Study on liquid dielectrophoresis based on double flexible electrodes simulating interdigitated pattern electrodes

Shang Xiu-Ting; Chen Tao; Chen Jing; Xu Rong-Qing

doi:10.7498/aps.73.20231485

Abstract

Authors and contacts

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1. 引　言
2. 结构及原理
2.1 结构设计
2.2 工作原理
3. 仿真及实验
3.1 仿真及结果分析
3.2 实验及结果分析
4. 结　论

References

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Abstract

Dielectrophoresis affects the surface wettability by applying a non-uniform electric field to dipoles inside dielectric liquid, achieving adjustable droplet contact angle and overcoming the saturation limitation of contact angle caused by the electrowettability effect. However, it is difficult to realize useful three-dimensional tunable optical devices because most of the driving electrodes need to be patterned. In this work, a model of double flexible electrodes simulating planar interdigitated pattern electrodes is proposed based on the dielectrophoresis. Double flexible electrodes, which are wrapped with an insulating dielectric layer and are not conductive to each other are arranged at close intervals and wound along the plane substrate to form a two-dimensional planar line wall. A hydrophobic layer is used to fill the gap and increase the initial contact angle. Ultimately, the “droplet-interdigitated planar line wall” dielectrophoresis driven-droplet model is formed after the dielectric droplets have been deposited on the line wall surface. Firstly, considering the influence of penetration depth and electrode gap area, Young’s equation is theoretically modified to adapt to this model. Then, the finite element algorithm simulation is used to used to comparatively analyze the potential distribution of this model and the planar interdigitated pattern electrode model. The field strength distributions of the electrodes with different wire diameters and insulating layer thickness values are analyzed. It can be found that with the increase of the diameter of the electrode wire and the thickness of the insulating layer, the morphology of the model changes from the tip electrode into the planar electrode, the surface field strength attenuates exponentially and the peak value decreases. This shows that the structure of this electrode in this model is superior to that of the planar electrode. After that, the contact angle of the model is measured experimentally in a range of 58°－90° under 0–250 V_rms voltage, which is in line with the theoretical expectation. At the same time, neither obvious contact angle lag nor saturation is observed in the experiment. Finally, the new electrophoretic driving droplet model constructed in this paper transforms the dielectric electrophoretic driving mode from a two-dimensional planar electrode to a one-dimensional flexible linear electrode. Because of its flexibility and plasticity, it is convenient to form a three-dimensional cavity and can be applied to more complex device structures.

Keywords:

dielectrophoresis /
simulated interdigitated patterned electrodes /
flexible electrodes /
contact angle

PACS:

47.55.dr	(Interactions with surfaces)
47.54.De	(Experimental aspects)
47.55.np	(Contact lines)

Authors and contacts

College of Electronic and Optical Engineering & College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Corresponding author: Chen Tao, chent@njupt.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11974188, 61905117), the China Postdoctoral Science Foundation (Grant Nos. 2021T140339, 2018M632345), the Postdoctoral Science Foundation of Jiangsu Province, China (Grant No. 2021K617C), and the Key Research and Development Program of Zhenjiang, China (Grant No. GY2023009).

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1. 引　言

润湿即流体在接触固体时沿其表面扩展, 发生在可能由气体或其他流体组成的环境中, 可通过改变固体表面材料、表面特性(表面化学、微米或纳米级形貌)、或引入外来的能量(电磁等)来改变润湿程度^[1]. 表征润湿系统的中心特征是接触角, 被定义为在三相接触线处固体表面的切线与液体-流体界面的切线之间的角度^[2].

