**3.2 Spiral waves (reverberators)**

We managed to observe the appearance and development of spiral waves (reverberators) in the near-electrode layer of magnetic fluid (Video 4 available at

**Figure 3.**

*"Fast" wave in the near-electrode layer of a cell with magnetic fluid.*

**Figure 4.** *Phase ("slow") autowaves in the near-electrode layer of a cell with magnetic fluid.*

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

#### **Figure 5.**

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

Further, the layer elements (ensembles of particles) fall into the cell, break apart, and lose the same charge as the electrode. They get oppositely charged in the cell and begin their movement to the electrode due to electro- and dipolar phoresis. Behind the first wave follows the second one; on the surface of the cell, there appears a picture of the autowave process (**Figure 4**). The waves move with a velocity of ≈1 cm/s. These are the so-called phase ("slow") autowaves. That is, the MF near-electrode layer is an excitable medium with a restoration. An example of such a process can be watched on

We managed to observe the appearance and development of spiral waves (reverberators) in the near-electrode layer of magnetic fluid (Video 4 available at

well-known problem solved by Zeldovich and Frank–Kamenetsky.

video (Video 3 available at https://yadi.sk/i/WR1vDK5IzGGxLg).

*"Fast" wave in the near-electrode layer of a cell with magnetic fluid.*

*Phase ("slow") autowaves in the near-electrode layer of a cell with magnetic fluid.*

*3.1.2 "Slow" autowave mode*

*Nanofluid Flow in Porous Media*

**3.2 Spiral waves (reverberators)**

**Figure 3.**

**Figure 4.**

**62**

*Spiral waves: reverberators in the autowave process. (A) Reverberator at the beginning of the rotation period, and (B) reverberator at half of the rotation period. Singular domains are marked.*

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 remains [11].

**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 existence comes from the reasoning described in [12].

### **3.3 Leading centers (pacemakers)**

**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

**Figure 6.** *(A) Two-arm reverberator and (B) three-arm reverberator. Singular domains are marked.*

**Figure 7** *Experiment: pacemakers with different periods. Frame width, 1.2 cm.*

pacemaker is determined only by its own properties and cannot be adjusted by external influence.
