Phase field simulation of single bubble behavior under an electric field<xref rid="cpb_27_9_094704fn1" ref-type="fn">*</xref><fn id="cpb_27_9_094704fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant Nos. 51661020, 11504149, and 11364024), the Postdoctoral Science Foundation of China (Grant No. 2014M560371), and the Funds for Distinguished Young Scientists of Lanzhou University of Technology, China (Grant No. J201304).</p></fn>

Phase field simulation of single bubble behavior under an electric field**

Project supported by the National Natural Science Foundation of China (Grant Nos. 51661020, 11504149, and 11364024), the Postdoctoral Science Foundation of China (Grant No. 2014M560371), and the Funds for Distinguished Young Scientists of Lanzhou University of Technology, China (Grant No. J201304).

Zhu Chang-Sheng^{1, 2, †}, Han Dan¹, Xu Sheng¹

(color online) Time-dependent bubble top positions under different vertical electric fields.