The tip radius $R_{tip}$ of ferrofluids deformed by magnetization is typically ~ 100 $$m, much larger than in conducting electrified liquids, even though in both cases the capillary stress {2$$/R}$_{tip}$ balances the electrostatic or magnetostatic stress. The reason for the relative dullness of magnetic tips appears to be the saturation of magnetization, $M_{max}$=$M_{sat}$. This hypothesis lacks quantitative experimental confirmation but is supported theoretically by the recently proposed high field asymptote $R_{tip}${$$ }$\frac{4\gamma }{{\mu }_o{M}_{sat}^2}$ obtained for isolated drops in strong and uniform magnetic fields. Here we confirm experimentally the controlling role of the magnetic saturation effect under more general conditions, by showing that the dimensionless group ${{\mu }_o{M}_{sat}^{2}R}_{tip}/(4\gamma )$ is always a quantity of order unity, even for ferrofluid menisci subject to the highly non-uniform magnetic fields created by supporting them at the tip of a ferrous needle facing a strong magnet. Four different ferrofluids are used, with high, medium and low surface tensions, including highly polar and nonpolar solvents. Substantial changes in $M_{sat}$ are achieved by letting the suspending solvent evaporate, with record tip radii down to 9.5 $$m demonstrated at high volume fractions of magnetic particles.

中文翻译：

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磁化的铁磁流体磁头的尖端如何？

尖端半径 ${\mathrm{[R}}_{Ť\mathrm{一世}p}$尽管在两种情况下毛细管应力{2 $ / R} $ _ {tip} $平衡了静电应力或静磁应力，但由于磁化作用变形的铁磁流体的数量通常约为100 $ m，远大于导电液体。磁头相对钝感的原因似乎是磁化饱和，${\mathrm{中号}}_{米\mathrm{一种}X}$=${\mathrm{中号}}_{s\mathrm{一种}Ť}$。该假设缺乏定量的实验证实，但在理论上得到了最近提出的高场渐近线的支持${\mathrm{[R}}_{Ť\mathrm{一世}p}${$$}$\frac{4\gamma }{{\mu }_{Ø}{\mathrm{中号}}_{s\mathrm{一种}Ť}^2}$是在强磁场和均匀磁场中分离出的液滴而获得的。在这里，我们通过证明无量纲的基团，在实验上证实了磁饱和效应在更一般条件下的控制作用。${{\mu }_{Ø}{\mathrm{中号}}_{s\mathrm{一种}Ť}^2\mathrm{[R}}_{Ť\mathrm{一世}p}/（4\gamma ）$即使对于铁磁流体的半月板，由于受到将其支撑在面对强磁体的铁质针头上而产生的高度不均匀磁场的影响，它始终是一个数量级的单位。使用四种具有高，中和低表面张力的铁磁流体，包括高极性和非极性溶剂。的重大变化${\mathrm{中号}}_{s\mathrm{一种}Ť}$ 通过使悬浮的溶剂蒸发可以实现上述目的，在磁性颗粒的高体积分数下，记录尖端的半径降至9.5 $$ m。