改变固液润湿程度的方式主要有电润湿和介电泳效应. 电润湿效应通过施加电压以修正三相接触线能量平衡, 来改变接触角大小^[3,4]. 其驱动采用平板电极, 表面沉积导电液体, 并在两者之间增加薄介电层以增强电容现象, 加强电荷累积, 产生更强的电场力, 但存在接触角滞后和饱和效应^[5,6]. 相比之下, 介电泳效应因克服电润湿的局限性而受到关注. 液体介电泳效应即介电液体中偶极子被极化后, 于非均匀电场中受力不平衡而产生的运动. 虽然液体介电泳调谐需要更高的驱动电压, 但与介电润湿消耗的功率数量级相同^[7], 且被广泛应用于微流控芯片^[8–10]和光流控^[11–13]等领域. 例如Frozanpoor 等^[14]利用液体介电泳中液滴的固-液界面处高电场开发了一个液滴驱动平台, 引入润滑层并使用迭代方法通过电压驱动不同体积的去离子水滴, 实现通过控制液体介电泳力来控制液滴的润湿行为和液滴-液界面的特性. Li等^[15]进行了一项结合使用介电泳立和惯性力的研究. 通过结合与通道相同高度的3D侧壁电极和收缩/膨胀(CEA)结构, 扩大介电泳力的作用范围, 实现了一种新的细胞分选和分离方法. Chen等^[16]制作了一种可调谐面内光流控透镜, 以图案化ITO (氧化铟锡)沉积玻璃作为电极, 0—260 V_rms电压下通过介电泳力连续调节硅油-空气界面从凹到凸, 实现焦距从–1—+1 mm的连续变化. 这里V_rms为交流电压的有效值. 同时为获得可控的非均匀电场, 最理想的方案是使用图案化电极, 这消除了对复杂控制系统或制造大量小电极的需要, 从而降低了总体复杂性和成本. 通常选择ITO等导电材料以光刻、离子束蚀刻等方式形成平面图案电极, 再通过喷涂、旋涂等方式形成介电层. 平面图案化电极在具有良好稳定性的同时, 制作工艺较为复杂且难以实现三维的可调光学器件的驱动, 目前对于驱动电极的探索, 主要集中于电极形状和材料的改进. 例如Lu等^[17]选择聚二甲基硅氧烷制成的柔性基板, 通过蚀刻形成透明同心电极以实现一定程度的弯曲, 制成柔性基底的介电液体透镜. Shahini等^[18]基于石墨烯透明且柔韧、可以传输可见光的特性, 将其作为电极材料, 在聚合物膜发生较大变形以实现不同透镜设计的要求且不损坏电极的情况下增加视野. Almoallem和Jiang^[19]采用双面电极的设计以增强电场强度, 驱动介电泳液体透镜实现14° 接触角变化的同时大幅度降低了驱动电压. Nakano等^[20]提出了一种具有形成正弦波形的蛇形间隙的微电极, 相比于多条平行放置和连接的直线组成的叉指微电极, 提高了介电泳阻抗测量的灵敏度, 可实现微通道层流中的细菌的捕获.

本文基于外裹绝缘介电层且互不导通的双柔性线性电极, 通过密排于平板基底形成二维平面线墙, 模拟叉指图案电极实现液体介电泳效应. 理论分析了“液滴-叉指平面线墙”介电泳驱动液滴模型, 得到了液滴接触角与外加电压的变化关系式. 进一步, 在0—250 V_rms电压下实验测量了新模型接触角变化范围可达 [58°, 90°], 同时实验未观察到明显的接触角滞后和饱和现象. 本文研究的“液滴-叉指平面线墙”介电泳驱动液滴模型为三维可调光器件提供了理论和实验基础.

2. 结构及原理

2.1 结构设计

图1展示了“液滴-叉指平面线墙”介电泳驱动液滴模型结构. 将互不导通的双柔性电极紧密间隔排布(颜色仅用于区分), 由于其灵活可塑的特性, 沿着平面基板缠绕, 形成平面矩形线墙. 两线各有一端预留部分的介电层被去除, 作为驱动电压输入输出端口, 另两端线头悬空弃用(图1(a)). 在柔性电极线墙的水平表面涂覆疏水层(图1(b)中绿色部分), 能够增大初始接触角且填充了柔性电极之间的缝隙, 因此本柔性电极线墙可模拟平面叉指图案电极. 但圆柱形电极密排后形成的模拟平面存在微观起伏, 与光滑平面相比, 液滴与线墙表面接触产生额外的面积增量, 在下文予以考虑. 外加电压时, 线墙表面的液滴(图1(c)中蓝色部分)将在介电泳力的驱动下形变. 与平面叉指图案电极一致的是, 由于周期性电极产生穿过电极的能量势垒, 液滴运动将被限制在沿电极方向, 这一现象会被后面实验验证.

