In addition to the CFU TCN TOC and ATP measurements

In addition to the CFU, TCN, TOC and ATP measurements, the glass bead surface was examined by scanning electron microscopy (SEM) and examples are shown in Fig. 12, at magnifications of 5000. The SEM images indicate attachment of biofilm after day 1 but, in addition, also some detachment of biofilm between days 3 and 4, an effect possibly related to the observed mass starvation, as indicated by the data in Fig. 11, and subsequent blooming of the bacteria culture at day 4. In order to relate the observed sensor response shown in Fig. 8 to the biofilm formation on the glass beads, model simulations were executed. Major objective was to investigate whether the changes in the AF responses, measured during the biofilm experiment, can be explained by changes in the dielectric properties of the composite material in the resonator, applying the model explained in Section 2.2. A major challenge for the model simulations is to obtain a realistic estimate of the biofilm volume in the resonator, even more so because the % mass fraction of Bioactive Compound Library in the biofilm strongly depends on process conditions. Reported values for the % mass fraction vary from 2% to 10%. [46,54–57]. For this reason, the model simulations were executed for these two limiting cases as well as for an assumed biomass fraction of 5%. The total amount of biomass in the biofilm and subsequently the volume fraction of biofilm were derived from the TOC measurements according to the procedure outlined in the “Supplementary information”. Table 4 gives an overview of the calculated volume fractions of the biofilm on the glass beads from day 1 to day 4 assuming biomass fractions (%) of the biofilm of 2%, 5% and 10%. It should be mentioned that, as Table 4 shows, at the start of the experiment (i.e., the recording labeled day 1) a significant amount of TOC was measured already. Most likely, this TOC concentration represents small amounts of TOC originating from the feed substrate attached to the glass bead surface during sampling. The two key parameters characterizing changes in the dielectric properties of the composite material in the resonator are and tan. The biofilm consists of E. coli and EPS with relative dielectric constants of 60 and 70, respectively. In the simulations, companion cells was assumed that the dielectric constant of the biofilm layer =60, thereby implicitly assuming that, at day 2, the dielectric properties of the biofilm are determined by the presence of E. coli rather than EPS (extracellular polymeric substance). Fig. 13 shows the measured and simulated third resonance AF plots for the biofouling experiments using the biofilm volume fractions in Table 4, for days 1 and 2. Two models were compared, Lichtenecker’s logarithmic law for composite material (model 1, Eq. (7)) versus a model description in terms of a system composed of parallel dielectric layers of glass, biofilm and feed substrate, respectively (model 2, Eq. (8)). As explained in Section 2.3, the “real life situation” is expected to represent an intermediate result between these two model simulations. Both the experimental data and the model simulations reveal that biofilm formation on the glass beads results in a shift of the minimum in the AF plots towards higher frequencies. This is expected since, from an electrical point of view, biofilm formation can be seen as replacing feed substrate dielectric (∼77) by biofilm dielectric (∼60). As a result, biofilm formation will decrease the effective dielectric constant , resulting in a shift of the minimum in the AF plot towards higher frequencies, see also Eq. (3a) (representing the ideal resonator case, the applied model is described in more detail in [28]. Fig. 13 further shows that application of Lichtenecker’s logarithmic law predicts a smaller shift of the AF plot towards higher frequencies than the “parallel dielectric layers” model, which results directly from the lower value of predicted by the “parallel dielectric layers” model.