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.     

Numerical and experimental investigations on the performance of a serpentine microchannel with semicircular obstacles

Microsystem Technologies - This paper focuses on computational and experimental analysis of a simple serpentine microchannel without obstacles and serpentine microchannel with semicircular...     

Passive mixing in a three-dimensional serpentine microchannel

A three-dimensional serpentine microchannel design with a “C shaped” repeating unit is presented in this paper as a means of implementing chaotic advection to passively enhance fluid mixing. The device is fabricated in a silicon wafer using a double-sided KOH wet-etching technique to realize a three-dimensional channel geometry. Experiments using phenolphthalein and sodium hydroxide solutions demonstrate the ability of flow in this channel to mix faster and more uniformly than either pure molecular diffusion or flow in a “square-wave” channel for Reynolds numbers from 6 to 70. The mixing capability of the channel increases with increasing Reynolds number. At least 98% of the maximum intensity of reacted phenolphthalein is observed in the channel after five mixing segments for Reynolds numbers greater than 25. At a Reynolds number of 70, the serpentine channel produces 16 times more reacted phenolphthalein than a straight channel and 1.6 times more than the square-wave channel. Mixing rates in the serpentine channel at the higher Reynolds numbers are consistent with the occurrence of chaotic advection. Visualization of the interface formed in the channel between streams of water and ethyl alcohol indicates that the mixing is due to both diffusion and fluid stirring     

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.     

Microfluidics analysis of nanoparticle mixing in a microchannel system

The microfluidics of controlled nanodrug delivery to living cells in a representative, partially heated microchannel was analyzed, using a validated computer model. The objective was to achieve uniform nanoparticle exit concentrations at a minimum microchannel length with the aid of simple static mixers, e.g., a multi-baffle-slit or perforated injection micro-mixer. A variable wall heat flux, which influences the local nanofluid properties and carrier-fluid velocities, was added to ensure that mixture delivery to the living cells occurred at the required (body) temperature of 37°C. The results show that both the baffle-slit micro-mixer and the perforated injection micro-mixer aid in decreasing the microchannel length while achieving uniform nanoparticle exit concentrations. The injection micro-mixer not only decreases best the system’s dimension, but also reduces the system power requirement. The baffle-slit micro-mixer also decreases the microchannel length; however, it may add to the power requirement. The imposed wall heat flux aids in enhanced nanoparticle and base-fluid mixing as well.     

Increment of mixing quality of Newtonian and non-Newtonian fluids using T-shape passive micromixer: numerical simulation

Microsystem Technologies - In this paper, a T-shape microchannel containing a mixing unit inserted in the straight main channel is designed to increase the mixing quality by geometrical changings...     

Realistic simulation of mixing fluids

Recently, simulation of mixing fluids, for which wide applications can be found in multimedia, computer games, special effects, virtual reality, etc., is attracting more and more attention. Most previous methods focus separately on binary immiscible mixing fluids or binary miscible mixing fluids. Until now, little attention has been paid to realistic simulation of multiple mixing fluids. In this paper, based on the solution principles in physics, we present a unified framework for realistic simulation of liquid–liquid mixing with different solubility, which is called LLSPH. In our method, the mixing process of miscible fluids is modeled by a heat-conduction-based Smooth Particle Hydrodynamics method. A special self-diffusion coefficient is designed to simulate the interactions between miscible fluids. For immiscible fluids, marching-cube-based method is adopted to trace the interfaces between different types of fluids efficiently. Then, an optimized spatial hashing method is adopted for simulation of boundary-free mixing fluids such as the marine oil spill. Finally, various realistic scenes of mixing fluids are rendered using our method.     

