## 4 Discussion  
### Dependence of Rheological Parameters from Non-Volatile Media  
Preliminary rheological comparison of two TBS coming from two diverse high-strength wastewater treatment plants highlighted how the results are apparently not in line with previous literature findings [14]. As shown in the Supplementary Materials, TBS with higher TS concentrations but lower VS was characterized by a lower consistency index with respect to that which characterized lower concentrated sludge. Therefore, NVS influence on the rheological properties of a biological matrix has been investigated. In this work, three types of non-volatile media were tested. Firstly, calcium carbonate (CaCO\({}_{3}\)) was tested as it represents a residual product of the lime reaction in water and its presence is very common in plants with chemical-physical processes (as in this specific case). Results highlight how calcium carbonate induced a relatively small effect on the rheological parameters of TBS, also increasing the concentration of NVS from 90 kg m\({}^{-3}\) up to 190 kg m\({}^{-3}\). This result can be attributed to the absence of chemical interaction of CaCO\({}_{3}\) with the water present inside the sludge. In fact, as reported by [PERSON] et al. [42], the influence of calcium carbonate on the rheological properties of fluids varies depending on  
Figure 3: Comparison between experimental data and single, double, and triple-exponential models to describe the shear stress as a function of time. (**a**–**c**) are referred to 100 s\({}^{-1}\). (**d**–**f**) are referred to 400 s\({}^{-1}\). (**g**–**i**) are referred to 1000 s\({}^{-1}\). particle size. They observed that higher increases in viscosity were appreciable with higher particle sizes of calcium carbonate [42]. In our study particle size was too small (1-3 \(\upmu\)m) to lead to a significant change on sludge rheological properties. Based on these results, the potential dosage before biological processes of lime composed of small-particle CaCO\({}_{3}\) will produce circumscribed effects on the rheological parameters of TBS. Sand was tested as NVS to understand if the rheology of BS can be affected by malfunctions of grit removal processes, which determine high quantity of granular materials entering the biological reactor. Results agree with [PERSON] et al. [43] who have explained that sand does not influence the consistency coefficient of a fluid given absence of chemical interaction between silica and water. On the contrary, [PERSON] et al. [44] have highlighted how fluid viscosity can be influenced by sand dimensions, increasing with particle size. In our study, results were obtained focusing only on sand with size of 0.16-0.24 mm, therefore different outcomes with sands of diverse sizes cannot be excluded. Moreover, an increase in consistency due to the contribution of interaction between biomass and sands over the long-term cannot be excluded, and other studies should be further developed. Probably, based on these results, the potential malfunction of grit removal processes will produce circumscribed effects on the rheological parameters of TBS, even if some experimental points in Figure 1b show a deviation from the above-described behaviour and deserve further investigation. Sodium bentonite is a non-volatile media reducing the filtering properties of membranes [45]. For this reason, understanding the influence of this substance in membrane biological processes is a key aspect for process optimization. In this work, results highlight how sodium bentonite strongly influences rheological parameters of the investigated biological mixture, enhancing the sludge consistency coefficient about 20 times when increasing NVS concentration from 90 kg m\({}^{-3}\) to 190 kg m\({}^{-3}\). These results agree with previous findings of [PERSON] et al. [46], which highlighted how even small concentrations of sodium bentonite in water produce a viscous thixotropic fluid with low filtration capacity. However, to date no results on a thermophilic biological substrate are available.