$图 1 基于双柔性线性电极构造的“液滴-叉指平面线墙”模型　(a)双柔性电极线墙排布; (b)疏水层涂覆; (c) “液滴-叉指平面线墙”模型\r\nFig. 1. The “droplet-interdigitated planar line wall” model based on double flexible linear electrodes: (a) Double flexible electrode wire wall arrangement; (b) coating hydrophobic layer; (c) the “droplet-interdigitated planar line wall” model.$

图 1 基于双柔性线性电极构造的“液滴-叉指平面线墙”模型　(a)双柔性电极线墙排布; (b)疏水层涂覆; (c) “液滴-叉指平面线墙”模型

Fig. 1. The “droplet-interdigitated planar line wall” model based on double flexible linear electrodes: (a) Double flexible electrode wire wall arrangement; (b) coating hydrophobic layer; (c) the “droplet-interdigitated planar line wall” model.

下载: 全尺寸图片幻灯片

2.2 工作原理

经典介电泳装置, 即“固体图案电极+绝缘层+电介质液滴”模型, (固体图案电极表面由薄绝缘介电层覆盖)通过给电极施加电势差V₀, 电势从固体表面指数衰减到液体中, 穿透深度为 $\delta$ , 由

$V(y) = {V_0}\exp ( - 2y/\delta )$

(1)

给出. 根据泊松方程, 半无限电介质液体中电势的解形式为

$\cos (kz)\exp ( - ky),$

(2)

其中 $k = {{2{\text{π }}}}/{T}$ , T为电场周期, 结合() 式, 可得 $\delta = {T}/{{\text{π }}}$ .

固体表面以气体作为环境介质的电介质液滴(厚度为 $h$ )润湿性由固-气、固-液、液-气界面产生的表面自由能的局部最小值给出, 以3种界面张力 ${\gamma _{{\text{sv}}}}$ , ${\gamma _{{\text{sl}}}}$ 和 ${\gamma _{{\text{lv}}}}$ 为特征, 由接触角 $\theta$ 来表征. 该局部能量最小值由杨氏方程描述:

$\cos \theta = \frac{{{\gamma _{{\text{sv}}}} - {\gamma _{{\text{sl}}}}}}{{{\gamma _{{\text{lv}}}}}}.$

(3)

由于电介质液滴被驱动, 固-液界面侵入固-气界面以致增加少量固-液接触面积 $\Delta A$ , 使表面自由能改变 $({\gamma _{\rm sl}} - {\gamma _{{\text{sv}}}})\Delta A$ , 同时液-气表面积增大 $\Delta A\cos \theta$ , 导致表面自由能增加 ${\gamma _{{\text{lv}}}}\Delta A\cos \theta$ . 在不均匀电场和液滴足够厚( $h\gg \delta$ )情况下, 会消耗外部的能量 $- {\varepsilon _0}({\varepsilon _{\text{l}}} - 1)V_0^2\Delta A/(2\delta )$ (液滴直接处于空气中). 液滴处于平衡状态时, 总的能量守恒, 因此接触角 ${\theta _{\text{V}}}$ 由下列公式给出 ^[21] :

$\cos {\theta _{\text{V}}} = \cos {\theta _0} + \frac{{{\varepsilon _0}({\varepsilon _{\text{l}}} - 1){V^2}}}{{2{\gamma _{{\text{lv}}}}\delta }}.$

(4)

基于本文模型结构考虑, 需要修改()式以适应相邻电极间起伏间隙面积的增量. 将施加电压 $V$ 后的固液界面张力 ${\gamma _{{\text{sl}}}}$ 从最初修改为

$\begin{split}& {\gamma _{{\text{sl}}}}(V) - {\gamma _{{\text{sl}}}}(0) \\ =\;& - \frac{{{\varepsilon _{\text{r}}}({\varepsilon _{\text{l}}} - 1)}}{{2\delta }}\left(\frac{{{A_{\text{d}}}}}{{{A_{\text{t}}}}}V_{\mathrm{d}}^2 + \frac{{{A_{\text{r}}}}}{{{A_{\text{t}}}}}V_{\text{r}}^{2} + \frac{{{A_{\text{g}}}}}{{{A_{\text{t}}}}}V_{\text{g}}^{2}\right),\end{split}$

