# Electromagnetic and Thermal Phenomena Modeling of Electrical Discharges in Liquids
## 3 Preliminary Research of Discharge Parameters in Juices  
In the previous section of the paper, most popular mechanisms describing the nature of the high voltage electrical discharges in liquids are detailed. These mechanisms usually describe specific electrical discharges, classified primarily, because of the speed of their propagation (fast and slow discharges) [27; 39]. In order to select the model for further analysis of electrical breakdown process in juices, basic parameters of physical model are measured. All presented measurements are performed to determine the energy values of pulsed discharges and specific discharge periods. The test stand, consisting of a high voltage pulse generator, working chamber, and a control system, is used. Sample of juice is placed between the two flat electrodes. Figure 4 shows the design of working chamber (Figure 4a) and block diagram of the test stand (Figure 4b). Figure 4: View of working chamber (**a**) and block diagram for HVED test stand (**b**). 1—electrodes; 2—juice container. The AS3-mini analyzer equipped with an oscilloscope to record voltage and current waveforms is used. During the measurements of high voltage pulses parameters, the initial voltage was kept at 20 kV. Recorded waveforms are presented in the Figure 5. Results show the oscillatory character of the voltage values of the generated pulses. Its initial amplitude depends on the applied voltage triggering the pulse. Tests results were used to determine the shape of the generated pulses, together with all the specific quantities (amplitudes, rise and fall times). They were used to model the electrical discharge process. According to the measurements results, it was assumed, that the theory of gas bubbles can be used to describe the discharge phenomena in the analyzed juice model [14; 16; 39]. In pursuance of the description of this process, the initiation of the discharge occurs as a result of the gas bubble generation because of the Joule heat effect or large field intensity gradient in vicinity of electrodes. Depending on the initial voltage and energy value, it is possible to develop \"slow\" (propagation speed within several km/s) or fast (propagation velocity from several to several tens km/s) discharges [27; 39]. Based on the measurements of current and voltage values in the tested device, the approximate propagation velocity (Figure 5) of the discharge was determined based on the current value of the rise time. Estimated propagation speed was at 3470 m/s, which allowed us to classify the discharge as \"slow.\" Under these conditions, it has been assumed that the electrical discharge is a result of ionization process in the gas phase filling the plasma channel [19; 41]. This fact is important in the discharge numerical modeling point of view. As it was mentioned above, the discharge parameters in liquids are determined by the value of the electric strength, the distance between the electrodes, their shape, temperature, and material parameters of the liquid (juice in analyzed case). When appropriate number of free electrons and positive ions occur in the discharge area, one or more plasma channels (streamers) can be created. Almost all electrons will flow through the channel characterized by minimal resistance value [40; 41]. Streamers starts at the cathode toward the anode. When the anode area is reached by plasma channel, the impedance of the discharge area decreases dramatically, which leads to a significant increment of the current. This stage, called the breakdown, is characterized by the occurrence of a plasma channel with almost cylindrical cross-section and duration depending on the capacity in the system [28; 42]. The discharge energy can be simply defined as:  
\[W=\frac{C}{2}\bigg{(}U_{i}^{2}-U_{f}^{2}\bigg{)}, \tag{3}\]  
where: \(U_{i}\)--voltage before breakdown, \(U_{f}\)--voltage after breakdown, \(C\)--capacitance  
The formula was used during determination of energy balance of the discharge presented in the next section of the paper. Figure 5: Time course of high voltage impulse.