Fluid mixing in a swirl-inducing microchannel with square and T-shaped cross-sections

This study investigated micromixers formed by a T-junction and a mixing channel consisting of serial modules formed by appropriately arranging the subsections with right shifted T-shaped, left shifted T-shaped and square cross-sections. The T-shaped cross-sections are constructed by protrusions and indentations on the channel wall. The variation of shape and size of the channel cross-section may induce a strong swirl structure of flow to enhance fluid mixing. Four parameters (the lengths of the three aforementioned subsections and the sequence of modules) were selected to optimize the micromixer, and computational fluid dynamics (CFD) together with Taguchi method was applied to select the values of the parameters. Then, the micromixer was fabricated by a lithography process and the mixing of pure DI water and a solution of Rhodamine B in DI water in the micromixer was observed by using a confocal spectral microscope imaging system. The numerical and experimental results, compared to those of a straight channel with the same hydrodynamic diameter, show that the novel micromixer with the deliberately designed geometry with a hydrodynamic diameter equal to 120 μm enhances fluid mixing efficiently at relatively low Reynolds numbers (0.01–10), corresponding to the mean velocities from 0.000081 to 0.081 m/s. The effects of the four parameters on fluid mixing in the proposed micromixer are examined by CFD simulation.

     

Microfluidic mixing via transverse electrokinetic effects in a planar microchannel

A new micromixer incorporating integrated electrodes deposited on the bottom surface of a glass/PDMS microchannel is used to induce a localized, perpendicular electric field within pressure driven axial flow. The presence of the electric field drives electro-osmotic flow in the transverse direction along the channel walls, creating helical motion that serves to mix the fluid. A numerical model is used to describe the three-dimensional flow field, where characterization is performed via particle tracking of passive tracer particles, and the conditional entropy (S _lc) is utilized to approximate the extent of mixing along cross-sectional planes. The geometrical parameters and operating conditions of the numerical model are used to fabricate an experimental device, and fluorescence microscopy measurements are used to verify mixing of rhodamine B across the width of the microchannel for a wide range of fluid flow rates. The results demonstrate that under certain operating conditions and selective placement of the electrode gaps along the width of the microchannel, efficient mixing can be achieved within 6 mm of the inlet.

Direct numerical simulation of rarefied turbulent microchannel flow

Direct numerical simulation (DNS) has been carried out to investigate the effect of weak rarefaction on turbulent gas flow and heat transfer characteristics in microchannel. The Reynolds number based on the friction velocity and the channel half width is 150. Grid number is 64 × 128 × 64. Fractional time-step method is employed for the unsteady Navier–Stokes equations, and the governing equations are discretized with finite difference method. Statistical quantities such as turbulent intensity, Reynolds shear stress, turbulent heat flux and temperature variance are obtained under various Knudsen number from 0 to 0.05. The results show that rarefaction can influence the turbulent flow and heat transfer statistics. The streamwise mean velocity and temperature increase with increase of Kn number. In the near-wall-region rarefaction can increase the turbulent intensities and temperature variance. The effects of rarefaction on Reynolds shear stress and wall-normal heat flux are presented. The instantaneous velocity fluctuations in the vicinity of the wall are visualized and the influence of Kn number on the flow structure is discussed.     

Numerical assessment of mixing performances in cross-T microchannel with curved ribs

Microsystem Technologies - The present study considers a measure for enhancing mixing capability in micromixers. It incorporates a new design of obstacle, in the form of thin curved ribs, inside...     

Electrokinetic power generation of non-Newtonian fluids in a finite length microchannel

In order to examine the effects of the fluid type as the electrolyte solvent on the efficiency of electrokinetic energy conversion, a comparative numerical study among three different fluid types of a transient electrokinetic flow through a single circular finite length microchannel has been conducted. The system was initially at an equilibrium non-flow state, and a step change in flow was applied and the calculation proceeding until steady state was achieved. The analysis was based on non-dimensional transport governing equations that were scaled using Debye length as the characteristic length scale and diffusion time as characteristic time scale. The fluid types considered were shear thinning, Newtonian, and shear thickening, and a power law modeled them with the scaled flow behavior index having values of 0.2, 1.0, and 1.8. In order to isolate the electrokinetic effects of the different relationships between the shear strain rate and shear stress, the flow consistency index was adjusted so that in all the cases the flow rate and total pressure drop matched that of water at 25 °C. All other fluid and interfacial properties were the same for all cases. The key observational difference between the various fluid types was that their different axial velocity profile acted on essential the same free charge density profiles. Consequently, the convection current density (i.e., the radial distribution of charge being advected along the channel) was strongly affected by the fluid type. Integration of this quantity to calculate the convection current showed that for the particular fluid properties chosen the shear thinning fluid was 20 % higher than the Newtonian fluid, while the shear thickening fluid was only 4 % lower than the Newtonian fluid. Combined with the effects, these different currents have on the streaming potential, the shear thinning fluid was 50 % more effective in converting flow work to electrical work than the Newtonian fluid, while the shear thickening fluid was only 16 % lower than the Newtonian fluid.     