(5)

其中 ${\gamma _{{\text{sl}}}}(0)$ 是未施加电压时的界面张力; ${A_{\text{d}}}$ , ${A_{\text{r}}}$ 和 ${A_{\text{g}}}$ 分别是驱动电极、接地电极和电极线径之间的间隙区域的面积; ${A_{\text{t}}}$ 是组合的总面积; ${V_{\text{d}}}$ , ${V_{\text{r}}}$ 和 ${V_{\text{g}}}$ 是各区域上方电介质层上的分压. ${V_{\text{d}}}$ 和 ${V_{\text{r}}}$ 的值与其面积的相对比率成反比( ${A_{\text{d}}}{V_{\text{d}}} = {A_{\text{r}}}{V_{\text{r}}}$ ). 在()式中, 因为没有电极嵌入间隙区域下方, 故 ${V_{\rm g}} = 0$ . 将(3)式与(5)式结合, 可以得到施加电压与接触角之间的关系^[22]:

$\begin{split} \cos {\theta _{\text{V}}} - \cos {\theta _0} =\;& \frac{{{\varepsilon _0}({\varepsilon _{\text{l}}} - 1)}}{{2{\gamma _{{\text{sl}}}}\delta }}\bigg[ \frac{{{A_{\text{d}}}}}{{{A_{\text{t}}}}}{{\left(\frac{{{A_{\text{r}}}}}{{{A_{\text{d}}} + {A_{\text{r}}}}}\right)}^2} \\ & + \frac{{{A_{\text{r}}}}}{{{A_{\text{t}}}}}{{\left(\frac{{{A_{\text{d}}}}}{{{A_{\text{d}}} + {A_{\text{r}}}}}\right)}^2} \bigg]{V^2}.\end{split}$

(6)

如()式所示, 接触角变化与驱动电极、接地电极之间的面积比以及它们之间的间隙面积有关. 本文所设计“液滴-叉指平面线墙”模型, 需要优化方程大括号中的修改几何因子, 对于给定的电压, 当 ${A_{\text{d}}}$ 和 ${A_{\text{r}}}$ 相等并且 ${A_{\text{g}}}$ 最小化时获得最大角度变化. 所设计的柔性电极线墙组成即驱动电极与接地电极规格相同, 通过假设液滴覆盖的每个子电极的面积远小于液滴所覆盖的总面积, 从而平均电极和间隙面积上方的界面能变化, 故 ${{{A_{\text{d}}}}}/{{{A_{\text{r}}}}} = 1$ . 又因为液滴到圆柱形电极之间的距离始终为绝缘介电层厚度, 且远小于电极尺寸, 可认为 ${A_{\text{g}}} = 0$ , 故 $\dfrac{{{A_{\text{d}}}}}{{{A_{\text{t}}}}} = \dfrac{{{A_{\text{r}}}}}{{{A_{\text{t}}}}} = \dfrac{1}{2}$ . 结合()式, 且在电极直径为 $d$ 的柔性线性电极线墙中, $T = {\text{π }}d$ , 故穿透深度 $\delta = d$ , 可得

$\cos {\theta _{\text{V}}} - \cos {\theta _0} = \frac{{{\varepsilon _0}({\varepsilon _{\text{l}}} - 1)}}{{8{\gamma _{{\text{sl}}}}d}}{V^2},$

(7)

为“液滴-叉指平面线墙”模型接触角变化公式.

3. 仿真及实验

3.1 仿真及结果分析

为验证本文模型电场分布类似于平面叉指图案电极电场分布, 选取3.5个周期通过COMSOL软件进行仿真. 电压归一化设置为0—100 V_rms, 频率设置为1000 Hz.

