## 4 Results and Discussion
### Discussion  
The developed simplified model of ESD protective textiles allows us to carry out a preliminary design of textiles that meet the requirements of the EN 1149-3 standard. Slice plots not previously presented in the literature illustrate the electric field shielding by such textiles. Based on the plots shown in Figures 9 and 10 (or the corresponding tabular data), the \(S\) parameter, determined by Equation (2), is easy to find. For conductive fibers with \(\sigma_{2}>0.0001\) S/m, the parameter almost does not depend on the value of \(\sigma_{1}\). For example, for the curves in Figure 9a, the \(S\) parameter equals 0.62, and for the curves in Figure 9c, \(S=0.59\). Additional analyses of the time just after switching on the electrode power supply allow for the plotting of charge decay plots usually not observed during laboratory tests due to the sampling time of the output signal (see Figures 19 and 20). From Figures 9 and 10, it can be seen that regardless of the conductivity of the conductive fibers (\(\sigma_{2}\)), the curves at \(\sigma_{1}<1\times 10^{-13}\) S/m run almost horizontally for \(t>10\) s. In fact, they very slowly and exponentially tend to zero. Such \(\sigma_{1}\) values correspond, for example, to polyester textiles without additional treatment of the final product (impregnation and firing). Analyzing the measurement outcome shown in Figure 19, it can be seen that the most similar characteristics, with the same \(S\), are obtained for the model considered in Section 4.3 at \(\sigma_{1}=1\times 10^{-9}\) S/m and \(\sigma_{2}=17,500\) S/m (see Figure 21). Although the base material is polyester, the conductivity of the material is reduced to \(\sigma_{1}=1\times 10^{-9}\) S/m by firing and impregnation. The absence of these steps would lead to the characteristics shown in Figure 9a at \(\sigma_{1}=1\times 10^{-13}\) S/m. Changes in the parameters of the textiles, particularly the thickness and conductivity of the base material and the conductive fibers within a range of up to 10%, do not cause significant changes in the shape of the charge decay plots. The curves practically overlap on the 0-30 s scale. Parametric studies can be carried out in the COMSOL environment. With a high-performance computer. families of charge decay plots can be found to determine the manufacturer's required textile manufacturing tolerances. However, due to the type of basic analysis performed (transient analysis), the time consumption of the process is very long. Some additional simulations were carried out to highlight the tolerance problem. A nonwoven fabric (felt) with nominal thickness values of 1.8 mm, \(\sigma_{1}=1\times 10^{-11}\) S/m, and \(\sigma_{2}=1\times 10^{-6}\) S/m was considered. For nominal parameters, \(t_{50}\) equals 480 ms. Changing the thickness to 1.62 mm and 1.98 mm hardly changes the time. A 10% change in \(\sigma_{1}\) results in a 1% change in \(t_{50}\), while a 10% change in \(\sigma_{2}\) leads to around an 8% change in \(t_{50}\). The occurrence of areas of non-uniform final treatment (impregnation and firing) in textiles can significantly affect local ESD protection properties. Such defects in textiles are, however, difficult to predict and model. In the testing process, according to the EN 1149-3 standard, if such a defect is only local and is not repeated across the whole material surface, tests on different specimens can identify such heterogeneity. Of course, the model can be  
Figure 20: Charge decay plots for ESD protective fabric at 23 °C and 25% RH measured in a laboratory. extended to include heterogeneity, but the results can only have a cognitive significance due to the randomness of such defects. As mentioned in Section 2, in the case of homogeneous textiles, the charge decay plots are described by Equation (1), which can be rewritten in the following form:  
\[\frac{E}{E_{max}}=\mathrm{e}^{-t/\tau}, \tag{3}\]  
where \(\tau=RC\) is a time constant.