Impact of calcination temperature, organic additive percentages, and testing temperature on the rheological behaviour of dried sewage sludge

In the case of our sludge samples, several non-Newtonian rheological models, such as Bingham, Ostwald–de Waele (Power law), Herschel–Bulkley, Sisko, Carreau, and Cross models, were applied in order to fit the shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) and apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves. These rheological models used to simulate and estimate the rheological parameters, like yield stress, flow behaviour index, zero-shear rate apparent viscosity, infinite-shear rate apparent viscosity, and flow consistency coefficient, are defined in the following equations [43,44,46,50,51]:

Ostwald–de Waele model (1) τ = K γ n . \tau =K{\gamma }^{n}.

(Shear-thinning, pseudoplastic: K > 0, 0 < n < 1)

(Shear-thickening, dilatant: K > 0, n > 1)

Bingham model (2) τ = τ 0 + η p γ . \tau ={\tau }_{0}+{\eta }_{\text{p}}\gamma .

(Plastic: K > 0, τ ₀ > 0, n = 1)

Herschel–Bulkley model (3) τ = τ 0 + K γ n . \tau ={\tau }_{0}+K{\gamma }^{n}.

(Shear thickening, yield dilatant: K > 0, τ ₀ > 0, 1 < n < ∞)

(Shear thinning, yield pseudoplastic: K > 0, τ ₀ > 0, 0 < n < ∞)

Sisko model (4) η = η ∞ K γ ̇ n − 1 . \eta ={\eta }_{\infty }K{\dot{\gamma }}^{n-1}.

Carreau model (5) η = η ∞ + ( η 0 − η ∞ ) ( 1 + ( λ γ ̇ ) 2 ) n − 1 2 . \eta ={\eta }_{\infty }+\left[({\eta }_{0}-{\eta }_{\infty }){(1+{(\lambda \dot{\gamma })}^{2})}^{\frac{n-1}{2}}\hspace{.25em}\right].

Cross model (6) η = η ∞ + ( η 0 − η ∞ ) 1 + ( λ γ ̇ ) m , \eta ={\eta }_{\infty }+\frac{({\eta }_{0}-{\eta }_{\infty })}{1+{(\lambda \dot{\gamma })}^{m}}, where τ ₀ is the yield stress (Pa), η _p is the plastic viscosity (Pa s), γ ̇ \dot{\gamma } is the shear rate (s⁻¹), n is the flow behaviour index, K is the flow consistency coefficient (Pa s), η _∞ is the infinite-shear rate apparent viscosity (Pa s), η ₀ is the zero-shear rate apparent viscosity (Pa s), λ is the time constant (s), and m is the Cross rate constant.

An example of an experimental rheological sequence (shear stress [τ]−shear rate [ γ ̇ \dot{\gamma } ] and apparent viscosity [η]−shear rate [ γ ̇ \dot{\gamma } ] curves) carried out on SS0 with TS = 4% is presented in Figure 5a and b (see Section 2.8).

Figure 5

(a) Shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) and (b) apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves of SS0 for TS = 4%, at 20°C.

The first step shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) and apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves of SS0 and SSAs, for different TS = 4, 7, 10, 13, and 15%, at 20°C, are plotted, respectively, with the best-fit rheological model in Figures 6 and 7.

Figure 6

Shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) curves of SS0 and SSAs for different TS = 4, 7, 10, 13, and 15%, at 20°C.

Figure 7

Apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves of SS0 and SSAs, for different TS = 4, 7, 10, 13, and 15%, at 20°C.

Figure 6 shows that for all sludge samples, the shear stress increases with increasing shear rate indicating non-Newtonian shear thickening (yield dilatant) flow behaviour. Such flow behaviour was also previously reported by a few authors [52,58]. From this figure, it could be realized that the thermal treatment of SS0 at different calcination temperatures has a decreasing impact on shear stress.

The shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) experimental data were fitted to different rheological models discussed in equations (1)–(3). Several rheological parameters estimated from different models are given in Table 2, where the Herschel–Bulkley model was selected, referring to the high values of linear correlation coefficient (R ²), as the best model fitting the experimental data. According to the Herschel–Bulkley model, the increase in TS of all sludges resulted roughly in an increase of yield stress (τ ₀). It can also be observed that an increase in TS from 4 to 13% caused a decrease in the flow consistency coefficient (K) and an increase in the flow behaviour index (n). However, at a higher value of TS (15%), these two rheological parameters (K and n) were significantly increased and decreased, respectively.