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.

     

Some numerical investigations in nonlinear optics

The problem of the self-focusing of a light beam in nonlinear media is the central problem in nonlinear optics. The powerful laser beam propagation through a real medium under certain conditions is accompanied with such a phenomenon.Mathematically the problem deals with the investigation of the asymptotic behaviour of the solution of the parabolic equation

$\text{2i}\text{?u}\text{?z}\text{=}\text{?}{}^2\text{u}\text{?r}{}^2\text{+}\text{1}\text{r}\text{?u}\text{?r}\text{+?(∣u∣}{}^2\text{)u}$

with given initial distribution u(r,0) and boundary condition u(∞, z) = 0 where u is the electromagnetic field amplitude, f is a function which describes the refractive index deviation from its constant value in the linear medium. It is complex in the case of nonconservative media. In our investigation we combine analytical and numerical methods. The computational study of the self-focusing problem is complicated due to the boundary condition at infinity and the abrupt light amplitude behaviour in the paraxial region. We managed to overcome these difficulties by introducing the socalled quasi-uniform grid for the radial variable and by using the special technique of the correct transfer of the boundary condition from infinity. The main physical results are: (1) the conditions for the light self-trapping and waveguide creation are found, (2) the self-focusing mechanism and the law of increasing beam amplitude when approaching the collapse point are discovered; (3) the influence of the different kinds of absorption is investigated and the process of light “turbulence” is explained;All the analytical and numerical results are comparable with the experimental situation as well as with treatments by other authors.     

Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow

In this work, we investigated the lateral migration of microparticles suspended in two different viscoelastic fluids with or without the second normal stress difference. For the viscoelastic fluid without the second normal stress difference, competing forces existed between microfluidic inertia and the first normal stress difference (N ₁), which resulted in a synergetic effect of particle focusing. For the fluid with the second normal stress difference (N ₂), particles were greatly affected by a N ₂-induced secondary flow, and the competition among the inertia, N ₁, and N ₂ determined the lateral migration trajectories of the particles. The obtained results were delineated with the blockage ratio, which showed good agreement with the results of a recent numerical study (Villone et al. in J Non Newton Fluid Mech 195:1–8, 2013). The present study also examined the possibility of particle separation in a size-dependent manner using the N ₂-induced secondary flow in microchannel flow.     

Depthwise averaging approach to cross-stream mixing in a pressure-driven microchannel flow

Microfluidic devices have many potential applications, such as BioMEMs (microelectromechanical systems for biomedical applications), miniature fuel cells, and microchannel cooling of electronic circuitry. One of the important considerations of microfluidic devices for analytical and bioanalytical chemistry is the dispersion of solutes. In this study, the dispersion of passive analyte between two miscible fluids of similar properties in a side-by-side pressure-driven creeping flow is examined. This study represents a first effort in applying the lubrication approximation together with the depthwise averaging method to analyze mass transport of passive analyte in a two-stream rectangular microchannel with consideration of the Taylor-Aris dispersion effect.

Interfacial configurations and mixing performances of fluids in staggered curved-channel micromixers

We present a parallel laminar micromixer with staggered curved channels for homogeneously mixing two fluids by Dean vortex. The secondary flows are produced in curved rectangular channels by the centrifugal forces; the diffusion distance of two fluids is reduced due to the staggered structures of the flow channels. The mixing strength is increased when one stream is injected into the other. Confocal microscopy and pH indicator have been used to study the mixing. Computational fluid dynamics simulations are utilized to examine the interfacial configurations and the mixing behaviors inside the channels. The interface of the two fluids is heavily distorted and increases the interfacial area because of the unique structures. The mixing index of the staggered curved-channel mixer with tapered channels is higher than those of the other curved-channel mixers. The effects of various Reynolds numbers and channel configurations on mixing performances are investigated in terms of the experimental mixing indices and the computational interfacial patterns. The comparison between the experimental data and numerical results shows a very similar trend.     

