Chaotic mixing using periodic and aperiodic sequences of mixing protocols in a micromixer

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.     

Control study on mixing enhancement in boundary layers of membrane systems

This paper proposes an activation scheme for improving the mixing in the boundary layer of pressure-driven membrane systems such as reverse osmosis and ultrafiltration. Through the application of an external electric field, a flow of ions in the vicinity of the membrane surface is generated, creating an electro-osmotic flow that should reduce the extent of concentration polarization. An optimal control problem is formulated and solved to determine the waveform of the control action required to produce an electric field that can effectively increase mixing in the vicinity of the membrane surface with improved energy efficiency. This paper uses a mixing index in terms of a measure of spatial gradients of the perturbation velocities, which describes the mixing caused by both length stretching and vortices. The efficacy of the proposed control is validated by Computational Fluid Dynamics (CFD) simulations.     

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.     

Analysis and measurements of mixing in pressure-driven microchannel flow

The mixing phenomena for two fluid streams in pressure-driven rectangular microchannels are analyzed and directly compared with the measurements of mixing intensity for a wide range of aspect ratio (width/depth = 1–20). In the analysis, the three-dimensional transport equation for species mixing was solved using the spectral method in a dimensionless fashion covering a large regime of the normalized downstream distance. The analysis reveals the details of non-uniform mixing process, which originates from the top and bottom walls of the channel and stretches out toward the center of the channel, and its transition to uniformity. Employing different length scales for the non-uniform and uniform mixing regimes, the growth of mixing intensity can be expressed in a simple relationship for various aspect ratios in the large range. The mixing experiments were carried out on silicon- and poly(methyl methacrylate) (PMMA)-based T-type micromixers utilizing fluids of pH indicator (in silicon channel) and fluorescent dye (in PMMA channel) to evaluate the mixing intensity based on flow visualization images. Using conventional microscopes, the experiments demonstrate the mixing intensity as a power law of the stream velocity for all the microfluidic channels tested. The variations of measured mixing intensity with the normalized downstream distance are found in favorable agreement with the numerical simulations. The comparison between the experiments and simulations tells the capabilities and limitations on the use of conventional microscopes to measure the mixing performance.     

GENMIX—A generalized petrological mixing model program

GENMIX is an interactive FORTRAN program to solve generalized petrological mixing models of the type, biotite + sillimanite + quartz = garnet + K-feldspar + water, as well as simple mixing models of the type, basalt = andesite + olivine + pyroxene. The driving program is designed for ease of use and provides facilities for printing, editing, changing and adding analyses or oxides to the data bank from which analyses are selected for use in the model. Analyses also can have Fe ratios changed, be recalculated to sum to 100 percent, or be restored to previous values. The program is suited ideally for teaching purposes, as it is impossible to crash by incorrect data input, due to innumerable error traps and all data being read as characters before being converted to numbers.     

频谱分析仪混频原理深层解析

为了更好的学习、理解及使用频谱分析仪,本文从频谱仪前端的混频器着手,依频段从低到高划分为三部分,重点分析了各个频段混频的原理及特点。并就其混频实现方法进行了详细的比较说明。     

基于循环神经网络的多传感信息融合系统的应用

本文综述了循环神经网络、多传感器信息融合技术的基本原理及方法,分析了信息融合中的关键问题,重点介绍了循环神经网络在多传感器信息融合系统中的应用。     

基于循环神经网络的多传感信息融合系统的应用

本文综述了循环神经网络、多传感器信息融合技术的基本原理及方法，分析了信息融合中的关键问题，重点介绍了循环神经网络在多传感器信息融合系统中的应用。     

A sequential injection microfluidic mixing strategy

A novel micromixing strategy is presented, which exploits the axial diffusion of a continuous sequence of discrete samples in a microchannel expansion. Mixing of a continuous sequence in an electroosmotic flow through a sudden expansion region is first modeled assuming an ideal, square-wave injection. The effect of expansion geometry and injection frequency is investigated. To facilitate sequential injection on-chip, two new sequential sample injection schemes are developed and coupled with an expansion region. The first of these designs produces two sample pairs that flow out of separate channels into a common expansion region. This design results in high axial mixing rates but an inherent bias in the injector produces significant cross-stream concentration gradients in the output. These results indicate that the effectiveness of this micromixing strategy is critically dependant on the injection method. A second injector design effectively eliminates the effect of the injection bias using a symmetric microchannel configuration with three solution inlets. The resulting symmetrical injection micromixer produces a continuous uniform stream, 99% mixed, in only 2.3 mm.     

