Multi-bubble motion behavior of uniform magnetic field based on phase field model<xref rid="cpb_29_3_034702fn1" ref-type="fn">*</xref><fn id="cpb_29_3_034702fn1"><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 (Grant No. J201304).</p></fn>

Multi-bubble motion behavior of uniform magnetic field based on phase field model**

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 (Grant No. J201304).

Zhu Chang-Sheng^{1, 2, †}, Hu Zhen¹, Wang Kai-Ming¹

Relative permeability distribution.