SUMMARY The magnetic anisotropy exhibited by ferrofluid-impregnated samples serves as a proxy for their pore fabrics, and is therefore known as magnetic pore fabric (MPF). Empirically, the orientation of the maximum susceptibility indicates the average pore elongation direction, and predicts the preferred flow direction. Further, correlations exist between the degree and shape of magnetic anisotropy and the pores’ axial ratio and shape, and between the degrees of magnetic and permeability anisotropies. Despite its potential, the method has been rarely used, likely because the large variability in reported empirical relationships compromises interpretation. Recent work identified an additional contribution of distribution anisotropy, related to the arrangement of the pores, and a strong dependence of anisotropy parameters on the ferrofluid type and concentration, partly explaining the variability. Here, an additional effect is shown; the effective susceptibility of the ferrofluid depends on the measurement frequency, so that the resulting anisotropy depends on measurement conditions. Using synthetic samples with known void geometry and ferrofluids with known susceptibility (4.04 SI and 1.38 SI for EMG705 and EMG909, respectively), magnetic measurements at frequencies from 500 to 512 kHz are compared to numerical predictions. Measurements show a strong frequency-dependence, especially for EMG705, leading to large discrepancies between measured and calculated anisotropy degrees. We also observe artefacts related to the interaction of ferrofluid with its seal, and the aggregation of particles over time. The results presented here provide the basis for a robust and quantitative interpretation of MPFs in future studies, and allow for re-interpretation of previous results provided that the ferrofluid properties and measurement conditions are known. We recommend that experimental settings are selected to ensure a high intrinsic susceptibility of the fluid, and that the effective susceptibility of the fluid at measurement conditions is reported in future studies.

中文翻译：

---

解释磁性孔隙结构和孔隙空间特性之间经验关系的巨大变化

总结 铁磁流体浸渍样品表现出的磁各向异性可作为其孔隙结构的代表，因此被称为磁孔结构 (MPF)。根据经验，最大磁化率的方向表示平均孔伸长方向，并预测了优选的流动方向。此外，磁各向异性的程度和形状与孔隙的轴比和形状之间存在相关性，并且在磁率和磁导率各向异性的程度之间存在相关性。尽管具有潜力，但该方法很少使用，可能是因为报告的经验关系的巨大可变性影响了解释。最近的工作确定了分布各向异性的额外贡献，与孔隙的排列有关，以及各向异性参数对铁磁流体类型和浓度的强烈依赖性，部分解释了可变性。这里显示了一个附加效果；铁磁流体的有效磁化率取决于测量频率，因此产生的各向异性取决于测量条件。使用具有已知空隙几何形状的合成样品和具有已知磁化率的铁磁流体（EMG705 和 EMG909 分别为 4.04 SI 和 1.38 SI），将 500 至 512 kHz 频率的磁测量与数值预测进行比较。测量显示出强烈的频率依赖性，特别是对于 EMG705，导致测量和计算的各向异性度之间存在很大差异。我们还观察到与铁磁流体与其密封的相互作用以及粒子随时间的聚集有关的人工制品。此处提供的结果为未来研究中对 MPF 进行稳健和定量解释提供了基础，并允许在已知铁磁流体特性和测量条件的情况下重新解释先前的结果。我们建议选择实验设置以确保流体的高固有敏感性，并且在未来的研究中报告测量条件下流体的有效敏感性。