设置柔性线性电极直径及平面叉指图案电极宽度为0.1 mm, 绝缘介电层厚度为8 μm, 平面叉指图案电极间距为16 μm, 其电场分布如图2所示, 其中曲线表示等势线, 不同颜色表示电势的强弱, 疏密的程度表示电场的强弱.

$图 2 不同形状电极仿真结果　(a)柔性电极线墙; (b)平面图案叉指电极; (c)柔性电极线墙电场模仿真结果\r\nFig. 2. Simulation results of electrodes with different shapes: (a) Flexible electrode wire wall; (b) planar pattern interdigitated electrodes; (c) simulation results of electric field mode of flexible electrode wire wall.$

图 2 不同形状电极仿真结果　(a)柔性电极线墙; (b)平面图案叉指电极; (c)柔性电极线墙电场模仿真结果

Fig. 2. Simulation results of electrodes with different shapes: (a) Flexible electrode wire wall; (b) planar pattern interdigitated electrodes; (c) simulation results of electric field mode of flexible electrode wire wall.

下载: 全尺寸图片幻灯片

图2(a), (b)分别为两种电极垂直于光轴方向的电势分布图. 从图中等势线的分布可以看出, 此方向的电场力是介电泳驱动力的主要组成部分, 两种电极结构此方向的电场分布规律也几乎相同, 但柔性线性电极等势线分布比平面图案叉指电极更加密集, 表明柔性线性电极周围电场更强, 具有更大的介电泳驱动力. 作近似计算, 将相应数值分别代入(6)式与(7)式, 计算出电压的二次项系数分别为8.16×10^–6与8.81×10^–6, 其中平面图案叉指电极的数值略小. 这表明实际情况下, 电压相同时, 柔性线性电极产生更强的电场对液体进行介电泳驱动, 这一结果也印证了仿真结果对比. 图2(c)为不同水平高度处, 柔性线性电极对应电场模数值. 红色和黑色曲线分别代表介电层内与介电层外电场模数值分布. 电场强度经过介电层后, 峰值由7.2×10⁶ V/m衰减至1.8×10⁶ V/m, 分布比较稳定, 利于驱动液体介电泳.

分别固定柔性线性电极绝缘介电层厚度为8 μm, 以电极线径为变量, 取值从0.08 mm增至0.2 mm. 固定柔性线性电极线径直径为0.1 mm, 以绝缘层厚度为变量, 取值从4 μm增至12 μm. 其位于电极绝缘介电层表面0—0.5 mm高度处电场模数值如图3所示.

$图 3 电极表面0—0.5 mm处电场模　(a) 不同线径下电极表面电场模; (b) 不同绝缘层厚度下电极表面电场模\r\nFig. 3. Electric field modes at 0–0.5 mm height on the electrode surface: (a) Electrode surface electric field modes with different wire diameters; (b) electrode surface electric field modes with different insulating layer thickness.$

图 3 电极表面0—0.5 mm处电场模　(a) 不同线径下电极表面电场模; (b) 不同绝缘层厚度下电极表面电场模

Fig. 3. Electric field modes at 0–0.5 mm height on the electrode surface: (a) Electrode surface electric field modes with different wire diameters; (b) electrode surface electric field modes with different insulating layer thickness.

下载: 全尺寸图片幻灯片

由图3(a)可知, 本模型中, 电极形状为圆柱形, 电极线径为0.08 mm较小时, 电极形貌接近尖端电极, 电场强度变大, 其数值峰值约为2.0×10⁶ V/m. 随着线径增大至0.2 mm, 电极形貌接近平板电极, 电场模数值峰值减小至1.1×10⁶ V/m, 这表明本模型中电极构造相对于平板电极具有优势. 由图3(b)可知, 经过绝缘介电层后, 电极表面电场强度呈指数衰减. 绝缘介电层厚度为4 μm较小时, 电场模峰值约为2.5×10⁶ V/m, 随着厚度增至12 μm, 电场模峰值减小至1.1×10⁶ V/m. 考虑到电极线径增大, 两电极中间也随之间隙增大, 即使涂覆疏水层后液体也可能会渗透. 同时相比于绝缘介电层厚度增加所导致的电场强度衰减, 线径增加影响程度较低, 所以可通过降低介电层厚度或是优化介电层材料来降低电场强度的衰减.

