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.     

Pressure-driven diffusive gas flows in micro-channels: from the Knudsen to the continuum regimes

Despite the enormous scientific and technological importance of micro-channel gas flows, the understanding of these flows, by classical fluid mechanics, remains incomplete including the prediction of flow rates. In this paper, we revisit the problem of micro-channel compressible gas flows and show that the axial diffusion of mass engendered by the density (pressure) gradient becomes increasingly significant with increased Knudsen number compared to the pressure driven convection. The present theoretical treatment is based on a recently proposed modification (Durst et al. in Proceeding of the international symposium on turbulence, heat and mass transfer, Dubrovnik, 3–18 September, pp 25–29, 2006) of the Navier–Stokes equations that include the diffusion of mass caused by the density and temperature gradients. The theoretical predictions using the modified Navier–Stokes equations are found to be in good agreement with the available experimental data spanning the continuum, transition and free-molecular (Knudsen) flow regimes, without invoking the concept of Maxwellian wall-slip boundary condition. The simple theory also results in excellent agreement with the results of linearized Boltzmann equations and Direct Simulation Monte Carlo (DSMC) method. Finally, the theory explains the Knudsen minimum and suggests the design of future micro-channel flow experiments and their employment to complete the present days understanding of micro-channel flows.     

A rapid magnetic particle driven micromixer

Performances of a magnetic particle driven micromixer are predicted numerically. This micromixer takes advantages of mixing enhancements induced by alternating actuation of magnetic particles suspended in the fluid. Effects of magnetic actuation force, switching frequency and channel’s lateral dimension have been investigated. Numerical results show that the magnetic particle actuation at an appropriate frequency causes effective mixing and the optimum switching frequency depends on the channel’s lateral dimension and the applied magnetic force. The maximum efficiency is obtained at a relatively high operating frequency for large magnetic actuation forces and narrow microchannels. If the magnetic particles are actuated with a much higher or lower frequency than the optimum switching frequency, they tend to add limited agitation to the fluid flow and do not enhance the mixing significantly. The optimum switching frequency obtained from the present numerical prediction is in good agreement with the theoretical analysis. The proposed mixing scheme not only provides an excellent mixing, even in simple microchannel, but also can be easily applied to lab-on-a-chip applications with a pair of external electromagnets.     

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.     

Water droplet properties on periodically structured superhydrophobic surfaces: a lattice Boltzmann approach to multiphase flows with high water/air density ratio

Surface roughness affects the contact angle (CA) due to the increased area of solid–liquid interface and due to the effect of sharp edges of rough surfaces. Roughness may also lead to another non-wetting regime, by forming a composite solid–liquid–air interface between the water and the textured surface; this composite interface exhibits strong water repellency due to the various pockets of air entrapped between the surface textures. The contact between water and a hydrophobic textured surface leads to one of these two regimes depending on the thermodynamics stability of the regimes. In this study, the projection method of lattice Boltzmann method is used to analyze the large density difference at the air and water interface. The method is applied to simulate two-phase flows with the density ratio of up to 1,000. A numerical model is presented to provide a relationship between roughness and CA, which is used to develop optimized texture topography and create a biomimetic superhydrophobic surface. The numerical models encompass the effects of contact area, solid–liquid–gas composite interface and shape edges. The models are reused to analyze different possible roughness distributions and to calculate the effect of the cross-sectional area of pillars, including rectangular, triangular, cross, and pyramidal pillars. The energy barrier is investigated to predict the position of the transition between the Cassie and Wenzel regime observed for each roughness parameter as well as a theoretical free surface energy model.     

