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. 2019 Mar 6;9:3629. doi: 10.1038/s41598-019-40248-8

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Effect of electrode shape on electric field strength. Electrostatic analysis: The mica has dimensions of 0.1 m × 0.1 m (a: mica substrate) and the water 0.1 m×0.1 m×0.03 m (b: water). The electrodes are placed on the bottom surface of mica and the gap between electrodes is 0.080 mm. When the peak to peak voltage of V_pp = 10 is applied, the streamline of electric field vector is shown in (c). Electric field for various electrode shapes: The red arrows represent the magnitude and direction of electric field in the space of water. The effect of electrode geometry on the electric field is investigated for the electrode angles of parallel 0° (d), 30° (e), 45° (f), 60° (g), in 2D; parallel 0° (h), 30° (i), 45° (j), 60° (k) in 3D.