The foam drainage mainly depends on the influence of gravity and foam surface tension. In this work, we consider the foam drainage in a microgravity condition, and its fractal modification is established by using the fractal derivative. The variational principle of the novel fractal model is successfully obtained by the semi-inverse method. Finally, an analytical solution is obtained by the variational iteration method; the effect of the fractal order on the solution property is illustrated.

中文翻译：

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微重力空间分形泡沫排水模型研究

泡沫排水主要取决于重力和泡沫表面张力的影响。在这项工作中，我们考虑了微重力条件下的泡沫排水，并通过使用分形导数建立了其分形修改。通过半逆方法成功地得到了新分形模型的变分原理。最后通过变分迭代法得到解析解；说明了分形顺序对解性质的影响。