**Abstract**

The chapter considers autowaves that were observed in the thin near-electrode layer of concentrated magnetic fluid. Autowave process is a unique object for the study of self-organization. We observed pacemakers (leading centers), reverberators (spiral waves), and wave diffraction. A mechanism for the appearance of an autowave process has been developed; its mathematical model has been proposed and realized by means of computer simulation. As a basic method of observation, we used electrically controlled interference. This method watches the changes in the spectrum of reflected light from a two-layer structure with variable thickness: "conductive ITO coating—a layer of concentrated magnetic fluid" in an electric field.

**Keywords:** interference, magnetic fluid, reflection, thin membrane, near-electrode layer, autowaves, pacemaker, reverberator, self-organization

### **1. Introduction**

In this chapter, we describe a new active excitable medium—a thin nearelectrode layer of magnetic fluid. The uniqueness of this environment lies in the fact that its electrophysical and optical properties can be controlled using a weak electric field. In addition, in a layer of concentrated magnetic fluid, we were able to observe and investigate the autowave process. Also, with the help of external periodic effects, it was possible to achieve synchronization of autowaves. While working on this chapter, we studied the latest innovative work on ferrofluids and modeling the processes occurring in them [1–3].

A unique phenomenon that we observed in the near-electrode layer of a magnetic fluid is an autowave process. The best known is the autowave process in the Belousov-Zhabotinsky reaction, when the color of the solution changes periodically. In nature, the autowave process is a change of predator–prey populations. In human body, autowaves spread in the heart muscle and the retina. Interest in the study of autowave processes is primarily due to the fact that in chemical, biological systems, neural networks, and the human brain, they follow the same rules of propagation [4].

We managed to observe an autowave process (Video 1 available at https://yadi. sk/i/rUBv-Mx12DqFLQ) in a thin near-electrode layer of a magnetic fluid (MF) placed between two electrodes in an electric field [5, 6].

The uniqueness of the experiments is that autowaves can be observed in laboratory conditions with the help of simple equipment, including transient processes and synchronization (Video 2 available at https://yadi.sk/i/-9l5aXD5aT3tKA). The purpose of this chapter is to study the autowave process in the near-surface layer of a magnetic fluid at the boundary with an electrode and to describe the physical model and the autowaves' appearance mechanism. Also, the goal of the chapter is to create a mathematical model and obtain its solution in the environment of modeling physical processes COMSOL Multiphysics 5.2.

## **2. Materials and methods**

Magnetizing liquid media—magnetic fluids—is colloidal solutions of ferromagnetic particles in a liquid (kerosene, water). In our experiments, we used a liquid like "magnetite in kerosene" [7]. The typical particle size is 10 nm, which corresponds to the single-domain state in such particles and determines the superparamagnetic behavior of these systems. A surfactant (*HOl* in our experiments) is used to prevent particles from coagulating. Oleic acid creates a stabilizing layer that compensates for the dipole-dipole attraction between the magnetic particles. The thickness of the stabilizing layer is 1–2 nm. The magnetic fluid that we used in the experiments has a concentration of 3.2 vol.%, dielectric constant ε = 2.1, and conductivity <sup>σ</sup> = 3.8 <sup>10</sup><sup>7</sup> (<sup>Ω</sup>m)<sup>1</sup> (measured at 1000 Hz).

the surface of the glass (5) and from the surface of the transparent ITO electrode. The complex refraction indices and thickness of the conductive coating (ITO) were measured by using a spectroscopic ellipsometer SE 800 SENTECH. The refraction index

*Model of a multilayer structure at the cell surface. (A) Model of a multilayer structure "glass – ITO – layer of magnetite particles – magnetic fluid." (B) Model of three optical layers "glass – ITO + a layer of magnetite*

^*n*<sup>2</sup> ¼ 1*:*76 1ð Þ þ 0*:*04*i* . The refraction index of magnetic fluid with a concentration of 3.2% vol. is ^*n*<sup>4</sup> ¼ 1*:*45 1ð Þ þ 0*:*01*i* . The rays of light with a wide range of wavelengths (white light) fall on the ITO electrode and are reflected from its upper and lower borders. Since the thickness of ITO is �200 nm, the interference of the reflected rays occurs. When voltage is applied to the electrodes, the magnetite particles move to the electrodes. Thin layers of a concentrated magnetic fluid (�27–30%) are formed near the electrodes, which corresponds to the dense packing of particles with a protective coating. The MF refraction index of such concentration is ^*n*<sup>3</sup> ¼ 1*:*76 1ð Þ þ 0*:*03*i* .