Electrokinetically driven flow mixing utilizing chaotic electric fields

This paper presents a novel microfluidic mixing scheme in which the species streams are mixed via the application of chaotic electric fields to four electrodes mounted on the upper and lower surfaces of the mixing chamber. Numerical simulations are performed to analyze the effects of the resulting chaotic electrokinetic driving forces on the fluid flow characteristics within the micromixer and the corresponding mixing performance. During simulation, chaotic oscillating electric potentials are derived using a Duffing–Holmes chaos system. Simulation results indicate that the chaotic electrokinetic driving forces induce a complex flow behavior within the micromixer which results in efficient mixing of the two species streams. It is shown that mixing efficiencies up to 95% can be obtained in the novel micromixer.     

Efficient mixing of viscoelastic fluids in a microchannel at low Reynolds number

In this paper, we examined mixing of various two-fluid flows in a silicon/glass microchannel based on the competition of dominant forces in a flow field, namely viscous/elastic, viscous/viscous and viscous/inertial. Experiments were performed over a range of Deborah and Reynolds numbers (0.36 < De < 278, 0.005 < Re < 24.2). Fluorescent dye and microshperes were used to characterize the flow kinematics. Employing abrupt convergent/divergent channel geometry, we achieved efficient mixing of two-dissimilar viscoelastic fluids at very low Reynolds number. Enhanced mixing was achieved through elastically induced flow instability at negligible diffusion and inertial effects (i.e. enormous Peclet and Elasticity numbers). This viscoelastic mixing was achieved over a short effective mixing length and relatively fast flow velocities.     

Silicon microstructures for high throughput mixing devices

Convective mixing in microstructures gives good mixing results in a very short time. In this work, a theoretical and experimental study is performed on convective micro mixing in different mixing structures and their combinations. Various mixing elements had been integrated on a silicon chip to achieve a device for a high mass-flow rate above 15 kg/h. These test structures are fabricated and tested concerning their flow behaviour and mixing characteristics. Flow measurements with pH neutralization and indication by bromothymol blue confirm the numerical simulations of the flow characteristics and mixing behaviour. The integral mixing quality in the micromixer is measured with the iodide–iodate-reaction (Villermaux–Dushman) and shows excellent values for high Re numbers. This opens the potential of microstructures for new applications in the production of chemicals.     

Non-homothetic granulometric mixing theory with application to blood cell counting

A granulometry is a family of morphological openings by scaled structuring elements. As the scale increases, increasing image area is removed. Normalizing removed area by the total area yields the pattern spectrum of the image. The pattern spectrum is a probability distribution function and its moments are known as granulometric moments. Modeling the image as a random set, the pattern spectrum is a random function and its moments are random variables. The original granulometric mixing theory provides closed-form representation of the granulometric moments, shows that the distributions of the moments are asymptotically normal, and gives asymptotic expressions for the means and variances of the granulometric moments. The theory applies to random-set models formed as disjoint unions of randomly scaled image primitives (grains). The scaled grains are known as homothetics. The theory can be used in a method-of-moments fashion to estimate the parameters governing the random scaling factors and mixture proportions. Application is limited by the homothetic assumption. This paper drops the homothetic requirement and provides a mixing theory for a disjoint union of fully randomized primitives. Whereas the original asymptotic theory gives expressions for the moments themselves and is applied by taking expectations afterwards, the non-homothetic theory involves the granulometric size density, which is the mean of the original size distribution prior to normalization. Hence, the representation concerns expectations, not random variables. Nonetheless, a similar method-of-moments approach can be used to estimate mixture proportions. A large part of the paper is devoted to estimate blood cell proportions that correspond to cell-age categories. Each cell class is represented by a random grain, and the problem is to estimate the proportions of cells occurring in the various age categories. The random behavior of the cells in each category makes the non-homothetic theory appropriate. Because the estimation strategy leads to a system of nonlinear equations whose solution presents computational difficulties, the estimation is accomplished via a divide-and-conquer strategy in which the full mixture problem is partitioned into smaller problems, and the solutions of these problems are joined to solve the full problem.     

3D modelling of hydrodynamics and mixing in a vegetation field under waves

Vegetation contributes to the sustainable development of aquatic environments. It provides food and shelter to many organisms and controls the ecological system in rivers, estuaries and coastal areas. In estuarine and coastal areas, wind waves can affect significantly the hydrodynamics and mixing processes there. In this work the wave-induced mixing process in a vegetation field is investigated by using a σ-coordinate 3D model. In the governing equations the vegetation field is represented by momentum sink terms. A random walk model is used to derive an expression for the mechanical dispersion coefficient used in the mass conservation equation. The numerical model is first validated through the simulation of the propagation of random waves, the attenuation of random waves over vegetation, as well as the flow and mixing in a unidirectional flow through vegetation. The numerical model is then used to simulate the mixing of a tracer in a vegetation field under regular and random waves. The results show that the mechanical dispersion and the reduced advection generated by the wave-vegetation interaction lead to a broader lateral spread and a narrower longitudinal spread of tracer plumes. The degree of randomness of waves will not affect the mixing significantly, as long as the peak period and the total energy of the waves remain unchanged.     