Two phase micromixing and analysis using electrohydrodynamic instabilities

Organic–aqueous liquid (phenol) extraction is one of many standard techniques to efficiently purify DNA directly from cells. Effective mixing of the two fluid phases increases the surface area over which biological component partitioning may occur. In this work, two phase mixing has been demonstrated in a three inlet microfluidic device geometry. Mixing between the two phases has been achieved by producing an electrohydrodynamic instability at the liquid–liquid interface between the two phases. The initial instability is modeled by considering the small signal linearized analysis for interfacial stresses from both fluid and electrical stress tensors for both inviscid and viscous models. These models predict the onset of instability and the stability criteria over a range of unstable wavenumbers of the mixing process. These models may be applied to relevant microscale geometries, where the unstable wavenumbers and fastest growth wavenumber are determined. At an applied electric field of ∼8.0×10⁵ V/m an instability is experimentally observed by labeling the organic phase with a fluorescent dye and visualizing interfacial perturbations by microscopy. Increasing the electric field increases the instability growth rate and results in an increase of the level of mixing. These results show an increase in conductive fluid entrainment into the nonconducting fluid core measured as a percentage of area of entrainment into the fluorescently labeled organic phase. The entrainment area is seen to increase from 1.9 to 28.6% as the applied field is increased from 8.0×10⁵ to 9.0×10⁵ V/m. The mixing images are converted into a power spectrum using a fast Hartley transform and the band of unstable wavenumbers of the mixing process are determined. From these results, the theoretical field strengths required to produce these unstable wavenumbers are calculated using the theoretical model, determining the maximum field strength required to excite the largest measured unstable wavenumber. At lower field strengths tested, the theoretically predicted maximum electric field and fastest growth wavenumber compare favorably with the initially applied field and measured fastest growth wavenumber whereas at higher field strengths the theoretical field is much larger than the initially applied field. This is attributed to the larger level of mixing and the ability of the instability to grow beyond the linear range and the field increases as the mixing process occurs due to entrainment of highly conductive fluid decreasing the effective dielectric spacing so that the linearized models underpredict the instability growth rates and interfacial perturbations.     

A method to predict the derailment of rolling stock due to collision using a theoretical wheelset derailment model

A wheelset derailment model on rolling stock was developed to predict train collision-induced derailment. This model is based on the theoretical derailment behaviors of a wheelset under suspension loads. This theoretical derailment model was numerically simulated using commercial dynamics software, wherein it is demonstrated that this model is useful for predicting train collision-induced derailment. Furthermore, this theoretical derailment model was incorporated into a virtual testing model that did not consider wheel–rail contact conditions in order to evaluate useful applications to the derailment prediction of a train collision. The derailment behaviors of this virtual testing model, which were predicted by applying the theoretical derailment model under the condition of no wheel–rail contact, were closely correlated to those derived from simulations that considered surface-to-surface contact conditions.     

Chaotic mixing using source�Csink microfluidic flows in a PDMS chip

We present an active fixed-volume mixer based on the creation of multiple source–sink microfluidic flows in a polydimethylsiloxane (PDMS) chip without the need of external or internal pumps. To do so, four different pressure-controlled actuation chambers are arranged on top of the 5 μl volume of the mixing chamber. After the mixing volume is sealed/fixed by microfluidic valves made using ‘microplumbing technology’, a virtual source–sink pair is created by pressurizing one of the membranes and, at the same time, releasing the pressure of a neighboring one. The pressurized air deforms the thin membrane between the mixing and control chambers and creates microfluidic flows from the squeezed region (source) to the released region (sink) where the PDMS membrane is turned into the initial state. Several schemes of operation of virtual source–sink pairs are studied. In the optimized protocol, mixing is realized in just a sub-second time interval, thanks to the implementation of chaotic advection.     

High Knudsen number fluid flow at near-standard temperature and pressure conditions using precision nanochannels

Gas flows over a wide range of Knudsen numbers (~0.5–10) are studied using silicon nanochannel arrays with slit-shaped pores. The pore sizes of the silicon nanochannel arrays range from micrometer to sub-10-nm scales. The flows are generated under conditions of room temperature and near-atmospheric pressure (~22°C and ~101–115 kPa) and span the continuum flow, continuum-slip flow, transition flow and free-molecular flow regimes. The measured flow rates of helium, argon and carbon dioxide are in good agreement with a theoretical model (Unified Slip Model) proposed by Beskok and Karniadakis (Nanoscale Microscale Thermophys Eng 3:43–77, 1999).     

