## 4 Discussion
### Biofilm Dynamics for Two Inoculum Levels
#### 4.2.1 Biofilm Population Density: Growth Parameters  
The [PERSON] and [PERSON] (1994) model, which was originally developed for the planktonic form, has previously been used to describe biofilms grown in different batch conditions [23; 44; 56]. In the present work, the model was adopted to fit the data related to biofilm growth. The biofilms investigated in this study were specifically grown using a protocol that has been developed by the authors. The use of the [PERSON] and [PERSON] (1994) model and the comparison of the growth curves lead to several findings that will be discussed in detail: (i) the initial population of attached biofilms was proportional to the inoculum concentration; (ii) the slight difference in the lag time between the growth curves was a result of the \"surface conditioning\"; (iii) the higher \(\mu_{max}\) for a lower initial concentration was the result of the nutrient availability; and (iv) the growth curves reached similar maximum cell densities [23]. First, the outcomes concerning the growth curves indicated that it can be reasonably assumed that the planktonic cells immediately begin the attachment to and growth on the substratum. The initial populations, \(ln(N_{0})\), were proportional to the inoculum concentrations, and these results corroborated that the number of attached bacteria was found to be dependent on these initial cell densities [20; 22; 55]. However, the bacteria did not need a lot of time to recover from the shock of being transferred onto the surface, as can be understood from the short lag phases (\(\lambda\)). This could be related to the type of substrate that was used in this work, i.e., polystyrene. Polystyrene is a hydrophilic material which facilitates the spread of water and bacterial suspension on it, promoting adhesion [29]. The slightly longer lag phase for the inoculum level of \(10^{4}\) CFU/mL was not surprising. If fewer viable cells were present, they would have spent more time to \"condition the surface\". The surface conditioning represents the first stage of biofilm formation. It consists in producing a film of proteins, lipids and polysaccharide molecules by bacteria, which attach to the surface and facilitate biofilm formation. In this specific study, the organic molecules produced by _P. fluorescens_ (e.g., alginate) plus the molecules present in the growth medium (e.g., glucose, soya and casein peptone) facilitated the conditioning of the surface. The microorganisms quickly formed a layer that neutralised excessive surface charges and surface free energy, facilitating growth. Some studies have found that bacteria can also alter the production of some components of the outer cell layer (e.g., lipopolysaccharide, peptidolipids, glycolipid, lipoteichoic acid) making the surface-cell interaction easier. Specifically, this was observed for _Pseudomonas aeruginosa_[57]. In this specific case, the lag phase can be considered as an adhesion step for biofilms. [PERSON] et al. investigated the adhesion step of _P. fluorescens_ and _Pseudomonas grimothi_ in different (static and hydrodynamic) conditions mimicking the fresh-cut food equipment process [56]. They highlighted that _P. fluorescens_ is characterised by a rapid adhesion step regardless of the flow conditions and shear stress, as the outcome of this work also confirmed. Although [PERSON] et al. already underlined that _P. fluorescens_ is characterised by a short lag phase during biofilm growth, a direct comparison of the \(\lambda\) and \(\mu_{max}\) values was not possible because of the differences in the protocol used to perform the experiments [56]. As can be seen from the mathematical model in Equations (1) and (2), the relative maximum growth rate of the microbial population (\(\mu_{max}\)), which is observed in the exponential phase of growth, is independent of the concentration of cells. However, a surprising result was to observe a higher maximum growth rate (\(\mu_{max}\)) of biofilms with an inoculum level of \(10^{4}\) CFU/mL compared to \(10^{7}\) CFU/mL.