JP2006007120A - Method and device for transporting droplet - Google Patents

Method and device for transporting droplet Download PDF

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JP2006007120A
JP2006007120A JP2004189147A JP2004189147A JP2006007120A JP 2006007120 A JP2006007120 A JP 2006007120A JP 2004189147 A JP2004189147 A JP 2004189147A JP 2004189147 A JP2004189147 A JP 2004189147A JP 2006007120 A JP2006007120 A JP 2006007120A
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droplet
electrode
transport
transport device
traveling direction
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JP4396417B2 (en
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Masao Washizu
正夫 鷲津
Masahide Gunji
昌秀 軍司
Hiroaki Nakanishi
博昭 中西
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Shimadzu Corp
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Abstract

<P>PROBLEM TO BE SOLVED: To make it possible to transport a droplet in an electrode system which can be manufactured by means of a simple single wiring. <P>SOLUTION: A pair of comb-line electrodes 2 are patterned such that one side becomes +45° and another side becomes -45° with respect to the center line X on a flat substrate 1, and are coated with an insulating layer 3 and, further, surface hydrophobic treatment 4 is applied thereon. In the initial state, the droplet has a shape 6 approximate to a sphere. When an alternate voltage is applied to the droplet, an inductive charge is generated on the surface of the droplet and is interacted with an applied electric field and, as a result, the droplet is deformed and is moved to the right side. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

本発明は、マイクロ化学分析装置やマイクロ化学合成装置など、基板上で数マイクロリットルからナノリットルオーダーの微量な移動操作を行なう分野に関するものである。   The present invention relates to a field of performing a small amount of transfer operation on the order of several microliters to nanoliters on a substrate, such as a microchemical analysis apparatus and a microchemical synthesis apparatus.

チップ上での微小液体の操作技術は、特にマイクロ化学分析システムやマイクロ化学合成装置において、微小液体の混合や、試料となる液体の目的の分析装置への輸送などに用いられる重要な技術である。   The technique for manipulating micro liquids on the chip is an important technique used for mixing micro liquids and transporting the liquid as a sample to the target analytical apparatus, particularly in micro chemical analysis systems and micro chemical synthesis devices. .

従来のチップ上での液体操作技術としては、閉じた流路を形成してその中で加圧や電気浸透流を利用して液体を駆動するものがある。しかし、この方法では開放系での操作が行えない、連続した流路の中での流体の一部だけを動かすことが困難である、デッドボリュームがさけられないなどの欠点がある。   As a conventional liquid manipulation technique on a chip, there is a technique in which a closed flow path is formed and liquid is driven using pressurization or electroosmotic flow. However, this method has disadvantages such that an open system cannot be operated, it is difficult to move only a part of the fluid in the continuous flow path, and a dead volume cannot be avoided.

そこで、このような問題点を解決するものとして、流路で完全に覆ってしまわない形、すなわち半開放系で液体を液滴の形として扱う技術がある。この方法については、基板上のストリップ状電極に電圧を印加して液体に働く誘電泳動力により電極に沿った動きを作り、これにより液体の駆動・液滴化や、混合を行う手段が開発されている(非特許文献1参照。)。しかしこの方法には、試料の導電率が高くなると発熱が大きくなり、駆動が困難になるという問題点がある。   Therefore, as a solution to such a problem, there is a technology that does not completely cover the flow path, that is, a technique that handles the liquid as a droplet in a semi-open system. For this method, a voltage is applied to the strip electrode on the substrate to create a movement along the electrode by the dielectrophoretic force acting on the liquid, thereby developing a means to drive and drop the liquid and mix it. (See Non-Patent Document 1). However, this method has a problem that when the conductivity of the sample is increased, heat generation is increased and driving becomes difficult.