Spectral characterization of mixing properties of annular MHD micromixers

We develop a quantitative analysis of mixing regimes in an annular MHD-driven micromixer recently proposed by Gleeson et al. as a prototype for biomolecular applications. The analysis is based on the spectral properties of the advection–diffusion operator, with specific focus on the dependence of the dominant eigenvalue–eigenfunction on the Peclet number and on the system geometry. A theoretical prediction for the dominant eigenvalue encompassing all mixing regimes is developed and validated by comparison with numerical simulations. The theoretical prediction is extended to an open inflow–outflow version of the reactor, which shows the occurrence of new regimes associated with the existence of a nonuniform axial flow.     

Numerical simulation on fluid mixing by effects of geometry in staggered oriented ridges micromixers

Owing to the enhancement of surface effects at the micro-scale, patterned grooves on a microchannel remain a powerful method to induce chaotic advection within a pressure driven system. Since the staggered oriented ridges static micromixers are presented, there are few results in the literature about the geometric effects of such micromixer on the fluid mixing. This paper presents simulations within the micromixer and identifies geometric factors that affect the generation of advection flow over staggered oriented ridges. By varying the inflow directions, the ridge height ratio and the ridge asymmetry index, the modes of fluid motion and the pressure drops are studied respectively. Furthermore, through a set of numerical simulations, the relation expression between a mixing index to evaluate the mixing performance and the mentioned geometric parameters is obtained and the value of this mixing index could be calculated continuously. It indicates that the mixing performance of every staggered oriented ridges static micromixer could be estimated.     

Control of mixing by boundary feedback in 2D channel flow

We address the problem of enhancing mixing by means of boundary feedback control in 2D channel flow. This is done by first designing feedback control strategies for the stabilization of the parabolic equilibrium flow, then applying this feedback with the sign of the input reversed. The result is enhanced instability of the parabolic equilibrium flow, which leads rapidly to highly complex flow patterns. Simulations of the deformation of dye blobs positioned in the flow indicate (qualitatively) that effective mixing is obtained for small control effort as compared with the nominal (uncontrolled) flow. A mixedness measure P_ε is constructed to quantify the mixing observed, and is shown to be significantly enhanced by the application of the destabilizing control feedback.     

A multiphase lattice Boltzmann study of buoyancy-induced mixing in a tilted channel

We study the buoyancy-induced interpenetration of two immiscible fluids in a tilted channel by a two-phase lattice Boltzmann method using a non-ideal gas equation of state well-suited for two incompressible fluids. The method is simple, elegant and easily parallelizable. After first validating the code for simulating Rayleigh–Taylor instabilities in a unstably-stratified flow, we applied the code to simulate the buoyancy-induced mixing in a tilted channel at various Atwood numbers, Reynolds numbers, tilt angles, and surface tension parameters. The effects of these parameters are studied in terms of the flow structures, front velocities, and velocity profiles. For one set of parameters, comparisons have also been made with results of a finite volume method. The present results are seen to agree well with those of a finite volume method in the interior of the flow; however near the boundary there is some discrepancy.     

Numerical modeling of the mixing flow of second-order fluids with helical ribbon impellers

Rheology is known to have a strong impact on the flow behavior and the power consumption of mechanically agitated tanks. In the case of viscoelastic fluids, the role of elasticity on power draw has yet to be elucidated, though recent studies with helical ribbon impellers indicate that elasticity increases torque. The objective of this paper is to show that, in the case of second-order fluids, the use of a simple constitutive equation derived from a second-order retarded-motion expansion succeeds in predicting a rise in power draw owing to elasticity. The equations of change governing fluid flow are solved using a finite element method combined with an augmented Lagrangian method for the treatment of the non-linear constitutive equation. We show, in particular, how the underlying non-linear tensor equations can be solved directly using a spectral decomposition of the related matrix operator. First, the numerical methodology is explained. Next, simulation results are presented in the case of a tank provided with a helical ribbon. These results are then compared with experimental data. A rise of power draw, similar in shape but smaller than that measured experimentally, may be noted when elasticity is increased.     

Bias associated with the discriminant analysis approach to the estimation of mixing proportions

The estimation of the mixing proportion π₁, in which the first of two multivariate normal groups occur is considered on the basis of a sample drawn from a mixture of them. Under the model studied, there are also data of known origin available from each of the groups for the formation of a discriminant rule R. The bias of the estimator of π₁, based on the proportion of the mixture data assigned to the first group by R, is investigated. Also, the case where the data of known origin are taken to be correlated is considered.