• ETRI Journal
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• v.30 no.1
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• pp.170-172
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• 2008

A substitution box (S-box) plays a central role in cryptographic algorithms. In this paper, an efficient method for designing S-boxes based on chaotic maps is proposed. The proposed method is based on the mixing property of piecewise linear chaotic maps. The S-box so constructed has very low differential and linear approximation probabilities. The proposed S-box is more secure against differential and linear cryptanalysis compared to recently proposed chaotic S-boxes.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.2 s.233
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• pp.232-238
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• 2005

The 'Mixing Index($D_I$)' is used as a conventional guidance measuring the degree of mixing for multiphase flows. For the case when insoluble solutions flow in a passive micromixer, a new method to calculate $D_I$ is proposed. The 'Vortex Index(${\Omega}_I$)' is suggested and formulated. We infer that ${\Omega}_I$ relates to the degree of chaotic advection. Various arbitrary shaped microchannels were tested to calculate the $D_I\;and\;{\Omega}_I$, and then a simple algebraic equation, $D_I=Aexp(B{\Omega}_I)$, is obtained. This equation may be used instead of the conventional partial differential equation, concentration equation, to estimate the degree of mixing.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.1-13
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• 2005

Fluid flows within microchannels are characterized by low Reynolds numbers. Therefore the effect of mixing is a crucial factor in design of the channels. Since the action of the electro-osmotic or magnetic forces used in the mixing enhancement is usually periodic in the three-dimensional channel configuration, use of the various concepts of chaotic advection is reasonable in the quantification of the stirring effect. In this paper, the details of the method of material-stretching mapping is explained. The actual application of the method to the screw extruder is also presented.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1841-1844
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• 2004

'Mixing Index($D_I$)'s generally used to measure the degree of mixing. A new method to calculate $D_I$ was proposed, when insoluble solution flows in micromixer. 'Vortex Index (${\Omega}_I$)'which indicate the degree of chaotic advection, is defined and formulated. A lots of arbitrary shaped microchannels were tested to calculate the $D_I$ and ${\Omega}_I$. And then a simple algebraic equation, $D_I=A{\Omega}_I+B$, was obtained. This equation may be used instead of partial differential equation, concentration equation.

• 한국가시화정보학회:학술대회논문집
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• 2006.12a
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• pp.96-101
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• 2006

3-D visualization using confocal laser scanning microscopy (CLSM) in a chaotic micromixer was performed as a reproduction experiment and the feasibility of 3-0 imaging technique in the microscale was confirmed. For diagonal micromixer (DM) and two types of staggered herringbone micromixers (SHM) designed by Whitesides et al., to verify the evolution of mixing, cross sectional images are reconstructed at the end of every cycle. In a DM, clockwise rotational flow motion generated by diagonal ridges placed on the floor of micromixer is observed and this motion makes the fluid commingle. On the contrary, there are two rotational flow structures in the SHM and the centers of rotation exchange their position each other every half cycle because of the V shape of ridges varying their orientation every half cycle. Local rotational flow and local extensional flow generated by the complicate ridge pattern make the flow be chaotic and accelerate the mixing of fluid. The dominant parameter that influences on the mixing characteristic of SHM is not the length of micromixer but the number of ridges under the same flow configurations.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1016-1020
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• 2003

In this paper, we present a technology of producing anew chaotic micromixer, named Micromixer with Arranged Blocks(MAB), and the experimental result of the mixing performance. Chaotic mixing was successfully achieved by introducing periodic perturbation in the field of the channel flow by means of slanted blocks. The MAB was made by an RP(Rapid Prototyping) technology. We performed flow visualization experiments for the quantification of the mixing performance with the MAB. Lyapunov exponent was measured to be 0.3557 and 0.1305 for the block height 0.8 and 0.2 times the channel width.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1758-1760
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• 2008

Under typical operating conditions, flows in microfluidic devices are laminar and molecular diffusion across the channels is slow, which makes an efficient mixing in microfluidic devices difficult to achieve. The mechanism to achieve effective mixing in laminar flows is that of repetitive stretching and folding. Essential is to generate spatially periodic flows with crossing cross sectional streamlines. A mapping method is employed to analyze mixing in micromixers, enabling us to investigate the progress of mixing both qualitatively and quantitatively. The progress of mixing is characterized by a measure of mixing, called the discrete intensity of segregation. The mapping method is applied to mixing in such micromixers as the staggered herringbone mixer, the barrier embedded micromixer, and the three-dimensional serpentine channel to demonstrate the capability of the numerical scheme to tackle general mixing problems in microfluidic devices.

