Composition and textural characterisation of sludge

The final TS content is determined by drying the wet sample in an oven at 105 °C for 24 h [37]. The volatile organic content is determined after igniting the dry solids at 550°C for 2 h [38]. To assess the consistency of the sludge (ie. its plastic or divided granular-like state), the plastic limit, TS୔, is quantified using standardized soil mechanics trials (Atterberg limits). TS୔ corresponds to the TS content at which transitions between plastic and divided granularlike states occurs. Experimentally, it corresponds to the maximum concentration at which the sludge can be rolled into threads of 3 mm in diameter without breaking into pieces [39,40]. 2.3. Rheological measurements Rheological measurements are performed with a controlled stress rheometer RS600 instrument (HAAKE), piloted by RheoWin software, at room temperature. The torque range varies from 0.1 to 200 000 µNm.To avoid wall slip, the experiments are carried out with serrated parallel plate geometry (radius 10 and 17.5 mm) at a constant gap of 2 mm. The upper plate is supplied with a sensor allowing to register the normal force F୬ (detection range: 0.02-30 N). Before each measurement, the sludge sample is subjected to a constant dynamic strain (γ=0.3 %) in the linear viscoelastic range (LVE) during 300 seconds to ensure reproducible results [26]. A sweep of shear stress τ (corresponding to γ=0.1 to 200 %) is performed at 1 Hz frequency. To avoid fracturing, the stress sweep is performed according to the experimental procedure of surface correction developed by Mouzaoui et al. [26,32]. This procedure consists of applying a stress sweep in successive steps of constant dynamic stress of increasing intensity. Prior each constant stress step, a step at a reference state defined by a constant dynamic rotational angle ϕ୰ୣ୤ is applied. The latter corresponds to a constant dynamic reference strain ɀ୰ୣ୤=0.3 % chosen in the linear viscoelastic plateau (LVE), where, by definition, stress and strain are proportional. By applying this reference state, edge effects (fractures) lead to a decrease of the corresponding stress and complex modulus (stress and strain ratio). As the complex modulus must be identical at the reference state before and after fractures, the surface really sheared (S) can be calculated, allowing the correction of the stress IJ and the corresponding strain γ. All tests have been made in triplicate to evaluate the reproducibility of results.

Sludge composition and textural characterization 

Samples with TS content ranging between 2 and 44.2 wt. % have been obtained. The plastic limit characterising the transition between plastic state and divided granular-like state is around TS୔=43 wt. %. As long as TS is lower than 14 wt. %, the surface profile of the sample looks like a cone when measuring tools of the rheometer are moved away, reflecting that the surface was fully sheared (no fracture). Then, for TS higher than 14 wt. %, the surface profile displays concentric circles and a plane surface in the center, reflecting the existence of fractures (Figure 2, right). Thus, the transitions between liquid and plastic states can be considered around TS୐=14 wt. %. According to these measurements, the plastic state ranges between 14 and 43 wt. % TS. This result is consistent with the scientific literature. Indeed, ranges of 21-38 wt. % TS and 16- 42 wt. % TS can be derived for sludge having a VS content of 53 % and 75 %, respectively . 

Rheological parameters determination 

Figure 3 presents the evolution of moduli (G’ and G”), shear stress (τ) and normal stress (σ=F୬/S) as function of strain (ɀ) for a sludge with TS=20.6 wt. %. Data show that both moduli are constant and strain-independent below ɀ୐V୉=0.5 %. G’ starts to become straindependent above ɀ୐V୉, pointing the end of the LVE region. When ɀ exceeds 3 %, the Paynelike effect appears: G’ decreases monotonically and G’’ goes through a maximum before decreasing well. This highlights a significant disruption of sludge internal structure . The Payne effect is a feature of soft glassy materials that is observed in variety of materials such as emulsions, gels, colloidal suspensions [43] and sludge. Then, at higher strain (10- 15 %), moduli decrease together until a crossover point at a strain around ɀ୷ =160 % where the corresponding yield stress is equal to τ୷~8.1 kPa. This point marks the transition from a viscoelastic solid behavior to a viscoelastic liquid one [42,45,46]. Beyond the crossover point, G’’ becomes higher than G’ as the strain increases, reflecting the viscous nature of the medium, as noticed by Mansoutre et al.[36]. Normal stress measurement clearly highlights 3 distinct zones: a decrease below a critical strain ɀୡ , then a jump of the normal stress (σ) before an abrupt fall beyond ɀ୤ corresponding to the decrease of G’’ (Figure 3). The jump is typical of dilatancy in granular pastes . This behaviour has also been reported for sludge by Mouzaoui et al.,

Impact of concentration on rheological parameters

The critical concentration from which a yield stress can be detected is 2 wt. %. This value is in agreement with the existent literature [21,30,47–49]. The maximum shear stress that the RS600 rheometer can reach with a plate-plate geometry of 10 mm radius is IJmax=2.M୫a୶/π.R ଷ =127 kPa. For TS>34.3 wt. %, the yield stress values exceed τ୫a୶ and measurements are no longer possible. Thus, the impact of TS on the yield stress will be limited to TS<34.3 wt. %. The literature on sludge rheology suggests that the yield stress evolves following a power law model of (TS-TS଴), where TS଴ corresponds to the lowest concentration below which no yield stress is noticeable, 2 wt. % in our case [21,30,47–49]. However, it is not possible in our case to describe the experimental values by a single power law model over the full range of investigated concentrations (Figure 4). The evolution of the yield stress values highlights two regions: values increase slightly up to a critical concentration TSୡ close to 6 wt. %, then, above this concentration, a change in curvature occurs suggesting the appearance of an additional contribution. The same macroscopic behaviour is reported in the literature of clay suspensions [50] and polymer/nanocomposites systems [51–55]. The critical concentration,where the change in curvature occurs, is defined as the rheological percolation threshold. Thus, parameters were described according to a first power law model up to the critical concentration, then above this concentration following a second power law model. Pignon et al. [50] have well described the change in rheological behaviour near the rheological percolation threshold, by light scattering measurements. They have shown that, below the rheological percolation threshold, the structure may be seen as a beam-type alignment of aggregates, leading to the formation of a mechanically weak fibrous structure. Beyond this critical concentration, the structure may be seen as a continuous and dense network of aggregates, which is mechanically more resistant. Hence, the first increase can be related to the viscous forces in the sludge (hydrodynamic effects of flocs and physico-chemical interactions), while the second increase can be attributed to the formation of a continuous network by physical contacts between components.