また、エレクトロウエッティング(Electrowetting)を利用し、タイル状に作られた電極配列に順次電圧を印加してX−Y平面上の任意の位置に液滴を移動させる手法(非特許文献2参照。)や、表面を疎水化した多相電極を基板上に配列し、表面上に電圧を順次印加していくことにより液滴がころがるように移動させていく手法(非特許文献3参照。)も開発されている。しかし、これらの方法は電気的結線が複雑になり、多層配線技術を用いる必要があるという問題点がある。
T. B. Jones, M. Gunji, M. Washizu and M. J. Feldman: "Dielectrophoretic liquid actuation and nanodroplet formation", JAP, Vol. 89, No.2, p.1441-1448 (2001) J. Lee, H. Moon, J. Fowler, T. Schoellhammer and C.-J. Kim, "Electrowetting on Dielectric for Microscale Liquid Handling," Sensors and Actuators A, 2002, vol. 95, pp. 259-268. Masao Washizu: "Electrostatic Actuation of Liquid Droplets for Micro-Reactor Applications", IEEE Transaction IA, Vol.34, No.4, p.732-737 (1998)
In addition, a method of moving a droplet to an arbitrary position on an XY plane by sequentially applying a voltage to an electrode array formed in a tile shape using electrowetting (see Non-Patent Document 2). ) And a method of moving the liquid droplets so as to roll by arranging a multiphase electrode having a hydrophobic surface on the substrate and sequentially applying a voltage on the surface (see Non-Patent Document 3). Has been developed. However, these methods have a problem that the electrical connection becomes complicated and it is necessary to use a multilayer wiring technique.
TB Jones, M. Gunji, M. Washizu and MJ Feldman: "Dielectrophoretic liquid actuation and nanodroplet formation", JAP, Vol. 89, No.2, p.1441-1448 (2001) J. Lee, H. Moon, J. Fowler, T. Schoellhammer and C.-J. Kim, "Electrowetting on Dielectric for Microscale Liquid Handling," Sensors and Actuators A, 2002, vol. 95, pp. 259-268. Masao Washizu: "Electrostatic Actuation of Liquid Droplets for Micro-Reactor Applications", IEEE Transaction IA, Vol.34, No.4, p.732-737 (1998)

本発明は、単純な1層配線で作製可能な電極系での液滴の輸送方法及び装置の提供を目的とする。   An object of the present invention is to provide a method and an apparatus for transporting droplets in an electrode system that can be manufactured with a simple single-layer wiring.

本発明は、基板上にパターニングされた輸送電極が形成され、その輸送電極上が絶縁膜で被われ、その絶縁膜上を液滴が輸送される液滴の輸送装置であって、前記輸送電極は液滴進行方向に沿って液滴よりも小さい間隔をもって両側に配置された一対の電極からなり、各電極は液滴進行方向に対して90度よりも小さい角度をもち、液滴よりも小さい間隔で互いに平行に配置された導体パターンを有し、前記輸送電極には交流電圧が印加されることを特徴とする液滴の輸送装置に関するものである。   The present invention relates to a droplet transport apparatus in which a patterned transport electrode is formed on a substrate, the transport electrode is covered with an insulating film, and a droplet is transported on the insulating film, and the transport electrode Consists of a pair of electrodes arranged on both sides along the droplet traveling direction with a smaller interval than the droplet, each electrode having an angle smaller than 90 degrees with respect to the droplet traveling direction and smaller than the droplet The present invention relates to a droplet transport device having conductor patterns arranged parallel to each other at an interval, wherein an alternating voltage is applied to the transport electrode.

基板上に、液滴を輸送しようとする方向の中心線を境に、進行方向に対し一方が+θ1、他方が−θ2の角度を持つような多数の電極を配置し、液滴をそれらの電極の一端の中心線上付近に置く。ここでθ1とθ2は等しくても異なっていてもよい。電極に交流電圧を印加すると、交流電圧のピーク付近では電気力により液滴が扁平化し、電圧が0になる瞬間付近では変形が解放されるような振動を生ずる。扁平化の生じるサイクルでは、電極のエッジの作る電界集中により、電極形状を越えた変形が生じにくいのに対し、解放されるサイクルでは等方的に球形に近い形に戻る。電極形状が進行方向の前後に対して非対称な形をしているため、変形サイクルが生ずるたびに、液滴は移動しやすい方向へと移動していくことになる。すなわち、このインチワームメカニズムにより、液滴は一方向へと輸送されることになる。 A large number of electrodes are arranged on the substrate such that one is + θ 1 and the other is −θ 2 with respect to the traveling direction from the center line of the direction in which the droplet is to be transported. The electrode is placed near the center line of one end. Here, θ 1 and θ 2 may be equal or different. When an AC voltage is applied to the electrodes, the droplets are flattened by an electric force in the vicinity of the peak of the AC voltage, and vibration is generated such that the deformation is released near the moment when the voltage becomes zero. In the cycle in which flattening occurs, deformation beyond the electrode shape is less likely to occur due to the electric field concentration created by the edge of the electrode, whereas in the released cycle, the shape returns to a nearly spherical shape. Since the electrode shape is asymmetric with respect to the front and rear in the traveling direction, the droplet moves in a direction in which it easily moves each time a deformation cycle occurs. That is, the inch worm mechanism causes the droplets to be transported in one direction.

