Correlated percolation patterns in PEF damaged cellular material

We present results of numerical and experimental investigation of the electric breakage of a cellular material in pulsed electric fields (PEF). The numerical model simulates the conductive properties of a cellular material by a two-dimensional array of biological cells. The application of an external field in the form of the idealised square pulse sequence with a pulse duration $t_{i}$, and a pulse repetition time $\Delta t$ is assumed. The simulation model includes the known mechanisms of temporal and spatial evolution of the conductive properties of different microstructural elements in a tissue. The kinetics of breakage at different values of electric field strength $E$, $t_{i}$ and $\Delta t$ was studied in experimental investigation. We propose the hypothesis for the nature of tissue properties evolution after PEF treatment and consider this phenomena as a correlated percolation, which is governed by two key processes: resealing of cells and moisture transfer processes inside the cellular structure. The breakage kinetics was shown to be very sensitive to the repetition times $\Delta t$ of the PEF treatment. We observed correlated percolation patterns in a case when $\Delta t$ exceeds the characteristic time of the processes of moisture transfer and random percolation patterns in other cases. The long-term mode of the pulse repetition times in PEF treatment allows us to visualize experimentally the macroscopic percolation channels in the sample.