• 한국가시화정보학회:학술대회논문집
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• 2003.11a
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• pp.79-80
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• 2003

This paper presents experimental results on stirring characteristics in a microchannel with structures changed. We fabricated a new chaotic micro mixer and made by a RP(Rapid Rrototyping) technology. Flow visualization for the stirring effect was performed by using pure orator in a reservoir and fluorescent dye in the other. Chaotic mixing was achieved by introducing periodic perturbation in the field of the microchannel flow by means of shaped structures. It was found that the stirring is enormously enhanced at larger bock-height.

• The Korean Journal of Rheology
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• v.8 no.3_4
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• pp.187-198
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• 1996

최근에 본 연구자에 의해서 단축 스크류 공정에서 카오스 스크류라고 명명되어진 카오스 혼합장치가 성공적으로 개발되었다. 기하학적 조건이나 공정조건에 대한 설계변수로 카오스 스크류를 설계하기 위하여 체류시간, 포인카레 단면 그리고 혼합패턴등에 대한 계산 과 해석이 이루어져야 하는데 이를 단지 Runge-Kutta 방법에 의해 속도장을 적분한다면 상당한 계산시간이 소비된다. 이러한 수치문제를 극복하기 위하여 본논문에서는 새로운 사 상법을 제안한다. 이 방법으　 사용하면 벽면 근처의 특이점 영역에서도 수치문제가 해결된 다. 본 논문에서 제안하는 수치사상법은 Runge-Kutta 방법에 비하여 수치계산의 효율성과 정확도 면에서, 특히 유안요소법으로 얻은 속도장에 대하여 우수함이 밝혀졌다. 이러한 사상 법은 공간주기 유동장뿐만 아니라 시간주기 유동장에서 적용할수 있다.

• The Korean Journal of Rheology
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• v.8 no.1
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• pp.11-29
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• 1996

스크류 채널 내에 주기적을 배리어를 설치함으로써 단축 스크류 압출 공정에서의 혼합 성능이 높여질수 있음이 S.J. Kim과 T.H. Kwom에 의해 밝혀진 바있다. 그들은 이새 로운 스크류를 통한 혼합이 카오틱하는 점으로부터 이 새로운 스크류를 카오스 스크류라고 명명했다. 우리는 카오스 스크류가 장착된 단축 압출공정에서 역학계 이론과 혼합운동학을 연계하여 연구를 수행하였다. 포인카레 단면을 통한 연구로부터 우리는 배리어의 배열이 islan의 크기에 대단히 밀접하게 관련되어 있음을 발견하였다. 연속적인 쉘 변형은 카오틱 유동에서 유체 요소를 지수 함수 형태로 늘이는 늘임과 접힘으로 이루어진 카오틱 혼합 메 카니즘을보여준다. 유체요소의 국부 늘임은 원리상으로는 계산되어질수 있으나 수치 해석상 의 어려운 점이 있다. 정규 유동에서와 달리 카오틱 유동에서는 입자 추적이 Runge-Kutta 적분중의 시간간격에 대단히 민감하다. 그래서 실제 사용될수 있는 시간 간격에 의해 계산 된 국부 늘임율 및 혼합효율의 정확도가 보장되어지지 않는다. 이러한 점들을 고려하여 우 리는 새로운 혼합 척도로 $\sigma$z를 제안하는데 이값은 비교적 긴 유체선분이 채널방향을 따라 늘어나는 비에 관련된 값이다. 배리어 영역의 길이가 짧을수록 $\sigma$z는 큰값으로 나타나지만 포인카레 단면에 의한 연구에 따르면 배리어의 주기가 너무 짧다면 두 개의 거대한 island 가 존재하는 것으로 밝혀졌다. 그리고 이러한 사실은 유체요소의 늘임비가 크다는 것이 항 상 좋은 혼합성능을 뜻하는 것은 아니라는 점을 보여준다. 이러한 관점에서 볼 때 혼합 스 크류를 설계하는데 있어서는 포인카레 단면을 병행하여 ${\sigma}_z$의 값을 사용하는 것이 바람직할 것이다.