The refraction indices of ITO and near-electrode layer are close in value: n2 ≈ n3. Therefore, the growth of near-electrode layer of concentrated magnetic fluid in the electric field is optically equivalent to the increase of conductive coating (ITO) thickness. The interference of falling rays is taking place in two-layer structure —"conductive ITO coating—a near-electrode layer." It can be visually observed by

Depending on the near-electrode layer thickness, the surface of a cell with a magnetic fluid changed its color. The visible color change of the layer is explained by the shift of spectrum maximum due to the increase of the structure "conductive ITO coating – near-electrode layer" optical thickness. If the voltage on electrodes is more than critical voltage (�12 V), particles in the near-electrode layer become

In our experiments, we considered the temperature of the liquid to be the same and did not take into account the heating during the passage of electric current and

A technique for the calculation of the near-electrode layer thickness is presented in [9]. Depending on the cell voltage applied to the electrodes, the thickness of the

of glass is n1 = 1.52, and the refraction index of conductive coating is

*Autowave Processes in Magnetic Fluid: Electrically Controlled Interference*

changing of the cell surface color from green to crimson. We called this electrooptical effect as electrically controlled interference (**Figure 2**).

unstable, and the autowave process (AW-process) starts [6].

heat transfer [8].

**61**

**Figure 2.**

*particles – magnetic fluid" with reflected rays.*

*DOI: http://dx.doi.org/10.5772/intechopen.85197*

**3. Experimental results**

*3.1.1 "Fast" autowave mode*

**3.1 Excitation autowave spreading modes**

The autowave process observation is described below. The experiment was carried out on the unit shown in **Figure 1**.

The magnetic fluid (1) is placed into a cell between two electrodes (2, 5), made of glass with a conductive transparent coating InSnO2 (ITO). The area of electrode surface is S = 30 40 mm2 with the glass thickness of 4 mm and conductive coating thickness of h0 = (160 5) nm; the thickness of magnetic fluid first layer is l–40 μm. A beam from a source of white light (8) falls on the surface of a cell with a magnetic fluid. The falling rays were reflected from the "electrode-magnetic liquid" border and were recorded by a camera (7). A constant or pulse voltage was applied to the electrodes (9). The prism (6) was used to separate the rays that reflected from

**Figure 1.**

*(A) Schematic drawing of the experimental unit: (1) "magnetite in kerosene" magnetic fluid; (2, 5) glass with conductive coating; (3, 4) insulating gaskets; (6) prism; (7) camera or photodiode; (8) lighting (white or monochromatic light); (9) electrodes. (B) Photo of the experimental unit.*

*Autowave Processes in Magnetic Fluid: Electrically Controlled Interference DOI: http://dx.doi.org/10.5772/intechopen.85197*

**Figure 2.**

We managed to observe an autowave process (Video 1 available at https://yadi. sk/i/rUBv-Mx12DqFLQ) in a thin near-electrode layer of a magnetic fluid (MF)

The uniqueness of the experiments is that autowaves can be observed in laboratory conditions with the help of simple equipment, including transient processes and synchronization (Video 2 available at https://yadi.sk/i/-9l5aXD5aT3tKA). The purpose of this chapter is to study the autowave process in the near-surface layer of a magnetic fluid at the boundary with an electrode and to describe the physical model and the autowaves' appearance mechanism. Also, the goal of the chapter is to create a mathematical model and obtain its solution in the environment of modeling

Magnetizing liquid media—magnetic fluids—is colloidal solutions of ferromagnetic particles in a liquid (kerosene, water). In our experiments, we used a liquid like "magnetite in kerosene" [7]. The typical particle size is 10 nm, which corresponds to the single-domain state in such particles and determines the superparamagnetic behavior of these systems. A surfactant (*HOl* in our experiments) is used to prevent particles from coagulating. Oleic acid creates a stabilizing layer that compensates for the dipole-dipole attraction between the magnetic particles. The thickness of the stabilizing layer is 1–2 nm. The magnetic fluid that we used in the experiments has a concentration of 3.2 vol.%, dielectric constant ε = 2.1, and con-

The autowave process observation is described below. The experiment was

thickness of h0 = (160 5) nm; the thickness of magnetic fluid first layer is l–40 μm. A beam from a source of white light (8) falls on the surface of a cell with a magnetic fluid. The falling rays were reflected from the "electrode-magnetic liquid" border and were recorded by a camera (7). A constant or pulse voltage was applied to the electrodes (9). The prism (6) was used to separate the rays that reflected from

The magnetic fluid (1) is placed into a cell between two electrodes (2, 5), made of glass with a conductive transparent coating InSnO2 (ITO). The area of electrode surface is S = 30 40 mm2 with the glass thickness of 4 mm and conductive coating

*(A) Schematic drawing of the experimental unit: (1) "magnetite in kerosene" magnetic fluid; (2, 5) glass with conductive coating; (3, 4) insulating gaskets; (6) prism; (7) camera or photodiode; (8) lighting (white or*

*monochromatic light); (9) electrodes. (B) Photo of the experimental unit.*

placed between two electrodes in an electric field [5, 6].

ductivity <sup>σ</sup> = 3.8 <sup>10</sup><sup>7</sup> (<sup>Ω</sup>m)<sup>1</sup> (measured at 1000 Hz).

carried out on the unit shown in **Figure 1**.

**Figure 1.**

**60**

physical processes COMSOL Multiphysics 5.2.

