We study the occurrence of a magnetoelastic fingering instability when a viscous ferrofluid is displaced by a nonmagnetic fluid of negligible viscosity in a horizontal, rectangular Hele-Shaw cell. Interfacial disturbances result from the interplay of viscous, elastic, and magnetic effects when the system is subjected to a uniform magnetic field, applied in the plane of the cell, and perpendicular to the initially flat interface separating the fluids. We approach the problem perturbatively through a third-order mode-coupling theory and investigate the development of interfacial patterns at early nonlinear stages of the flow. A representative collection of possible magnetoelastic fingering structures is presented which differ significantly from the classical Saffman-Taylor fingers that arise in such a rectangular cell setup in the absence of magnetic and elastic effects.

中文翻译：

---

矩形Hele-Shaw单元中磁弹指法模式的发展

我们研究了在水平矩形Hele-Shaw细胞中，粘性铁磁流体被粘度可忽略不计的非磁性流体置换后，磁弹性指法不稳定的情况。当系统受到均匀磁场的作用时，界面扰动是由粘性，弹性和磁效应的相互作用所引起的，该磁场施加在细胞平面中，并且垂直于分隔流体的初始平面界面。我们通过三阶模式耦合理论来扰动地解决该问题，并研究在流体的早期非线性阶段的界面模式的发展。