前記輸送電極は、液滴進行方向に対して10度から80度の角度をもって配置されていることが好ましい。
そのような電極の好ましい形状は櫛歯状電極である。
前記絶縁膜の膜厚は0.1μmから100μmであることが好ましい。
液滴を形成する液体と接触する基板側の表面に疎水処理がされている液滴の輸送装置であることが好ましい。
2以上の輸送電極列を進行方向に1点で集合するように配置し、その集合点に複数の液滴を集合させることにより、液滴の混合を行なわせる液滴の輸送装置とすることができる。
本発明の輸送方法は、前記記載の液滴の輸送装置を用い、前記交流電圧の印加により液滴に変形振動を引き起こし、その振動により液滴を移動させる方法である。
印加電圧の周波数が、液滴粒子の固有振動数と共振するように選ばれた液滴の輸送装置とすることが好ましい。
The transport electrode is preferably arranged at an angle of 10 degrees to 80 degrees with respect to the droplet traveling direction.
The preferred shape of such an electrode is a comb-like electrode.
The insulating film preferably has a thickness of 0.1 μm to 100 μm.
It is preferable that the apparatus is a droplet transport device in which the surface on the substrate side that comes into contact with the liquid forming the droplet is subjected to a hydrophobic treatment.
By arranging two or more transport electrode rows so as to gather at one point in the traveling direction, and gathering a plurality of droplets at the gathering point, a droplet transport device that mixes the droplets is provided. it can.
The transport method of the present invention is a method in which the droplet transport device described above is used, deformation deformation is caused in the droplet by application of the AC voltage, and the droplet is moved by the vibration.
It is preferable that the droplet transport device is selected so that the frequency of the applied voltage resonates with the natural frequency of the droplet particles.

本発明の装置は、一対の電極により構成されるため、単純な1層のプロセスにより作製が可能である。そのため、信頼性の高い作製及び運転が可能で、かつ低コストであるため、チップ自体のディスポーサブル化も可能である。また、駆動のための電源系の単純化やローコスト化も実現できる。   Since the device of the present invention includes a pair of electrodes, it can be manufactured by a simple single-layer process. Therefore, it is possible to manufacture and operate with high reliability and low cost, so that the chip itself can be made disposable. In addition, the power supply system for driving can be simplified and the cost can be reduced.

電極を櫛歯状にすることによって電源装置への接続を簡単にすることができ、構成を単純化できる。
液滴と接触する基板側の表面に疎水処理を施すことによって、交流電圧0付近では液滴をより球形に近い形状にすることができ、交流電圧のピーク付近での扁平形状との間の形状変形量を大きくすることができて、液滴の移動量を大きくすることができる。
印加電圧の周波数が、液滴粒子の固有振動数と共振するように選ぶことによって、液滴の移動量をより大きくすることができる。
By making the electrodes comb-like, the connection to the power supply device can be simplified, and the configuration can be simplified.
By applying a hydrophobic treatment to the surface of the substrate in contact with the droplet, the droplet can be made more spherical in the vicinity of the alternating voltage 0, and the shape between the flat shape near the peak of the alternating voltage The amount of deformation can be increased, and the amount of droplet movement can be increased.
By selecting the frequency of the applied voltage so as to resonate with the natural frequency of the droplet particles, the amount of droplet movement can be further increased.

