Abstract
The energy dissipation in a magnetic fluid placed in AC magnetic field of the sound frequency is studied experimentally. The aim of the paper is to obtain information on the amplitude dependence of the dynamic susceptibility and the limits of applicability of the simplest (linear) relaxation equation for magnetization. Two independent methods are used: direct measurement of the dynamic susceptibility of the mutual inductance bridge in weak probing field and measurement of heat release in the magnetic fluid at elevated magnetic field amplitudes. In the latter case, a well-known formula was used that relates the heat release power to the imaginary part of the dynamic susceptibility, which directly follows from the linear relaxation equation. The comparison of the results obtained by different methods revealed a systematic discrepancy between two series of experiments, which is explained by the existence in the magnetic fluid of multiparticle clusters (aggregates) with uncompensated magnetic moments. At frequencies of the order of 10 4 Hz, the Brownian mechanism of relaxation of the magnetic moments is blocked because of the large dimensions of the aggregates ( w t B >> 1). In addition, for small amplitudes of the magnetic field, the Neel relaxation mechanism is also blocked because of the high energy of interparticle interactions inside the aggregate and the appearance of high potential barriers. The situation changes with increasing field amplitude, when the energy of interaction of the aggregated particles with the external field becomes comparable with the height of the potential barrier. Aggregates are included in the process of magnetization reversal, increasing the dynamic susceptibility and the dissipation of energy in the magnetic fluid.
Highlights
The energy dissipation in a magnetic fluid placed in AC magnetic field of the sound frequency is studied experimentally
A well-known formula was used that relates the heat release power to the imaginary part of the dynamic susceptibility, which directly follows from the linear relaxation equation
The comparison of the results obtained by different methods revealed a systematic discrepancy between two series of experiments, which is explained by the existence in the magnetic fluid of multiparticle clusters with uncompensated magnetic moments
Summary
Магнитные жидкости – коллоидные растворы ферромагнитных наночастиц в жидкости-носителе являются типичными представителями суперпарамагнитных систем [1,2,3,4]. Где μ0 = 4π⋅10-7 Гн/м – магнитная постоянная, ω и H0 – циклическая частота и амплитуда переменного магнитного поля, соответственно. Спектральные амплитуды Ai обозначают вклад i-й «броуновской» фракции в равновесную восприимчивость, а первое слагаемое в (4) описывает частотно независимый (на частотах до 105 Гц) вклад самых мелких частиц с неелевским механизмом релаксации. Если фракция представлена отдельными частицами, спектральные амплитуды можно описать известным выражением для начальной восприимчивости магнитной жидкости в рамках модифицированной модели эффективного поля [9]. Появление кластеров в магнитной жидкости не приводит к качественному изменению ситуации: основной вклад в равновесную восприимчивость вносят крупнодисперсные фракции. Цель данной работы – экспериментальная оценка диапазона зондирующих полей, при которых динамическая восприимчивость может считаться постоянной величиной, не зависящей от амплитуды поля, и формулы (4) могут быть использованы для расчёта диссипации энергии в магнитной жидкости. Решение обеих проблем требует подбора частоты и амплитуды переменного магнитного поля и корректной оценки мощности тепловыделения
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