3.2 实验及结果分析

采用直径为0.1 mm的金属铜线作为柔性导电芯, 表面涂有主要组成为8 μm厚度聚酯(ε_r = 3, Elektrisola定制)的柔软绝缘介电层, 缠绕于玻璃基板上形成线墙, 并涂覆6%的Teflon@AF1600烘干固化作为疏水层. 将5 μL乙二醇(ε_r = 37)液滴置于柔性电极线墙中央. 函数发生器(ATF20A, ATTEN)产生频率为1000 Hz的正弦交流信号, 通过电压放大器(PZD350, Trekinc.)放大作为交流驱动电压源. 为更准确表达接触角的变化情况, 采用接触角测量仪以俯视(xOz面)和侧视(xOy面)两视角相结合的方式对液滴形貌进行拍摄记录, 对侧拍图像进行接触角拟合测量.

图4为在电压由0升至250 V_rms时液滴形貌的拍摄结果, 其中图4(a), (b)为俯拍视图, 图4(c), (d)为侧拍视图. 液滴轮廓初始状态俯视图中为圆形, 升高电压时, 在介电泳力作用下沿着柔性电极纵向扩展为圆角矩形, 无横向扩展变化. 电压回退时, 从侧视图中可见液滴轮廓恢复至原始状态, 电压升高的前进和电压后退的过程中无明显的迟滞. 在整个实验过程中, 没有观察到接触角饱和的现象.

$图 4 液滴形貌变化示意图　(a), (b)分别为初始状态及250 Vrms电压下液滴俯视图; (c), (d)分别为电压升高和下降时液滴侧视形貌\r\nFig. 4. Schematic diagram of droplet morphology changes: (a), (b) Vertical view of droplet in initial state and 250 Vrms voltage respectively; (c), (d) side view of droplet during voltage rise and fall.$

图 4 液滴形貌变化示意图　(a), (b)分别为初始状态及250 V_rms电压下液滴俯视图; (c), (d)分别为电压升高和下降时液滴侧视形貌

Fig. 4. Schematic diagram of droplet morphology changes: (a), (b) Vertical view of droplet in initial state and 250 V_rms voltage respectively; (c), (d) side view of droplet during voltage rise and fall.

下载: 全尺寸图片幻灯片

以20 V_rms为电压间隔对液滴变化过程进行侧拍记录, 通过拟合法测量前进和后退接触角数据如图5所示. 在图5(a)中, 黑色和红色的曲线分别代表实验测量的前进和后退接触角, 蓝色曲线为(7)式代入相应参数值计算出的理论值. 0升至250 V_rms电压的过程中, 接触角逐渐从90°下降到58°, 变化过程基本符合理论预期, 变化范围约为32°, 前进与后退接触角无明显迟滞. 图5(b)为接触角余弦差值拟合图, 显然初始接触角与加压后接触角余弦差值和电压平方成线性关系, 符合(7)式的理论预期, 余弦值的变化范围约为0.5.

$图 5 液滴接触角及余弦差值关系图　(a)液滴前进及后退接触角与理论接触角对比; (b)接触角余弦差值拟合\r\nFig. 5. Schematic diagram of droplet contact angle and cosine difference diagram: (a) The comparison between the forward and backward contact angle of the droplet and the theoretical contact angle; (b) the fitting of the contact angle cosine difference.$

图 5 液滴接触角及余弦差值关系图　(a)液滴前进及后退接触角与理论接触角对比; (b)接触角余弦差值拟合

Fig. 5. Schematic diagram of droplet contact angle and cosine difference diagram: (a) The comparison between the forward and backward contact angle of the droplet and the theoretical contact angle; (b) the fitting of the contact angle cosine difference.

下载: 全尺寸图片幻灯片

4. 结　论

本文设计了基于双柔性线性电极构造的“液滴-叉指平面线墙”介电泳模型, 理论研究了新模型接触角随外加电压变化关系, 实验演示0—250 V_rms电压范围内接触角变化了32° 符合理论预期. 利用柔性电极线墙模拟叉指图案电极, 使介电泳驱动方式由二维化的平面电极转换为一维化的柔性线性电极, 因其灵活可塑, 方便形成三维立体腔体, 可适用于更加复杂的器件结构.