Optimization and experimental investigations of stiffened, axially compressed CFRP-panels

Thin-walled, unstiffened and stiffened shell structures made of fibre composite materials are frequently applied due to their high stiffness/strength to weight ratios in all fields of lightweight constructions. One major design criterion of these structures is their sensitivity with respect to buckling failure when subjected to inplane compression and shear loads. This paper describes how the structural analysis program BEOS (Buckling of Eccentrically Orthotropic Sandwich shells) is combined with the optimization procedure SAPOP (Structural Analysis Program and Optimization Procedure) to produce a tool for designing optimum CFRP-panels against buckling. Experimental investigations are used to justify the described procedures.Nomenclature C, C _b material stiffness matrices (shell, beam stiffener) - f objective function - F _cr buckling load - g vector of inequality constraints - K,K _g , stiffness matrix, geometrical stiffness matrix, condensed stiffness matrix - n _s ,n _b vector of stress resultants (shell, beam stiffener) - N _x ,N _y ,N _xy membrane forces of the shell - P _x ,P _y ,P _xy membrane forces of the stiffener - r _x ,r _y ,r _xy radii of curvature - ⁿ n-dimensional Euclidean space - W strain energy - u, v, w deformations inx, y, z direction - x, y, z global coordinate system - x vector of design variables - y, z right-hand side, left-hand side eigenvector - variational symbol - _i ^k Kronecker's delta - e _s ,e _b strain vectors (shell, beam stiffener) - , _cr load factor, buckling load factor - , e total energy, external potential energy A (^) sign above a variable points out that this variable belongs to the prebuckling state.     

Experimental and numerical investigations of thermo-mechanically stressed micro-components

Reliability and functionality of microsystems, i.e. of small scale integrated electronic, mechanical and optical components, largely depend on their mechanical and thermal constitution. Thermo-mechanical aspects of component and system reliability become more and more important with growing miniaturization as the local physical parameters and field quantities show an increase in sensitivity due to inhomogeneities in local stresses, strains and temperature fields. Since there is usually a lack of information about the local material parameters, a pure field simulation cannot, as a rule, solve the problem.The state of the art of microsystem design more and more requires direct coupling between simulation tools (including e.g. FE modelling) and advanced physical experiments. The authors have combined various laser technique, scanning microscopy, and X-ray diffraction with numerical field simulation. The investigations have been directed towards current problems of mechanical and thermal reliability in electronic packaging, crack and fracture behaviour within the interconnected regions and life time estimation. Special problems of mechanical behaviour in solder joints are discussed taking into account local plasticity as well as creep effects.Dr. J. Auersperg, R. Döring, and Dr. R. Kühnert, Center of Micromechanics, Chemnitz, carried out some FEM calculations and the micromoiré experiments respectively.This scientific work was supported by the Deutsche Forschungsgemeinschaft Bonn under Contract No. Mi 362/2-3 and Mi 362/3-1     

Investigations into mixing of fluids in microchannels with lateral obstructions

This work presents a study of a passive micromixer with lateral obstructions along a microchannel. The mixing process is simulated by solving the continuity, momentum and diffusion equations. The mixing performance is quantified in terms of a parameter called ‘mixing efficiency’. A comparison of mixing efficiencies with and without obstructions clearly indicates the benefit of having obstructions along the microchannel. The numerical model was validated by comparing simulation results with experimental results for a micromixer. An extensive parametric study was carried out to investigate the influence of the geometrical and operational parameters in terms of the mixing efficiency and pressure drop, which are two important criteria for the design of micromixers. A very interesting observation reveals that there exists a critical Reynolds number (Re _cr  ~ 100) below which the mixing process is diffusion dominated and thus the mixing efficiency is reduced with increase in Re and above which the mixing process is advection dominated and mixing efficiency increases with increase in Re. Microchannels with symmetric and staggered protrusion arrangements were studied and compared. The mixing performance of the staggered arrangement was comparable with that of symmetric arrangement but the pressure drop was lower in the case of staggered arrangements making it more suitable.