A lattice model based on percolation theory for cold atmospheric DBD plasma decontamination kinetics

The tailing phenomenon, where the survival curve of bacteria shows a slow tailing period after a rapid decline, is a ubiquitous inactivation kinetics process in the advanced plasma sterilization field. While classical models suggest that bacterial resistance dispersion causes the tailing phenomenon, experiments suggest that the non-uniform spatial distribution of spores (clustered structure) is the cause. However, no existing inactivation kinetics model can accurately describe spatial heterogeneity. In this paper, we propose a lattice model based on percolation theory to explain the inactivation kinetics by considering the non-uniform spatial distribution of spores and plasma. Our model divides spores into non-clustered and clustered types and distinguishes between short-tailing and long-tailing compositions and their formation mechanisms. By systematically studying the effects of different spore and plasma parameters on the tailing phenomenon, we provide a reasonable explanation for the kinetic law of the plasma sterilization survival curve and the mechanism of the tailing phenomenon in various cases. As an example, our model accurately explains the 80-second kinetics of atmospheric pressure plasma inactivation of spores, a process that previous models struggled to understand due to its multi-stage and long-tail phenomena. Our model predicts that increasing the spatial distribution probability of plasma can shorten the complete killing time under the same total energy, and we validate this prediction through experiments. Our model successfully explains the seemingly irregular plasma sterilization survival curve and deepens our understanding of the tailing phenomenon in plasma sterilization. This study offers valuable insights for the sterilization of food surfaces using plasma technology, and could serve as a guide for practical applications.