## 3 Results and Discussion
### Modeling Inactivation Kinetics  
The Weibull model has been proven suitable to describe inactivation curves when applying CAP [9; 35; 41] or other non-thermal systems for bacterial inactivation such as essential oils and high hydrostatic pressure freezing [40; 42]. The Weibull model is based on the response observed on the cellular tolerance to lethal stress on the cells. This allows the model to represent linear and nonlinear curved survival kinetics with upward and downward concavity, with or without lag phase [40]. Moreover, a modified Weibull with a tail model was proposed by [PERSON] and [PERSON] (2005), which has the advantage of fitting the most typical survivor curves and considers a new parameter, \(N_{res}\), when the tail is assumed [28]. The survival curves in our results showed that the inactivation rate slowed down between 240 and 300 s, indicating a tail shape (i.e., \(p\) > 0.1). Hence, the Weibull and Weibull + tail models were compared for best fit. According to the parameters of the goodness of fit in Table 2, both models showed similar accuracy. However, the values of the RMSE estimated for Weibull + tail were slightly smaller than those of the Weibull model. Furthermore, the R\({}^{2}\) values were slightly higher for Weibull + tail indicating higher accuracy. More recent studies have reported a better fit using a Weibull + tail model when a corona discharge plasma jet (CDP) device was used against _E. coli_, \(S\). Typhimurium  
and 46.7 s for \(S\). Typhimurium, \(S\). Choleraseusus, \(E\). _coli_ ATCC 25922, and \(E\). _coli_ ATCC 11775, respectively, using a high-voltage DBD plasma on apples [9]. The authors used a Weibull model, which does not consider a residual concentration of cells (\(N_{res}\)), and the \(\delta\) values were generally lower than those predicted by the Weibull + tail model [9]. However, previous studies employing the Weibull model using a high-voltage output Argon/O\({}_{2}\) (98:2) plasma jet device reported \(\delta\) values of 2.266-2.447 min for \(L\). _monocytogenes_[41]. Another study using a high-voltage DBD against a multiple antibiotic-resistant strain of \(S\). _aureus_ showed \(\delta\) values of 2.9, 1.98, and 0.95 min at 8, 6, and 4 mm of distance, respectively, also employing a Weibull model [35]. Since the antimicrobial efficiency of cold plasma is greatly influenced by the cleanliness of the treated surfaces, it is suggested that a cleaning stage should be applied prior to cold plasma treatment. Figures 2 and 3 for \(L\). _monocytogenes_ and _Salmonella_, respectively, showed a concave shape (\(\mathbf{p}<1\)) with the 10 mm distance indicating a quick inactivation rate during the first minutes, which slows down as time progresses, forming a tail shape after 240 s. The experiments carried out at a 20 mm distance showed less pronounced antimicrobial efficiency compared to 10 mm. Interestingly, for most of the conditions at 20 mm, there is a stepwise log decrease from 180 to 240 s. We hypothesize that this effect implies an accumulation of critical concentrations of reactive compounds necessary to kill a more resistant subpopulation. Moreover, the \(\mathbf{p}\)-value that correlates with the scale and shape of the survival curve is similar in both models. In nearly all cases, \(\mathbf{p}\) is \(<\)1, indicating a concave upward survival curve, except for \(L\). _monocytogenes_ at 20 mm with protein-soiled surfaces where \(\mathbf{p}>1\), showing a concave downward curve shape in Figure 2b. The inactivation curve models clearly show a difference in the CAP antimicrobial effectiveness between the clean and the protein-soiled SS surface, indicating a protective effect of BSA. This is closer to real conditions in the food industry where the surfaces can be soiled with residual protein pertaining to foodstuff [3]. It is important to note that the inactivation was tested on dried cells, and biofilms were not allowed to form. This would add an extra protective barrier to the cells, which was not investigated as it was beyond the aim of this study.