**2. Materials and methods**

*Nanofluid Flow in Porous Media*

*Model of a multilayer structure at the cell surface. (A) Model of a multilayer structure "glass – ITO – layer of magnetite particles – magnetic fluid." (B) Model of three optical layers "glass – ITO + a layer of magnetite particles – magnetic fluid" with reflected rays.*

the surface of the glass (5) and from the surface of the transparent ITO electrode. The complex refraction indices and thickness of the conductive coating (ITO) were measured by using a spectroscopic ellipsometer SE 800 SENTECH. The refraction index of glass is n1 = 1.52, and the refraction index of conductive coating is ^*n*<sup>2</sup> ¼ 1*:*76 1ð Þ þ 0*:*04*i* . The refraction index of magnetic fluid with a concentration of 3.2% vol. is ^*n*<sup>4</sup> ¼ 1*:*45 1ð Þ þ 0*:*01*i* . The rays of light with a wide range of wavelengths (white light) fall on the ITO electrode and are reflected from its upper and lower borders. Since the thickness of ITO is �200 nm, the interference of the reflected rays occurs. When voltage is applied to the electrodes, the magnetite particles move to the electrodes. Thin layers of a concentrated magnetic fluid (�27–30%) are formed near the electrodes, which corresponds to the dense packing of particles with a protective coating. The MF refraction index of such concentration is ^*n*<sup>3</sup> ¼ 1*:*76 1ð Þ þ 0*:*03*i* .

The refraction indices of ITO and near-electrode layer are close in value: n2 ≈ n3. Therefore, the growth of near-electrode layer of concentrated magnetic fluid in the electric field is optically equivalent to the increase of conductive coating (ITO) thickness. The interference of falling rays is taking place in two-layer structure —"conductive ITO coating—a near-electrode layer." It can be visually observed by changing of the cell surface color from green to crimson. We called this electrooptical effect as electrically controlled interference (**Figure 2**).

Depending on the near-electrode layer thickness, the surface of a cell with a magnetic fluid changed its color. The visible color change of the layer is explained by the shift of spectrum maximum due to the increase of the structure "conductive ITO coating – near-electrode layer" optical thickness. If the voltage on electrodes is more than critical voltage (�12 V), particles in the near-electrode layer become unstable, and the autowave process (AW-process) starts [6].

In our experiments, we considered the temperature of the liquid to be the same and did not take into account the heating during the passage of electric current and heat transfer [8].

#### **3. Experimental results**

#### **3.1 Excitation autowave spreading modes**

#### *3.1.1 "Fast" autowave mode*

A technique for the calculation of the near-electrode layer thickness is presented in [9]. Depending on the cell voltage applied to the electrodes, the thickness of the

layer varies up to 100 nm. The specific resistance of this thickness layer is several orders of magnitude greater than the specific resistance of the liquid in the cell (the thickness of the liquid layer in the cell is ≈40 μm). Hence, the field strength at a steady-state current in a layer of such thickness also will be several orders of magnitude greater. At some critical voltage on the electrodes, the tension in the layer becomes <sup>10</sup><sup>7</sup> V/m, and it becomes conductive (Wien effect). Individual elements (ensembles of particles) get the same charge from the electrode and move away from it. A running wave is visible on the surface of the cell (**Figure 3**).

Note that complete information about the autowave structure evolution can be obtained by describing only the time evolution of the wave front position. This is the basis for the kinematic approach to the description of autowave structures [10]. Since the cell has dimensions of 3 4 cm, we can estimate the average velocity of the wave front motion. Approximately 0.25 s passes from the appearance of green color areas (**Figure 3A**) before filling the entire surface of the cell with this color. Such wave is called "fast"; the velocity of its movement is about 16 cm/s. It looks like a flame spreading over the steppe by setting fire in different places. This is a well-known problem solved by Zeldovich and Frank–Kamenetsky.

https://yadi.sk/i/8OcbP4y831nPMQ). These were single reverberators (**Figure 5**) and multiple ones (**Figure 6**). The reverberator's lifetime is limited to a few turns. If several reverberators appear in the observation field, then after 20 s, only one

*Spiral waves: reverberators in the autowave process. (A) Reverberator at the beginning of the rotation period,*

**Figure 5** shows a photograph of the reverberator: (A) the beginning of the reverberator rotation period and (B) half of the period. As seen in the figure, there is a region in the center of the reverberator core, corresponding to the interference pattern of reflection from the electrode at a constant layer thickness. So in this region, there is no oscillation of the layer. This is the so-called singular domain. Its

**Figure 7** shows the pacemaker (leading center), which we observed in the considered active medium. Pacemakers can emit waves with different periods, as can be seen in **Figure 7A** and **B**. The larger the radius of curvature of the cylindrical wave, the lower the speed of the wave. So in **Figure 7A**, the period of the wave emitted by the pacemaker is 0.31 s. Since all characteristics in the autowave process are determined by the system itself, the period of the waves emitted by each

*(A) Two-arm reverberator and (B) three-arm reverberator. Singular domains are marked.*

existence comes from the reasoning described in [12].

*and (B) reverberator at half of the rotation period. Singular domains are marked.*

*Autowave Processes in Magnetic Fluid: Electrically Controlled Interference*

*DOI: http://dx.doi.org/10.5772/intechopen.85197*

**3.3 Leading centers (pacemakers)**

remains [11].

**Figure 6.**

**63**

**Figure 5.**