References

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[2]	Huhtamäki T, Tian X, Korhonen J T, Ras R H 2018 Nat. Protoc. 13 1521 Google Scholar
[3]	Armstrong S, McHale G, Ledesma-Aguilar R, Wells G G 2020 Langmuir 36 11332 Google Scholar
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[5]	Renaudot R, Daunay B, Kumemura M, Agache V, Jalabert L, Collard D, Fujita H 2013 Sens. Actuat. B Chem. 177 620 Google Scholar
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[7]	Frozanpoor I, Cooke M D, Ambukan V, Gallant A J, Balocco C 2021 Langmuir 37 6414 Google Scholar
[8]	Mahani M A, Karimvand A N, Naserifar N 2023 J. Sep. Sci. 46 2300257 Google Scholar
[9]	Jiang L X, Liang F, Huo M X, Ju M Q, Xu J, Ju S, Xu J J, Ju S W, Jin L H, Shen B J 2023 Microelectron. Eng. 282 112100 Google Scholar
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[11]	Xu S, Ren H, Wu S T 2013 J. Phys. D Appl. Phys. 46 483001 Google Scholar
[12]	Xu S, Lin Y J, Wu S T 2009 Opt. Express 17 10499 Google Scholar
[13]	Zhang Z, Li L, Liu X, Li L, Li Y 2023 Opt. Lasers Eng. 163 107450 Google Scholar
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[15]	Li X, Duan J, Qu Z, Wang J, Ji M, Zhang B 2022 Micromachines 13 117.Google Scholar
[16]	Chen Q, Li T, Zhu Y, Yu W, Zhang X 2018 Opt. Express 26 6532.Google Scholar
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Cited By

期刊类型引用(2)

1.	姚欢民，穆海宝，李鹤，李元，李文栋，张大宁. 不同频段下IGBT自组装非线性绝缘材料介电性能的温度依赖性. 高电压技术. 2025(02): 322-335 . 百度学术
2.	姚欢民，穆海宝，李鹤，李元，李文栋，张大宁. 不同频段下IGBT自组装非线性绝缘材料介电性能的温度依赖性. 高电压技术. 2025(01): 322-335 . 百度学术

其他类型引用(0)

图 1 基于双柔性线性电极构造的“液滴-叉指平面线墙”模型　(a)双柔性电极线墙排布; (b)疏水层涂覆; (c) “液滴-叉指平面线墙”模型

Figure 1. The “droplet-interdigitated planar line wall” model based on double flexible linear electrodes: (a) Double flexible electrode wire wall arrangement; (b) coating hydrophobic layer; (c) the “droplet-interdigitated planar line wall” model.

DownLoad: Full-Size Img PowerPoint

图 2 不同形状电极仿真结果　(a)柔性电极线墙; (b)平面图案叉指电极; (c)柔性电极线墙电场模仿真结果

Figure 2. Simulation results of electrodes with different shapes: (a) Flexible electrode wire wall; (b) planar pattern interdigitated electrodes; (c) simulation results of electric field mode of flexible electrode wire wall.

DownLoad: Full-Size Img PowerPoint

图 3 电极表面0—0.5 mm处电场模　(a) 不同线径下电极表面电场模; (b) 不同绝缘层厚度下电极表面电场模

Figure 3. Electric field modes at 0–0.5 mm height on the electrode surface: (a) Electrode surface electric field modes with different wire diameters; (b) electrode surface electric field modes with different insulating layer thickness.

DownLoad: Full-Size Img PowerPoint

图 4 液滴形貌变化示意图　(a), (b)分别为初始状态及250 V_rms电压下液滴俯视图; (c), (d)分别为电压升高和下降时液滴侧视形貌

Figure 4. Schematic diagram of droplet morphology changes: (a), (b) Vertical view of droplet in initial state and 250 V_rms voltage respectively; (c), (d) side view of droplet during voltage rise and fall.

