Chaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microfluidic device

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.

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Mathematical modeling of dielectrophoresis single-cell capture in a microfluidic device

2017 IEEE Conference on Electrical Insulation and Dielectric Phenomenon (CEIDP) ◽

10.1109/ceidp.2017.8257583 ◽

2017 ◽

Author(s):

A. Buke Hiziroglu

Keyword(s):

Mathematical Modeling ◽

Single Cell ◽

Microfluidic Device ◽

Cell Capture

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Application of the Fourier Expansion Method to the Problem of Stability of a Plane Jet

Journal of the Physical Society of Japan ◽

10.1143/jpsj.27.1035 ◽

1969 ◽

Vol 27 (4) ◽

pp. 1035-1040 ◽

Cited By ~ 2

Author(s):

Norito Ikeda

Keyword(s):

Fourier Expansion ◽

Expansion Method ◽

Plane Jet

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Electrothermal Blinking Vortices for Chaotic Mixing

Volume 9: Micro- and Nano-Systems Engineering and Packaging, Parts A and B ◽

10.1115/imece2012-88269 ◽

2012 ◽

Author(s):

Sophie Loire ◽

Paul Kauffmann ◽

Paul Gimenez ◽

Igor Mezić ◽

Carl Meinhart

Keyword(s):

Step Function ◽

Time Dependent ◽

Chaotic Mixing ◽

Electric Signal ◽

Dynamical System Theory ◽

Mixing Efficiency ◽

Lab On Chip ◽

Micro Particle Image Velocimetry ◽

Phase Signal ◽

On Chip

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.

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Formula for the calculation of integral cross sections in a Fourier expansion method

Physical Review A ◽

10.1103/physreva.55.812 ◽

1997 ◽

Vol 55 (1) ◽

pp. 812-814 ◽

Cited By ~ 3

Author(s):

Zhifan Chen ◽

Alfred Z. Msezane

Keyword(s):

Cross Sections ◽

Fourier Expansion ◽

Expansion Method

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Application of the implicit Fourier-expansion method to the calculation of three-dimensional equilibria by the iterative method

Computer Physics Communications ◽

10.1016/0010-4655(84)90047-x ◽

1984 ◽

Vol 31 (2-3) ◽

pp. 227-233 ◽

Cited By ~ 6

Author(s):

Aleksei I. Shestakov

Keyword(s):

Iterative Method ◽

Fourier Expansion ◽

Three Dimensional ◽

Expansion Method

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Mathematical Modeling of Dusty-Gas Boundary Layers

Applied Mechanics Reviews ◽

10.1115/1.3101716 ◽

1997 ◽

Vol 50 (6) ◽

pp. 357-370 ◽

Cited By ~ 26

Author(s):

A. N. Osiptsov

Keyword(s):

Mathematical Modeling ◽

Boundary Layers ◽

Expansion Method ◽

Heat Fluxes ◽

Matched Asymptotic Expansion ◽

Dusty Gas ◽

Two Phase ◽

Flat Surfaces ◽

Laminar Boundary Layers ◽

Further Development

This article reviews the state of the art in the mathematical modeling of dusty-gas laminar boundary layers in the framework of the two-fluid approach. Main attention is paid to the strict formulation of the two-phase boundary layer approximation, using the matched asymptotic expansion method. The low and high-velocity boundary layers both on curve and flat surfaces are considered. The particle accumulation in the boundary layers and the effects of particles on the friction and heat fluxes are examined. Important advances in the field of study are summarized and the areas deserving further development are discussed. This review article has 107 references.

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