本発明の一実施例を詳細に説明する。
図1に示すように、平面基板であるガラス基板1上に、進行方向Xの中心線に対して一方が+45度、他方が−45度となるように一対の櫛歯状電極2a,2bがパターンとして形成され、検出部が対向するように配置されている。電極2a,2bはその上が絶縁層3でコートされている。絶縁層3の上には表面疎水処理層4が施されている。櫛歯状電極2は電源5につながれる。
絶縁層3としてはSiO2膜、疎水処理層4としてはアモルファステフロン(登録商標)のスピンコート膜、電源としては50Hzの周波数で170Vの電源5を用いる。
電極2は、基板1上に銅やアルミニウムなどの導電膜を形成し、写真製版とエッチングによりパターニングして形成することができる。
An embodiment of the present invention will be described in detail.
As shown in FIG. 1, a pair of comb-like electrodes 2 a and 2 b are formed on a glass substrate 1 which is a flat substrate so that one is +45 degrees and the other is −45 degrees with respect to the center line in the traveling direction X. It is formed as a pattern and is arranged so that the detection parts face each other. The electrodes 2a and 2b are coated with an insulating layer 3 thereon. A surface hydrophobic treatment layer 4 is provided on the insulating layer 3. The comb-like electrode 2 is connected to a power source 5.
An SiO 2 film is used as the insulating layer 3, an amorphous Teflon (registered trademark) spin coat film is used as the hydrophobic treatment layer 4, and a power source 5 of 170 V at a frequency of 50 Hz is used as the power source.
The electrode 2 can be formed by forming a conductive film such as copper or aluminum on the substrate 1 and patterning it by photolithography and etching.

本発明は前記記載の絶縁層、処理方法などに限定されず、電極形状としても角度45度の直線的な櫛歯状電極以外に、30度、60度など45度以外の直線的な櫛歯状電極や、曲線的な櫛歯状の電極、スパイラル状の電極など、電極間に交流電圧を印加した際に液滴に一定方向の重心移動を伴う振動を生じさせることができるものなら、任意の形状を用いることができる。   The present invention is not limited to the above-described insulating layer, processing method, and the like, and in addition to the linear comb-shaped electrode having an angle of 45 degrees as an electrode shape, linear comb teeth other than 45 degrees such as 30 degrees and 60 degrees. Any electrode that can cause vibration with a center of gravity movement in a certain direction when an AC voltage is applied between the electrodes, such as a ring-shaped electrode, a curved comb-shaped electrode, or a spiral electrode Can be used.

図1において、電極2a,2bの一端に2つの電極2a,2bをまたぐように液滴6を配置し、電源5により電極2a,2bを励起すると、交流電圧のピーク付近では電気力により液滴6が扁平化し、電圧が0になる瞬間付近では変形が解放されるような振動を生ずる。
ここで、扁平化の生じるサイクルでは、櫛歯状電極2a,2bのエッジの作る電界集中により櫛歯を越えた変形が生じにくいのに対し、扁平化の解放されるサイクルでは、等方的に球形に近い形に戻る。この結果、液滴は図1に示す右側である液滴進行方向Xに移動していく。
In FIG. 1, when a droplet 6 is disposed so as to straddle two electrodes 2a and 2b at one end of electrodes 2a and 2b, and the electrodes 2a and 2b are excited by a power source 5, the droplet is generated by an electric force near the peak of the AC voltage. In the vicinity of the moment when 6 becomes flat and the voltage becomes zero, a vibration is generated so that the deformation is released.
Here, in the cycle in which flattening occurs, deformation beyond the comb teeth is unlikely to occur due to the electric field concentration created by the edges of the comb-like electrodes 2a and 2b, whereas in the cycle in which flattening is released, it is isotropic. Return to a shape close to a sphere. As a result, the droplet moves in the droplet traveling direction X on the right side shown in FIG.

液滴移動のメカニズムをさらに詳細に説明したのが図2である。図2a)に示すように、液滴の変形を生じない初期状態においては、疎水性表面処理のため、液滴はほぼ球形に近い形7をとる。
周波数fの交流電圧を印加すると、液滴の誘電率又は導電率が周囲の媒質の誘電率又は導電率と異なる場合には、液滴表面に誘導電荷が生じ、これと印加電界が相互作用する結果、液滴には周波数2fの電気力が働き、それにより液滴は変形を受ける。
FIG. 2 illustrates the mechanism of droplet movement in more detail. As shown in FIG. 2a), in the initial state where no deformation of the droplet occurs, the droplet takes a shape 7 that is almost spherical due to the hydrophobic surface treatment.
When an alternating voltage of frequency f is applied, if the dielectric constant or conductivity of the droplet is different from the dielectric constant or conductivity of the surrounding medium, an induced charge is generated on the surface of the droplet, and the applied electric field interacts therewith. As a result, an electric force having a frequency of 2f acts on the droplet, and the droplet is deformed.

