Chaotic mixing efficiency in different geometries of Hele-Shaw cells

2010 ◽  
Vol 53 (4) ◽  
pp. 684-693 ◽  
Author(s):  
Aurélien Beuf ◽  
Jean-Noël Gence ◽  
Philippe Carrière ◽  
Florence Raynal
2016 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Yasser Aboelkassem

AbstractChaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microffluidic device is presented in this article. Mathematical modeling for the induced flow motions by moving a Stokeslet along the x-axis is derived using Fourier expansion method. The solution is formulated in terms of the velocity stream function. The model is then used to explore different stirring dynamics as function of the Stokeslet parameters. For instance, the effects of using various oscillation amplitudes and force strengths are investigated. Mixing patterns using Poincaré maps are obtained numerically and have been used to characterize the mixing efficiency. Results have shown that, for a given Stokeslet’s strength, efficient mixing can be obtained when small oscillation amplitudes are used. The present mixing platform is expected to be useful for many of biomicrofluidic applications.


Author(s):  
Sophie Loire ◽  
Paul Kauffmann ◽  
Paul Gimenez ◽  
Igor Mezić ◽  
Carl Meinhart

Thanks to its favorable reduction scale law, and its easy integration, electrokinetics has emerged over the last fifteen years as one of the major solution to drive flows in fully integrated lab-on-chip. At microscale, an efficient mixing is a keystep which can dramatically accelerate bio-reactions. For thirty years, Dynamical System theory has predicted that chaotic mixing must involve at least 3 dimensions (either time dependent 2D flows or 3D flows). However, in microfluidics, few works have yet presented efficient embedded micromixers. This paper presents experimental and theoretical study of 2D time dependent chaotic mixing using AC electrothermal fluid flows. Experiments and numerical simulations are performed on a top view device and a sideview device. In both devices, a sinusoidal electric signal is applied between 3 interdigitated gold electrodes. A phase signal Vpp = 11V and a ground are switched between the two side electrodes using a step function, whereas the opposite phase signal –Vpp is steadily applied to the center electrode (Figure 1). Flow velocity is measured by micro particle image velocimetry μ PIV. The velocity profile shows a dramatic asymmetry between the two vortices. Therefore, during the switch, vortices overlap, leading to stretching and folding flows required to obtain chaotic mixing (Figure 3 and 4). The experimental measurements validate our electrothermal models based on our previous work [1]. The mixing efficiency of low diffusive particles is studied at multiscale using the mix-variance coefficient (MVC) [2] to evaluate mixing at different scales (Figure 4). To do so, the domain is successively divided in boxes along the x and y direction up to nx and ny boxes, respectively. For each box configuration, average bead concentration is computed. The variance of these concentrations is then evaluated: MVCs=1nxny∑i=1ny∑j=1nxρij-0.52. The result of numerically evaluated MVC in Figure 2 show a dramatic increase of mixing efficiency with blinking vortices compared to steady flow. Theoretical, experimental and simulation results of the mixing process will be presented.


Author(s):  
Hua Yang ◽  
Shi-Xiao Wei ◽  
Han Chen ◽  
Lang Chen ◽  
Chak-tong Au ◽  
...  

Owing to high mixing efficiency, microreactors are used to synthesize uniform BaSO4 nanoparticles, but application in industrial scale is limited due to poor throughput. In this work, a high-throughput passive four-stage asymmetric oscillating feedback microreactor using chaotic mixing mechanism was developed to prepare BaSO4 nanoparticles of high size uniformity. Three-dimensional unsteady simulations showed that chaotic mixing could be induced by three unique secondary flows (i.e., vortex, recirculation, and oscillation), and the fluid oscillation mechanism was examined in detail. Simulations and Villermaux-Dushman experiments indicate that almost complete mixing in molecular level could be achieved when total volumetric flow rate Qtotal was larger than 10 mL/min, and the prepared BaSO4 nanoparticles were with narrow particle size distribution (PSD). Through the adjustment of Qtotal and reactant concentrations, it is easy to control the average size. An average size of 26 nm with narrow PSD could be achieved at Qtotal = 160 mL/min.


Author(s):  
Xi-Ze Niu ◽  
Patrick Tabeling ◽  
Yi-Kuen Lee

In this paper, the Finite Time Lyapunov Exponent (FTLE) approach is used to analyze and optimize chaotic mixing in an active microchannel and a static mixer. The characteristics of FTLE related to chaotic mixing are discussed. By comparing the similarity of Poincare´ mapping and FTLE contour, it is shown that FTLE can be used to evaluate the chaotic mixing of liquid in the micromixer qualitatively and quantitatively. The minimum channel length needed for full mixing in the mixers can be estimated by the mean FTLE. The results are consistent with CFD simulations directly solving the Navier-Stokes equations coupled with the diffusion equation. More than 3 orders of CPU time can be saved by using FTLE compared with the classical infinite time Lyapunov exponent approach. Moreover, the FTLE is used to optimize the design and operation of the chaotic micromixers to improve the mixing efficiency for the first time.


