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Chaotic mixing in a curved-square channel flow is studied experimentally and numerically. Two walls of the channel (inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flows. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient or the Reynolds number) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In the present paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing experimental and numerical results. We produced a micromixer model of the curved channel several centimeters long with square cross section of a few millimeters side. The secondary flow was measured using laser induced fluorescence (LIF) method to examine secondary flow characteristics. We also performed three-dimensional numerical simulations for the exactly same configuration as the experimental system to study the mechanism of chaotic mixing. It is found that good mixing performance is achieved for the case of De ≤ 0.1Tr, and that mixing efficiency changes according to the difference in inflow conditions. The flow is studied both experimentally and numerically, and both results agree with each other very well.

Recently, great attention has been paid to the development of a micro-chemical-analysis device called the micro total analysis systems (μTAS) in the field of engineering. This device, which consists of various microflow devices and sensors, functions through a series of operations such as mixture, reaction, separation, and extraction. However, the flow is in the very low Reynolds number region because of the microsize of the channel, where mechanical mixing by turbulence cannot be expected without a special artifice. Currently, a micromixer is needed to mix low-Reynolds-number flows efficiently. Stroock et al. [

On the other hand, a micromixer that uses chaos of the flow caused by a time-periodic perturbation was studied by Niu and Lee [

We then proposed a micromixer making use of chaos of the secondary flow, specifically, a micromixer in which the secondary flow becomes chaotic through a curved channel where two walls of the channel rotate [

A diagram of the experimental setup is shown in

The dimension of the curved channel is shown in

Other nondimensional parameters concerned are the Reynolds number Re, the Dean number De [

where

2a [mm] | R [mm] | δ | l [mm] |
---|---|---|---|

3 | 15 | 0.1 | 58.9 |

Next we explain the method of visualization of the flow. A scheme of the method of visualization is shown in

We acquired the fluorescence only of the rhodamine B by installing the high-pass filter (transmitted wave length of 570 nm or more) in a high speed camera for LIF to calculate the concentration distribution. We also measured the viscosity of glycerol aqueous solution using the precision rotational viscometer before and after the experiment and confirmed that there was no change of viscosity throughout the experiment. The density of glycerol aqueous solution was calculated by use of the gravimeter.

To examine the secondary flow characteristics in detail, we also performed three-dimensional numerical simulations for exactly the same configuration as the experimental setup. We used OpenFOAM [

When

Therefore, the experimental results have shown that mixing is highly promoted around the range of

In

Therefore it is concluded that the numerical simulations are validated since the results of the numerical simulations reproduce the experimental results very well. Thus, the discussion on the physical mechanism of mixing will be conducted using the numerical simulation results.

Using the results of the numerical simulations, the mixing rate in the cross section at 180˚ is calculated. In order to quantitatively assess the effect of mixing, the mixture rate

In this equation

When the two fluids are completely mixed,

The mixing rate

For Tr = 3 and −3, the mixing rate is much greater than the case for Tr = 0, where no rotation is applied. On the other hand, it is interesting that the effect of the change of inflow condition of the concentration distribution is different for Tr > 0 or <0. Here we focus the secondary and axial flow velocities in the channel cross section.

For Tr = 3 as shown in

For Tr = −3 as shown in

In the present paper, we made the micromixer with a rotor and curved channel, which can mix very low Reynolds number flows efficiency, and obtained good agreement between experimental and numerical results:

When

The highest mixing rate is

The inflow conditions at the entrance have large effect on the promotion of mixing, and the maximum promotion is achieved when the reverse flow due to rotation and secondary flow is combined.

The authors would like to express their cordial thanks to Naoyuki Yasuda and Koichiro Tabara for their help in the experiments.