## 4 Discussion  
As established in the experiments presented above with the pulse-periodic SD, in the regimes with the ODP and the electrodes' asymmetric arrangement during the NP synthesis, their protruding parts are increasingly worn out by electrical erosion, forming parallel surfaces that increase in area and are covered with craters from spot discharges. At each moment of time, a certain area of the electrode is involved in electric discharge processes, usually in the form of a segment of the electrode cross-section (for example, in Figure 4b). Thus, we can say that from the start of the pulse-periodic SD process, equivalent working areas of electrodes, in the case of their ends arranged at an angle, increase from a minor value to the full cross-sectional area of the electrode perpendicular to its axis. The kinetics of the increase in the working area of the electrodes arranged at an angle is correctly displayed by the observed patterns of decreasing time dependencies of the average NP agglomerate size and their concentration measured in the flow by NP electrical mobility (Figure 5). Additionally, the role of the small working area of electrodes initially arranged at an angle is in the greater average energy efficiency \(m_{e}^{s}\) over 6 h of the process for higher angles between electrodes end faces (Table 1). The average energy efficiency is the integral with respect to time from current energy efficiency function, monotonically decreasing from the start highest value. Experimental data obtained allow us to estimate the decrease in kinetics of the current energy efficiency and its maximum initial value. The current energy efficiency  
\[m_{e}(t)=\mu(t)/P_{d}(t) \tag{6}\]  
is followed from (5) and expressed as the mass loss rate by synthesized NPs \(\mu(t)\) per current power released in the interelectrode gap determined from (2) and (4):  
\[P_{d}(t)=\frac{R_{s}}{R_{e}}\frac{CU_{c}^{2}(t)}{2}v(t). \tag{7}\]  
The mass loss rate by synthesized NPs \(\mu(t)\) can be estimated from experimental dependencies of the concentration \(N(t)\), the average size of NP agglomerates \(D(t)\), measured by their electrical mobility (Figure 5), and from the value of the electrode mass loss \(\Delta M\) (Table 1) [39]:  
\[\mu(t)=\frac{dM}{dt}=A\frac{\pi}{6}D^{3}(t)\rho N(t)V=\Delta M\ \frac{N(t)D^{3}(t)}{\int_{0}^{T}N(t)D^{3}(t)dt}, \tag{8}\]  
where \(\rho\) is the density of the NP material, \(V\) is the gas flow through the synthesis chamber and \(A\) is the constant coefficient that takes into account the analyzed fraction of the aerosol flow and the difference between the mass-weighted average NP size and the average size in terms of electrical mobility, which are reduced in the final expression. The calculations  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Angle,**\({}^{\circ}\) & \(\Delta M_{\textit{a}ndere}\)**mg** & \(\Delta M_{\textit{c}ndere}\)**mg** & \(\Delta M\)**mg** & \(\mathbf{E_{f}^{d}}\)**kJ** & \(m_{e}^{d}\)**kg** \\ \hline
0 & \(-0.68\pm 0.01\) & 3.41 \(\pm\) 0.01 & 2.73 \(\pm  
also use the expression for the total electrode mass loss during the time \(T\) as the integral from the mass loss rate by the synthesized NPs:  
\[\Delta M=\int\limits_{0}^{T}\mu(t)dt=A\rho V\frac{\pi}{6}\int\limits_{0}^{T}N(t )D^{3}(t)dt. \tag{9}\]  
Dependences \(\mu(t)\), \(m_{e}(t)\) and \(P_{d}(t)\) calculated from experimental data for the three cases of the degree of electrode asymmetry are shown in Figure 14. The electrical power \(P_{d}(t)\) entering the spark gap varies slightly with time except for the first 5 min, during which the working area is heated by SDs. However, the mass loss rate and the energy efficiency are described by steeply and monotonically decreasing functions.