Author(s):  
Yifeng Wang ◽  
Jianzhong Lin ◽  
Ruijin Wang

Mixing multiple fluids based on plugs flow is a better approach in microfluidic system. In order to understand the mixing mechanism based on plug flow, theoretical analysis based on chaotic mixing was carried out, and a micro-resolution particle image velocimetry (Micro-PIV) is used to measure the flow field in liquid plug involving liquid species to be mixed. Two recirculation flows forming in plugs can enhance the mixing efficiency because folding and stretching of the liquids occured deterministically in plugs. In addition, the Lagrangian velocity were determinated on the basis of Eulerian velocity by subtracting this droplet velocity vector from the measured Eulerian velocity field of the tracing particles results inside the moving droplet. These results are helpful to optimize the structure of micromixer and develop droplet based microfluidic system.


2019 ◽  
Vol 39 (3) ◽  
pp. 287-299 ◽  
Author(s):  
Jian Liu ◽  
Xiangzhe Zhu

Abstract The single-screw extruder with a perturbation baffle is a novel piece of equipment for polymer processing, in which the polymer melts undergo complex chaotic mixing. In this paper, from a new Lagrangian perspective, the fluid transporting mechanism in chaotic flow of the unwound screw channel was analyzed based on the finite element method. Firstly, two-dimensional velocity distributions in the unwound screw channel were calculated based on the mesh superposition technique. Fluid particle evolution processes in the extruder were tracked based on the fourth-order Runge-Kutta scheme. The numerical method used in this paper was validated by grid independence and experiments obtained from literature. Moreover, the finite-time Lyapunov exponent (FTLE) and Poincaré sections were adopted to discuss the chaotic mixing in the novel single-screw extruder. The effects of baffle width and height on the manifold structures in the flow dynamic system were analyzed. The results show that the homoclinic point of the manifold structure can give rise to chaotic mixing in the single-screw extruder. The height of the baffle is an important parameter to control the chaotic strength. In a way, increasing the height of the baffle can enlarge the kink scale and increase the stretching and folding actions, which results in the decrease of regular regions and an increase of the mixing efficiency in the single-screw extruder.


Materials ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2272 ◽  
Author(s):  
Xiang Zhu ◽  
Ying Tong ◽  
Yue Hu

The four-screw extruder (FSE) is a novel equipment for polymer processing. In this paper, from a new viewpoint of Lagrangian coherent structures (LCS), two-dimensional fluid transport and chaotic mixing characteristics within three kinds of novel industrial FSEs are explored based on LCS to better understand the flow and mixing natures in the FSEs. Firstly, based on the finite-time invariant manifold theory, the finite-time Lyapunov exponent (FTLE) and LCS of FSEs are calculated by considering the different initial time. Hyperbolic LCSs from the FTLE maps are adopted to identify chaotic mixing manifolds in FSEs. Moreover, particle tracking and Poincaré sections are used to illustrate the different fluid motions in the above three isolated regions. Finally, the effects of relative rotating directions and layout of four screws on the chaotic manifolds in FESs are discussed in order to enhance local mixing performance. Furthermore, quantitative mixing measures, such as the segregation scale, logarithmic of stretching, and mean-time mixing efficiency are employed to compare the mixing efficiencies in three kinds of FSEs. The results show that the relative rotating directions and positions of four screws can change the chaotic manifolds and increase mixing performance in local poor mixing regions. FTLE and LCS analysis are helpful to better understand the chaotic mixing nature in the novel screw extruders.


1996 ◽  
Vol 06 (12b) ◽  
pp. 2627-2634 ◽  
Author(s):  
A.T. PÉREZ ◽  
R. CHACÓN ◽  
A. CASTELLANOS

This paper studies the effect of continuous and discontinuous time dependent forcings onto dynamical systems. We compare these different forcings in the context of laminar chaotic mixing. It is shown that the response of a Hamiltonian two-dimensional system to a time periodic sinusoidal forcing differs qualitatively and quantitatively from the response to a square wave function of the same frequency. Consequently, the mixing efficiency of both types of forcings are different. Also a periodic function of the same shape as that of the velocity of the unperturbed system is tested as a forcing, its mixing efficiency being intermediate.


Author(s):  
A. K. Rai ◽  
R. S. Bhattacharya ◽  
M. H. Rashid

Ion beam mixing has recently been found to be an effective method of producing amorphous alloys in the binary metal systems where the two original constituent metals are of different crystal structure. The mechanism of ion beam mixing are not well understood yet. Several mechanisms have been proposed to account for the observed mixing phenomena. The first mechanism is enhanced diffusion due to defects created by the incoming ions. Second is the cascade mixing mechanism for which the kinematicel collisional models exist in the literature. Third mechanism is thermal spikes. In the present work we have studied the mixing efficiency and ion beam induced amorphisation of Ni-Ti system under high energy ion bombardment and the results are compared with collisional models. We have employed plan and x-sectional veiw TEM and RBS techniques in the present work.


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