変形が最大になった状態を模式的に表したのが図2b)である。電気力線8により、液滴は基板に引きつけられて扁平になるような変形9を受ける。このとき、斜めに設けられた櫛歯状電極のエッジと液滴の表面が平行に接するようになる部位10では、エッジ部の強電解が液滴を引きつけるため、このエッジを越えて液体が移動することが困難になる。そのため部位10では、液滴の表面が電極エッジと平行になるような変形をするのに対し、電極エッジと液滴表面が直行する部位11ではそのような制限はなく、電極に沿って広がって変形する。   FIG. 2b) schematically shows a state in which the deformation is maximized. The electric lines of force 8 cause the droplets 9 to be deformed 9 such that they are attracted to the substrate and become flat. At this time, in the portion 10 where the edge of the comb-like electrode provided obliquely and the surface of the droplet come into contact with each other in parallel, the strong electrolysis at the edge attracts the droplet, so that the liquid moves beyond this edge. It becomes difficult to do. For this reason, the portion 10 is deformed so that the surface of the droplet is parallel to the electrode edge, whereas the portion 11 where the electrode edge and the surface of the droplet are orthogonal is not such a restriction and spreads along the electrode. Deform.

液滴の変形は図2b)に示すように、図中右上及び右下により広がる非対称なものになり、その重心位置は変形前よりも図中右側にシフトしたものになる。電気力は周波数2fで0とピーク値の間を変化しているため、印加周波数の1/2周期後には図2c)に示すように変形が解放されるが、この際、液滴は非対称に変形した時の重心を中心として、球状化13する。従って変形の1サイクルを減るごとに、液滴は図中右方向に距離14ずつ移動することになる。   As shown in FIG. 2 b), the deformation of the droplet becomes asymmetrical in the upper right and lower right in the figure, and the center of gravity shifts to the right in the figure than before the deformation. Since the electric force changes between 0 and the peak value at the frequency 2f, the deformation is released after a half period of the applied frequency as shown in FIG. 2c). The spheroidizing 13 is performed with the center of gravity at the time of deformation as the center. Accordingly, each time one cycle of deformation is reduced, the droplet moves by a distance of 14 in the right direction in the figure.

このメカニズムによる移動距離は、(1ステップあたりの移動距離)×(変形サイクル数)によって決まり、1ステップあたりの移動距離は、変形の大きさに依存し、電極ピッチの整数倍となる。変形が小さい場合は移動は起こらないが、大きな変形の場合には電極ピッチ1つ以上の移動を生ずることも可能である。この変形を大きくとるには、液滴の固有振動と共振するように印加周波数を選ぶこと、すなわち、(電源周波数)=(液滴の固有周波数)÷2、となるように選ぶことが有効である。
ここで、液滴の固有振動数とは、液滴を構成する液体の表面張力と質量による生じる、液体表面の変形の自由振動の固有振動数のことで、空間中に孤立した直径1mmの水滴の扁平化と偏長化を繰り返すモードに対しては、固有振動数は約340Hzとなる。
The movement distance by this mechanism is determined by (movement distance per step) × (number of deformation cycles), and the movement distance per step depends on the size of the deformation and is an integral multiple of the electrode pitch. If the deformation is small, no movement occurs, but if the deformation is large, it is possible to move one or more electrode pitches. In order to make this deformation large, it is effective to select an applied frequency so as to resonate with the natural vibration of the droplet, that is, select so that (power supply frequency) = (natural frequency of the droplet) / 2. is there.
Here, the natural frequency of the liquid droplet is a natural frequency of free vibration of deformation of the liquid surface caused by the surface tension and mass of the liquid constituting the liquid droplet. A water droplet having a diameter of 1 mm isolated in the space. For a mode that repeats flattening and lengthening, the natural frequency is about 340 Hz.

本発明は、マイクロ化学分析やマイクロ化学合成装置などに用いることができる。   The present invention can be used for microchemical analysis, microchemical synthesis apparatus, and the like.

