Relative permeability is an important magnetic characteristic for ferrofluid to exhibit its magnetized potential during the magnetization process. To understand above physical property varying with field intensity, a popular analytic model, based on Langevin theory, has been usually considered and widely used. Unfortunately, an implicit model, derived from above hypothesis, for solving the instantaneous magnetization of ferro-particle will be carried out unless the determination of saturated magnetization should be conducted in advance. Just for the study dealing with magnetic property of testing ferro-sample is concerned, the previous acquisition of magnetization curve is impossible and unpractical without the precise measurement of magnetization-degree. On the other hand, required experimental expense is still so costly that it seems to be unaffordable for general laboratory. Thus a self-designed electromagnetic mechanism with special facility of smaller size, economical cost and efficient operation to quantify the reduced gravity of ferro-sample attracts our interest and is set up in this study. Meantime, an auxiliary numerical method, Newton interpolatory divided-difference formulas in trapezoidal rule, involved in this study successfully avoids the essentiality of saturated magnetization determined previously, and which also provides a numerical approximation through the weight loss of ferrofluid experienced by the designed experimental system. As compared with the result measured by VSM (vibration sample magnetometer) method, the estimated profile shows an excellent agreement except the extraordinary outcome occurring at B=6 mT, where a drastic increase of relative permeability will be evaluated due to the faster magnetization starts.
Implicit model specialization through dag-based decentralized federated learning
