Advances in Materials Science and Engineering

Volume 2018 (2018), Article ID 6143607, 7 pages

https://doi.org/10.1155/2018/6143607

## Magnetic Fluids’ Heating Power Exposed to a High-Frequency Rotating Magnetic Field

Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, Slovenia

Correspondence should be addressed to Miloš Beković; is.mu@civokeb.solim

Received 18 August 2017; Revised 8 December 2017; Accepted 16 December 2017; Published 31 January 2018

Academic Editor: Gianluca Gubbiotti

Copyright © 2018 Miloš Beković et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Magnetic fluids are superparamagnetic materials that have recently been the subject of extensive research because of their unique properties. Among them is the heating effect when exposed to an alternating magnetic field, wherein the objective is to use this property in medicine as an alternative method for the treatment of tumors in the body. The heating effect characterization for the alternating magnetic field (AMF) has been studied widely, whilst for the rotational magnetic field (RMF), no systematic study has been done yet. In this article, we present the characterization of the heating power of magnetic fluids in a high-frequency rotational magnetic field. The results show similar behavior of heating power or specific absorption rate characteristics as in AMF.

#### 1. Introduction

Magnetic fluids are stable colloidal suspensions of superparamagnetic nanoparticles in a carrier liquid and have been the subject of numerous researches due to their specific properties. Their specific characteristics attracted attention when they were subjected to a time-changing magnetic field, which may have pulsating form (alternating magnetic field (AMF)) or rotary form (rotational magnetic field (RMF)).

This article will highlight the behavior of the magnetic fluid in the RMF, which has been at the forefront of research since 1980, in which Popplewell et al. [1] were interested in the rotational motion of the liquid due to low-frequency magnetic fields.

More recently, applications of magnetic fluids and magnetic nanoparticles have penetrated increasingly into the field of biomedicine, as proposed in [2]. Possible fields of application include magnetic resonance imaging, cell sorting, drug delivery, magnetic hyperthermia, and others [3].

The latter represents a medical treatment where a magnetic-fluid tumor-loaded tissue is exposed to a high-frequency alternating magnetic field with the aim of raising the temperature of the diseased tissues. An ideal hyperthermia treatment should destroy the tumor cells selectively without damaging the surrounding healthy tissue. This can be achieved with an increase in the temperature of the tissue to a value between 41 and 43°C. The limitations of such a process, advantages, and disadvantages are gathered in [4, 5].

Magnetic fluids exposed to AMF show immense heating effect, which is a direct consequence of the different physical mechanisms of conversion of the energy of a magnetic field into heat. The intensity of the heating depends strongly on the parameters of the magnetic field (frequency, amplitude, field homogeneity, etc.), as well as the structure of the magnetic fluid (particle size distribution and its type, carrier liquid, surfactant, etc.). Changing these parameters and measurement methods is fairly well known, and their summary is found in [6–10].

The behavior of magnetic fluid exposed to the RMF is not new, since already in 1999 Lacis [11] attempted to demonstrate the movement of fluid in certain field frequencies. For frequencies up to 40 Hz, an s-shape, or spiral, formation of the ferrofluid has also been investigated [12, 13].

Dieckhoff et al. [14] had been studying the behavior of magnetic nanoparticles exposed to RMF and AMF at low frequencies by means of phase-lag research. This would also be possible with the system used in this research, but the amplitude of the magnetic field is too small for accurate determination of magnetic field intensity.

It is also possible to simulate the dynamic behavior of particles in a magnetic field solving Fokker–Planck equations, as was done in [14, 15], and the results have been verified experimentally, again only for low frequencies. The basis for the construction of an RMF was taken from [13] and [15–17] and modified in such a way that magnetic fields could be generated suitable for medical hyperthermia.

In this paper, a new measuring system is presented for generating an RMF of high frequencies and satisfactory amplitudes, suitable for medical hyperthermia. The main novelty of this article is the systematic characterization of magnetic flux losses in both types of magnetic fields (AMF and RMF), where we have confirmed experimentally the thesis given in [18]. The results of the analysis and improvement of the measurement system for a better determination of the magnetic field are presented in the following sections.

#### 2. Theory of Power Dissipation

Cantillon-Murphy et al. [19] extended the theory of magnetic fluid losses from Rosensweig [18], who studied the physical mechanisms of heat generation in a time-changing magnetic field. Heat is caused by the delay in relaxation of the magnetic moment through either the rotation within the particle or the rotation of the particle itself. The first mechanism is called the Néel relaxation and the second one the Brownian relaxation. Relaxation times of a particle are given in (1) for the Néel relaxation (*τ*_{N}) and in (2) for the Brownian relaxation (*τ*_{B}):where *τ*_{0} is the characteristic time constant 10^{−9}, *K*_{a} is the anisotropy constant, *V*_{p} is the volume of the magnetic nanoparticle, *k* is Boltzmann’s constant, *T* is the temperature, *V*_{h} is the hydrodynamic volume of the magnetic nanoparticle and surfactant, and *η* is the dynamic viscosity of the carrier fluid.

Magnetic relaxation of magnetic nanoparticles is derived from the Shilomis equation, and relaxation time *τ* constant depends on the particle size, where the Brownian relaxation dominates the large particles, whilst the Néel relaxation dominates smaller particles:

The maximum value of chord susceptibility *χ* is field-dependent magnetic susceptibility, and it is calculated in the following equation:where it is strongly dependent on the amplitude of the exposed magnetic field, ; volume fraction of magnetic nanoparticles in fluid, ; the saturation magnetization of bulk material, *M*_{d} (in the case of magnetite 445 kA/m); and the permeability of free space, *µ*_{0}.

When magnetic fluid is exposed to a rotational magnetic field, a vector of magnetic field strength can be divided into *x* and *y* components, *H*_{x} and *H*_{y}, and also the magnetization components can be separated into the *x* and *y* directions and calculated by the following equation:where Ω is the circular frequency of magnetic field (2*πf*). In the case of *s* purely alternating magnetic field, one of the field components is set to zero, either *H*_{x} or *H*_{y}, whilst in a rotational magnetic field both amplitudes are the same.

The heating power of the specific absorption rate (SAR), or the power dissipation *P*, is derived from the physical properties of the fluid and the variables of the rotating magnetic field from [19], and it corresponds to the following equation:

#### 3. Rotating Magnetic Field

##### 3.1. Supply Coil Assembly

The easiest RMF can be generated with a rotating magnet, but such systems rarely exceed the frequency of 50 Hz, which is completely useless for the application; in addition, the magnetic field strength cannot be changed. Another approach to creating RMF is with a stator of a three-phase induction motor, where locally distributed coils are powered with the appropriate time-shifted voltages, as is done in [17]. This approach is not applicable for this application because of two problems. The first one is frequency-exponential growth of magnetic core losses in regard to 50 Hz that the core is built for. In our frequency range (kHz), this would produce a lot of heat; hence, it is unusable. The second problem is the heating of supply coils, as, due to the eddy current effect, they are also highly dependent on the frequency. The solution of the first problem is to use a set of coils without a magnetic core, where the coils should have significantly larger turns, or increase the current to achieve satisfactory magnetic conditions. The other problem is solved by using a coil made from copper pipes, connected to the cooling water which dissipates the heat produced by eddy currents and, at the same time, allows substantially higher currents and, consequently, greater magnetic field amplitudes. The basic distribution of supply coils is seen in Figure 1, where two half coils are perpendicular to each other. This represents a two Helmholtz coil pair.