本発明の一実施例を示す図であり、(A)は平面図、(B)はそのA−A’線位置での断面図である。It is a figure which shows one Example of this invention, (A) is a top view, (B) is sectional drawing in the A-A 'line position. (a)〜(c)は同実施例の動作説明図であり、いずれも左図は平面図、右図はその液滴位置での断面図である。(A)-(c) is operation | movement explanatory drawing of the Example, all are a top view in the left figure, and a right figure is sectional drawing in the droplet position.

符号の説明Explanation of symbols

1 基板
2 電極
3 絶縁層
4 表面疎水処理
5 電源
6 液滴
7 液滴の初期位置及び形状
8 電気力線
9 電界印加による変形した液滴
10 電極エッジと液滴表面が接する部位
11 電極エッジと液滴表面が直交する部位
12 b)における変形時の液滴形状
13 変形が戻った時の液滴位置
14 1サイクル中の液滴の移動距離
DESCRIPTION OF SYMBOLS 1 Substrate 2 Electrode 3 Insulating layer 4 Surface hydrophobic treatment 5 Power supply 6 Droplet 7 Droplet initial position and shape 8 Electric field lines 9 Droplet deformed by electric field application 10 Electrode edge and contact area of drop surface 11 Electrode edge Droplet shape at the time of deformation in the part 12 b) where the surface of the liquid droplet intersects at right angle 13 Droplet position when the deformation is restored 14 Droplet moving distance in one cycle

Claims (8)

基板上にパターニングされた輸送電極が形成され、その輸送電極上が絶縁膜で被われ、
その絶縁膜上を液滴が輸送される液滴の輸送装置であって、
前記輸送電極は液滴進行方向に沿って液滴よりも小さい間隔をもって両側に配置された
一対の電極からなり、
各電極は液滴進行方向に対して90度よりも小さい角度をもち、液滴よりも小さい間隔で互いに平行に配置された導体パターンを有し、
前記輸送電極には交流電圧が印加されることを特徴とする液滴の輸送装置。
A patterned transport electrode is formed on the substrate, and the transport electrode is covered with an insulating film,
A droplet transport device for transporting droplets on the insulating film,
The transport electrode comprises a pair of electrodes arranged on both sides with a smaller interval than the droplet along the droplet traveling direction,
Each electrode has an angle smaller than 90 degrees with respect to the droplet traveling direction, and has conductor patterns arranged in parallel to each other at an interval smaller than the droplet,
An apparatus for transporting droplets, wherein an alternating voltage is applied to the transport electrode.
前記輸送電極は櫛歯状電極である請求項1に記載の液滴の輸送装置。   The droplet transport device according to claim 1, wherein the transport electrode is a comb-like electrode. 前記輸送電極は液滴進行方向に対して10度から80度の角度をもって設置された請求項1又は2に記載の液滴の輸送装置。   The droplet transport device according to claim 1 or 2, wherein the transport electrode is installed at an angle of 10 degrees to 80 degrees with respect to a droplet traveling direction. 前記絶縁膜の膜厚は0.1μmから100μmである請求項1から3のいずれかに記載の液滴の輸送装置。   The droplet transport device according to claim 1, wherein the insulating film has a thickness of 0.1 μm to 100 μm. 液滴を形成する液体と接触する基板側の表面に疎水処理を施した請求項1から4のいずれかに記載の液滴の輸送装置。   The droplet transport device according to claim 1, wherein a hydrophobic treatment is applied to a surface on a substrate side that comes into contact with a liquid forming the droplet. 2以上の輸送電極列を進行方向に1点で集合するように配置し、その集合点に複数の液滴を集合させることにより、液滴の混合を行なわせる請求項1から5のいずれかに記載の液滴の輸送装置。   6. The liquid droplet mixing is performed by arranging two or more transport electrode arrays so as to gather at one point in the traveling direction and collecting a plurality of liquid droplets at the gathering point. The droplet transport device described. 請求項1から6のいずれかに記載の液滴の輸送装置を用い、前記交流電圧の印加により液滴に変形振動を引き起こし、その振動により液滴を移動させる液滴の輸送方法。   A droplet transport method using the droplet transport device according to claim 1, causing deformation vibration to the droplet by application of the alternating voltage, and moving the droplet by the vibration. 印加電圧の周波数が、液滴粒子の固有振動数と共振するように選ばれた請求項1に記載の液滴の輸送装置。
The droplet transport device according to claim 1, wherein the frequency of the applied voltage is selected so as to resonate with the natural frequency of the droplet particle.
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