tested on a synthetic test set and UCI dataset. The proposed method can be used in a variety of applications such as a recommender systems for web contents of IPTV services.     

Robust DEA efficiency scores: A probabilistic/combinatorial approach

In this paper we propose robust efficiency scores for the scenario in which the specification of the inputs/outputs to be included in the DEA model is modelled with a probability distribution. This probabilistic approach allows us to obtain three different robust efficiency scores: the Conditional Expected Score, the Unconditional Expected Score and the Expected score under the assumption of Maximum Entropy principle. The calculation of the three efficiency scores involves the resolution of an exponential number of linear problems. The algorithm presented in this paper allows to solve over 200 millions of linear problems in an affordable time when considering up 20 inputs/outputs and 200 DMUs. The approach proposed is illustrated with an application to the assessment of professional tennis players.     

On uniform convergence rates for Eulerian and Lagrangian finite element approximations of convection-dominated diffusion problems

Abstract Standard error estimates in the literature for finite element approximations of nonstationary convection-diffusion problems depend either reciprocally on the diffusion parameter or on higher order norms of the solution. Therefore, the estimates generally become worthless in the convection-dominated case with 0 < 1. In this work we develop a rigorous -uniform convergence theory for finite element discretizations of convection-dominated diffusion problems in Eulerian and Lagrangian coordinates. Here, the constants that arise in the error estimates depend on norms of the data and not of the solution and remain bounded in the hyperbolic limit 0. In particular in the Lagrangian case this requires modifications to standard finite element error analyses. In the Eulerian formulation -uniform convergence of order one half is proven whereas in the Lagrangian framework -uniform convergence of optimal order is established. The estimates are based on -uniform a priori estimates for the solution of the continuous problems which are derived first.     

An Eulerian approach for constructing a map between surfaces with different topologies

3D objects of the same kind often have different topologies, and finding correspondence between them is important for operations such as morphing, attribute transfer, and shape matching. This paper presents a novel method to find the surface correspondence between topologically different surfaces. The method is characterized by deforming the source polygonal mesh to match the target mesh by using the intermediate implicit surfaces, and by performing a topological surgery at the appropriate locations on the mesh. In particular, we propose a mathematically well‐defined way to detect the topology change of surface by finding the non‐degenerate saddle points of the velocity fields that tracks implicit surfaces. We show the effectiveness and possible applications of the proposed method through several experiments.     

Enhanced bioreaction efficiency of a microfluidic mixer toward high-throughput and low-cost bioassays

Microscale bioreactors are an important tool in performing bioassays. The speed and efficiency of these devices is often limited by the rate of reagent mixing. In spite of the various micromixing approaches, the coupled mixing/reaction process has yet to be clearly understood. This article presents experimental and computational studies on the enhancement of bioreaction rates using a novel cilia reactor. In the experiments, a biotin-avidin assay and a DNA hybridization assay were conducted to show the benefit of a cilia bioreactor compared with a simple diffusion reactor. A cilia reactor showed a shorter reaction time for approaching equilibrium. A numerical computation examined the bioreaction rate of the cilia reactor compared with the diffusion for (1) a biotin-avidin assay, (2) an immunoassay, and (3) a DNA hybridization assay. The reaction rate was characterized for each assay using the Damk?hler number (Da). When Da was greater than 10², the ratio of reaction time for the diffusion to cilia reactors linearly increased with Da, which could also save reagent usage by lowering the concentration of reagent probes. However, when the system had a Da smaller than 10², the reaction time of a cilia reactor could not be shortened because the assay was dominated by reaction rather than fluid mixing. The results offer a general approach for enhancing bioreaction rates by employing microfluidic mixers for a bioassay.