Cycles in economic systems with open labor markets

A dynamic macromodel of an economic system with a monopsonic labor market and variable labor resources is considered. The initiation conditions for classical business cycles are investigated for this model. Bifurcation analysis of the model is performed to estimate the effect of the minimum wage on the way such cycles form. The results of theoretical analysis are supplemented with numerical experiments. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 48–72, July–August 2008.     

A Note on the Stability of Gauss–Jordan Elimination for Diagonally Dominant Matrices

Peters and Wilkinson [2] state that “it is well known that Gauss–Jordan is stable” for a diagonally dominant matrix, but a proof does not seem to have been published [1]. The present note fills this gap. Gauss–Jordan elimination is backward stable for matrices diagonally dominant by rows and not for those diagonally dominant by columns. In either case it is forward stable. Received February 28, 2000     

A predictive bottom-up parser

Despite all advances in parsing, parser size, conflict resolution and error recovery are still of important consideration. In this research, we propose a predictive bottom-up parser. The parser is implemented in two versions. Both versions constitute an algorithm that simulates the run of a shift–reduce automaton, defined and constructed in a way that integrates its parsing actions with reduction prediction, conflict resolution and error recovery. However, the first implementation version performs explicit shift–reduce parsing actions based on implicit prediction of the reduction sequences. The second one performs parsing actions based on explicit prediction of the reduction sequences with implied shift–reduce actions. The proposed parser has been experimented against the ones based on similar approaches. 10–20% reduction of the parser size has been achieved, with a parsing behaviour proportional to a factor reflecting the grammar ambiguity.     

Simulation and characterization of microreactors for aerosol generation

This paper shows the application of T-shaped micromixers for the generation of aerosols with nanoscale droplets by the mixing of a hot vapor–gas mixture with a cold gas. The fast mixing within a T-shaped micromixer leads to a high supersaturation of the vapor and therefore to an instantaneous, homogeneous nucleation and particle growth. Different mixer geometries, mixing ratios, and gas temperatures have been investigated by numerical simulation to yield optimum mixing results over a wide range of operational parameters. Optimized microreactor geometries were designed and fabricated in silicon with Pyrex glass lids. Special attention was paid to thermal insulation and particle deposition at the channel walls. This concerns not only the mixing chip, but also the design of the fluidic mount with only few bends and corners. Initial experimental results for particle deposition and aerosol generation are presented. High temporal temperature gradients up to 10⁶ K/s lead to a rapid condensation and forming of nanosized particles with a mean diameter of 20–50 nm and a narrow size distribution.     

Using a model of cellular automata and classification methods for prediction of time series with memory

The paper deals with the problem of prediction of time series with memory for which classical prediction methods are frequently inadequate. A method is proposed that is based on a model of cellular automata, classification methods, and fuzzy set theory. The accuracy of models based on this method is estimated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 43–54, November–December 2006.     

Capillary and electrostatic limitations to the contact angle in electrowetting-on-dielectric

The shape of a conducting liquid droplet placed on a hydrophobic dielectric surface is simulated numerically by solving the Laplace–Young capillary equation. The electric force, acting on the conducting surface, distorts the droplet shape leading to a change in the apparent contact angle; its variation is compared with a theoretical Young–Lippman prediction. At sufficiently large values of voltage, applied to the droplet, the numerical algorithm fails to converge, which is interpreted as the break-up of the droplet surface with small droplets being ejected from the surface. These highly charged droplets, as well as any other electric charges near the triple contact line, generated for example by the electric corona discharge, cause a change of the distribution of the electric forces. This effect can be helpful in explaining saturation of the apparent contact angle: an appropriately selected surface charge near the contact line can completely stop droplet distortion, and the contact angle variation, despite the increased droplet voltage. Furthermore, the simulation results show the effect of the permittivity of the medium surrounding the droplet, on the contact angle variation.     

