In-depth description of electrohydrodynamic conduction pumping of dielectric liquids: Physical model and regime analysis

Abstract

In this work we discuss fundamental aspects of Electrohydrodynamic (EHD) conduction pumping of dielectric liquids. We build a mathematical model of conduction pumping that can be applied to all sizes, down to micro-sized pumps. In order to do this, we discuss the relevance of the Electrical Double Layer (EDL) that appears naturally on non-metallic substrates. In the process we identify a new dimensionless parameter, related to the value of the zeta potential of the substrate-liquid pair, that quantifies the influence of these EDLs on the performance of the pump. This parameter also describes the transition from EHD conduction pumping to electroosmosis. We also discuss in detail the two limiting working regimes in EHD conduction pumping: ohmic and saturation. We introduce a new dimensionless parameter, accounting for the electric field enhanced dissociation, that along with the conduction number, allows to identify in which regime the pump operates.

Numerical analysis of electro-convection in dielectric liquids with residual conductivity

“…Meanwhile, both analytical and numerical solutions are performed to discuss the effect of the electric field strength, system geometry, and alternating current (AC) frequency on the velocity and pattern of the aforementioned EHD flow. Furthermore, the electrohydrodynamic flow based on the conduction model attracts the attention of researchers for the application of conduction pumping 3,[27][28][29] . This specific application is expected to be used in many engineering fields, including space thermal control and flexible microscale pumping, due to its advantages of having no mechanical components, no noise, easy miniaturization 30 .…”

“…Electrohydrodynamics (EHD), a multidisciplinary science that describes the interaction between the flow field and the electric field, has been employed in many practical applications, such as electrostatic precipitation and thrust 1,2 , EHD pumping 3,4 , heat transfer enhancement 5,6 , EHD mixing 7 , electrophoretic display 8 . Electro-convection (EC) driven by Coulomb force in nonpolar dielectric fluids is a fundamental problem in EHD [9][10][11] .…”

Overview of electrohydrodynamic conduction pumping

“…其中， [56][57][58] 。宏观尺度下， 双电层对于电导泵性能的影响可忽略，但随着电导 泵特征尺寸的减小，双电层对于泵性能的 影响必须 考虑。为深入理解传导模型和其工作状态，Vázquez 等人 [59] 建立了适用于不同空间尺度的传导泵模型，…”

“…diminishing scheme)格式相结合用于介电液体电对流 和电热对流的研究 [98][99][100] ，其中有限体积法用于求解 整个电对流耦合方程组，TVD 格式用于处理对流占 优的电荷密度守恒方程。该求解方法应用于二维刀 片-平板电极结构 [101] 和三维方腔内平嵌电极 [102] 电导 泵的数值分析。另外，该求解策略已经被植入了开源 数值平台 OpenFOAM,并拓展到多相问题 [103][104][105] 。近年 来，一些新的方法也开始应用于单种电荷电对流问 题，包括格子 -Boltzmann 方法(LBM) [106][107][108][109][110][111][112] , 谱元法 [113] , 散统一动理学方法(DUGKS) [114] , 能量稳定有限元 法 (Energy stable FEM) [115] , 能 量 无 条 件 稳 定 格 式 (Unconditionally energy stable schemes) [116] 等。其中， LBM 已经被拓展应用于电导泵问题 [117] 。事实上， LBM 在电流体领域的应用发展非常迅速，除了单相 流以外，已经被广泛应用于多相电流体动力学问题。 图 17 流线和非对称电极配置  =0.35(br=2) [50] Fig 17 Flow streamlines and asymmetric electrode configuration  =0.35(br=2) [50] 最早，Jeong 等 [23] 基于有限体积法求解了电导泵 静压模型。紧接着，他们考虑了流场和昂萨格-维恩 效应 [25] 。之后，人们开展了大量电导泵性能影响参数 研究，尤其是电极尺寸、布置和正负离子迁移系数比 等物性参数。Yazdani 和 Seyed-Yagoobi [50] 模拟研究发 Seyed-Yagoobi [52,118] 通过数值模拟研究，量化电荷注 入对电导泵性能的影响，得出双极电荷注入对流动 的影响不如单极电荷注入。Nishikawara 等 [51] 模拟研 V/m，而电极表面电场强度小于 10 5 V/m，可避免电 荷注入。中心孔强电场区的非线性电流电压特性，仅 由场强解离现象引起。阴、阳离子主要分布在中心孔 两端，流体流动未穿过中心孔。中心孔形状的改变可 使孔两侧出现不均匀的电场分布，即可产生通过中 心孔的净流 [121] 。文献 [119,121] 还开展了实验研究，测量 了压降和流速，数值和实验结果总体吻合良好。 泵性能与电场强度密切相关，随着电场强度增 加，维恩-昂萨格效应也更加显著，会对电导泵性能 产生显著影响。2019 年，Vázquez 等人以平行平板电 极为对象推导了维恩-昂萨格效应对电导泵压力产生 以及电流的影响，这是理论研究的一个重要进展 [59] 。 量的速度分布 [122] ，因此可视为电导泵数值模拟的一 [122,123] 和 我 们 利 用 OpenFOAM 计算的 FVM 结果 [124] ，均与实验结果吻 合良好。 Talmor 和 Seyed-Yagoobi 基于文献 [58]数值研 究了微尺度泵的流动方向和流体惯性对异号电荷层...…”

Numerical analysis of electrohydrodynamic (EHD) instability in dielectric liquid-gas flows subjected to unipolar injection

“…It attracts a wide range of fundamental research interest due to its complex flow structures and rich bifuractions [1][2][3][4][5]. This type of flow motion also plays the center role in several engineering applications, such as electrosprays, ink-jets, boiling heat transfer, and EHD pumping [6][7][8][9][10].…”