We study the development of interfacial magnetoelastic patterns when an initially circular droplet of a field-activated fluid (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. Elasticity takes effect when the fluids are brought into contact, and due to a chemical reaction, the interface separating them becomes a gel-like elastic layer. By modeling the interface as an elastic membrane having a curvature-dependent bending rigidity, a perturbative mode-coupling theory is employed to investigate the weakly nonlinear dynamics of the system. In this context, we examine how the interface responds to the influence of magnetic, elastic, and yield stress forces. Our findings support the relevance of a curvature weakening effect, in the sense that magnetoelastic fingering structures tend to arise and protrude in regions of lower bending rigidity. We contrast the magnetoelastic patterns with the corresponding usual shapes of magnetic fluid interfaces without bending rigidity, but with surface tension.

中文翻译：

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场响应性流体中的磁弹性模式形成

我们研究了当被非磁性流体包围的场活化流体（铁磁流体或磁流变流体）的初始圆形液滴在Hele-Shaw单元中受到径向磁场作用时，界面磁弹模式的发展。当流体接触时，弹性起作用，并且由于化学反应，将它们分开的界面变成凝胶状的弹性层。通过将界面建模为具有曲率相关的弯曲刚度的弹性膜，采用摄动模式耦合理论来研究系统的弱非线性动力学。在这种情况下，我们检查界面如何响应磁力，弹性和屈服应力的影响。我们的发现支持曲率减弱效果的相关性，在某种意义上，磁弹性指状结构倾向于在弯曲刚度较低的区域中出现并突出。我们将磁弹性模式与相应的通常的磁性流体界面形状进行了对比，没有弯曲刚度，但具有表面张力。