Theoretical and experimental characterization of a low-Reynolds number split-and-recombine mixer

A mixing device based on the split-and-recombine (SAR) principle is characterized using both theoretical and experimental methods. The theoretical model relies on solving a 1D diffusion equation in a frame of reference comoving with the flow, thus avoiding the usual numerical artefacts related to the prediction of high-Péclet number mixing. It accounts both for the hydrodynamic focusing of the flow inside the mixing channel and the nontrivial flow topology. The experimental technique used for quantifying the degree of mixing utilizes two initially transparent salt solutions that form a colored compound in a fast chemical reaction. The degree of mixing is derived from the average color saturation found at specific positions along the mixing channel. The data obtained from the theoretical model are in reasonable agreement with the experiments and underline the excellent performance of the SAR mixer, with a mixing length growing only logarithmically as a function of Péclet number.     

Mixing and flow regulating by induced-charge electrokinetic flow in a microchannel with a pair of conducting triangle hurdles

The induced-charge electrokinetic flow (ICEKF) in a rectangular micorchannel with a pair of conducting triangle hurdles embedded in the middle is investigated in this paper. A correction method is suggested to numerically estimate the induced zeta potential on the conducting surface. Two-dimensional pressure-linked Navier-–Stokes equation is used to model the flow field in the channel. The numerical results show flow circulations generated from the induced non-uniform zeta potential distribution along the conducting hurdle surfaces. It is demonstrated numerically that the local flow circulations provide effective means to enhance the flow mixing between different solutions; by adjusting the electric field applied through the microchannel with a non-symmetric triangle hurdle pair, an electrokinetic flow regulating effect can be obtained and this effect depends on the dimensions of the conducting converging–diverging section. The mixing and flow regulating using ICEKF described in this paper can be used in various microfluidics and lab-on-a-chip (LOC) applications.     

Realistic Brownian Dynamics simulations of biological molecule separation in nanofluidic devices

We present a Brownian Dynamics model of biological molecule separation in periodic nanofilter arrays. The biological molecules are modeled using the Worm-Like-Chain model with Hydrodynamic Interactions. We focus on short dsDNA molecules; this places the separation process either in the Ogston sieving regime or the transition region between Ogston sieving and entropic trapping. Our simulation results are validated using the experimental results of Fu et al. (Phys Rev Lett 97:018103, 2006); particular attention is paid to the model’s ability to quantitatively capture experimental results using realistic values of all physical parameters. Our simulation results showed that molecule mobility is sensitive to the device geometry. Moreover, our model is used for validating the theoretical prediction of Li et al. (Anal Bioanal Chem 394:427–435, 2009) who proposed a separation process featuring an asymmetric device and an electric field of alternating polarity. Good agreement is found between our simulation results and the predictions of the theoretical model of Li et al.     

Investigation of a one-channel queueing system with an unlimited queue and the markovian anticipatory switching

Acondition of stability on the second approximation is obtained for a pulse system with anticipatory switching based on the diffusive approximation of normalized deviations of solutions of the system from the solution of an averaged system. The theoretical results obtained are used for investigating a one-channel queueing system with an unlimited queue. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 168–173, July–August, 2000.     

Full field measurement at the micro-scale using micro-interferometry

This paper presents micro-interferometry as a measurement technique to extract temperature profiles and/or mass transfer gradients rapidly and locally in micro-devices. Interferometry quantifies the phase change between two or more coherent light beams induced by temperature and/or mass concentration. Previous work has shown that temporal noise is a limiting factor in microscale applications. This paper examines phase stepping and heterodyne phase retrieval techniques with both CCD and CMOS cameras. CMOS cameras are examined owing to the high speed at which images can be acquired which is particularly relevant to heterodyne methods. It is found that heterodyne retrieval is five times better than phase stepping being limited to 0.01 rad or λ/628. This is twice the theoretical limit of λ/1,000. The technique is demonstrated for mixing in a T-junction with a 500 μm square channel and compared favourably to a theoretical prediction from the literature. Further issues regarding application to temperature measurements are discussed.