DownLoad: Full-Size Img PowerPoint

图 5 液滴接触角及余弦差值关系图　(a)液滴前进及后退接触角与理论接触角对比; (b)接触角余弦差值拟合

Figure 5. Schematic diagram of droplet contact angle and cosine difference diagram: (a) The comparison between the forward and backward contact angle of the droplet and the theoretical contact angle; (b) the fitting of the contact angle cosine difference.

DownLoad: Full-Size Img PowerPoint

[1]	McHale G, Brown, C V, Newton M I, Wells G G, Sampara N 2011 Phys. Rev. Lett. 107 186101 Google Scholar
[2]	Huhtamäki T, Tian X, Korhonen J T, Ras R H 2018 Nat. Protoc. 13 1521 Google Scholar
[3]	Armstrong S, McHale G, Ledesma-Aguilar R, Wells G G 2020 Langmuir 36 11332 Google Scholar
[4]	Kedzierski J, Holihan E 2018 Sci. Robot 3 eaat5643 Google Scholar
[5]	Renaudot R, Daunay B, Kumemura M, Agache V, Jalabert L, Collard D, Fujita H 2013 Sens. Actuat. B Chem. 177 620 Google Scholar
[6]	Quinn A, Sedev R, Ralston J 2005 J. Phys. Chem. B 109 6268 Google Scholar
[7]	Frozanpoor I, Cooke M D, Ambukan V, Gallant A J, Balocco C 2021 Langmuir 37 6414 Google Scholar
[8]	Mahani M A, Karimvand A N, Naserifar N 2023 J. Sep. Sci. 46 2300257 Google Scholar
[9]	Jiang L X, Liang F, Huo M X, Ju M Q, Xu J, Ju S, Xu J J, Ju S W, Jin L H, Shen B J 2023 Microelectron. Eng. 282 112100 Google Scholar
[10]	Huang K, Lu B, Lai J, Chu H K H 2019 IEEE Trans. Biomed. Circuits Syst. 13 1063 Google Scholar
[11]	Xu S, Ren H, Wu S T 2013 J. Phys. D Appl. Phys. 46 483001 Google Scholar
[12]	Xu S, Lin Y J, Wu S T 2009 Opt. Express 17 10499 Google Scholar
[13]	Zhang Z, Li L, Liu X, Li L, Li Y 2023 Opt. Lasers Eng. 163 107450 Google Scholar
[14]	Frozanpoor I, Cooke M, Racz Z, Bossons I, Ambukan V, Wood D, Gallant A, Balocco C 2021 J. Micromech. Microeng. 31 055014 Google Scholar
[15]	Li X, Duan J, Qu Z, Wang J, Ji M, Zhang B 2022 Micromachines 13 117.Google Scholar
[16]	Chen Q, Li T, Zhu Y, Yu W, Zhang X 2018 Opt. Express 26 6532.Google Scholar
[17]	Lu Y S, Tu H, Xu Y, Jiang H 2013 Appl. Phys. Lett. 103 261113 Google Scholar
[18]	Shahini A, Xia J, Zhou Z, Zhao Y, Cheng M M C 2016 Langmuir 32 1658 Google Scholar
[19]	Almoallem Y D, Jiang H 2017 J. Microelectromech. Syst 26 1122 Google Scholar
[20]	Nakano M, Inaba M, Murakami T, Sakurai M, Suehiro J 2023 IEEE Sens. Lett. 7 1 Google Scholar
[21]	Edwards A M, Brown C V, Newton M I, McHale G 2018 Curr. Opin. Colloid Interface Sci. 36 28 Google Scholar
[22]	Yi U C, Kim C J 2006 J. Micromech. Microeng. 16 2053 Google Scholar

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期刊类型引用(2)

1.	姚欢民，穆海宝，李鹤，李元，李文栋，张大宁. 不同频段下IGBT自组装非线性绝缘材料介电性能的温度依赖性. 高电压技术. 2025(02): 322-335 . 百度学术
2.	姚欢民，穆海宝，李鹤，李元，李文栋，张大宁. 不同频段下IGBT自组装非线性绝缘材料介电性能的温度依赖性. 高电压技术. 2025(01): 322-335 . 百度学术

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