Table 2

Sludge	TS (%)	Herschel–Bulkley model				Ostwald–de Waele model
		τ = τ 0 + K γ n \tau ={\tau }_{0}+K{\gamma }^{n}				τ = K γ n \tau =K{\gamma }^{n}
		τ 0 (Pa)	K (Pa s)	n	R 2	K (Pa s)	n	R 2
SS0	4	0.1123	6.43 × 10−5	1.6082	0.9992	2.93 × 10−4	1.3765	0.9944
	7	0.1584	5.20 × 10−5	1.6558	0.9981	3.82 × 10−4	1.3510	0.9900
	10	0.1628	2.15 × 10−5	1.8161	0.9976	1.61 × 10−4	1.5076	0.9900
	13	0.2282	1.62 × 10−5	1.8736	0.9955	2.39 × 10−4	1.4594	0.9834
	15	0.2413	7.17 × 10−5	1.6555	0.9958	7.39 × 10−4	1.2872	0.9854
SSA800	4	0.0640	6.65 × 10−5	1.5952	0.9992	1.67 × 10−4	1.4551	0.9973
	7	0.0699	5.73 × 10−5	1.6302	0.9993	1.49 × 10−4	1.4844	0.9973
	10	0.0846	5.81 × 10−5	1.6344	0.9989	1.75 × 10−4	1.4665	0.9962
	13	0.1545	4.82 × 10−5	1.6764	0.9986	3.15 × 10−4	1.3896	0.9915
	15	0.2013	5.36 × 10−5	1.6634	0.9980	5.45 × 10−4	1.3086	0.9872
SSA850	4	0.0670	6.46 × 10−5	1.5974	0.9991	1.71 × 10−4	1.4489	0.9970
	7	0.0645	5.99 × 10−5	1.6169	0.9991	1.49 × 10−4	1.4781	0.9973
	10	0.0698	5.63 × 10−5	1.6359	0.9992	1.44 × 10−4	1.4926	0.9972
	13	0.1135	5.37 × 10−5	1.6532	0.9992	3.15 × 10−4	1.4352	0.9948
	15	0.1855	4.47 × 10−5	1.6948	0.9984	3.92 × 10−4	1.3622	0.9890
SSA900	4	0.0615	7.46 × 10−5	1.5755	0.9990	1.80 × 10−4	1.4417	0.9973
	7	0.0665	4.77 × 10−5	1.6548	0.9994	1.24 × 10−4	1.5092	0.9975
	10	0.0768	5.10 × 10−5	1.6507	0.9990	1.58 × 10−4	1.4788	0.9967
	13	0.0941	4.03 × 10−5	1.7012	0.9992	1.36 × 10−4	1.5153	0.9960
	15	0.1729	5.53 × 10−5	1.6554	0.9983	4.25 × 10−4	1.3438	0.9898
SSA950	4	0.0640	6.91 × 10−5	1.5860	0.9992	4.84 × 10−3	1.4441	0.9973
	7	0.0629	5.34 × 10−5	1.6364	0.9992	1.30 × 10−4	1.5001	0.9975
	10	0.0657	3.98 × 10−5	1.6962	0.9991	9.70 × 10−5	1.5599	0.9974
	13	0.1012	3.90 × 10−5	1.7070	0.9988	1.43 × 10−4	1.5086	0.9952
	15	0.1097	5.22 × 10−5	1.6521	0.9991	1.49 × 10−4	1.4919	0.9967

Figure 7 displays that, in the first regime, the apparent viscosity of all sludge samples decreases with an increase in shear rate until a critical shear rate (η _C = η _∞), exhibiting a shear-thinning laminar behaviour. In the second regime, the apparent viscosity increases gradually with increasing shear rate to reach a maximum constant value (η _max), revealing a shear-thickening turbulent behaviour. Similar evolution behaviours have been reported by many researchers, such as Rosales et al. [77], Ratkovich et al. [43], Gienau et al. [57], and Edifor et al. [78], for other sludge systems.

From Figure 7, it could also be distinguished that the thermal treatment of SS0 at different calcination temperatures has a decreasing impact on the apparent viscosity. The apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) experimental data of the first regime were fitted to different rheological models discussed in equations (4)–(6).

The various rheological parameters estimated from different models are given in Table 3, where the Cross model was selected, based on the high values of linear correlation coefficient (R ²), as the best model fitting the experimental data. According to the Cross model, the increase in sludge TS resulted in an increase of the infinite-shear rate apparent viscosity (η _C = η _∞). This increase in viscosity is possibly due to the improvement of particle–particle interactions forming a network of particles during sludge addition [43,78]. Furthermore, for each sludge's TS, the increase in calcination temperature is accompanied by a decrease of the infinite-shear rate apparent viscosity (η _C = η _∞). This is probably due, respectively, to the decrease of the weight LOI (organic matter content) (Table 1), the specific surface area, and the average pore diameter (Figure 3b) during the increase of the calcination temperature (800–950°C). A decrease in specific surface area and average pore diameter can result in the minimization of the water pathway, which in turn hinders the efficient interaction between sludge particles.

Table 3

Sludge	TS (%)	Cross model					Carreau model
		η = η ∞ + ( η 0 ‒ η ∞ ) 1 + ( λ γ ̇ ) m \eta ={\eta }_{\infty }+\frac{({\eta }_{0}‒{\eta }_{\infty })}{1+{(\lambda \dot{\gamma })}^{m}}					η = η ∞ + ( η 0 ‒ η ∞ ) ( 1 + ( λ γ ̇ ) 2 ) n ‒ 1 2 \eta ={\eta }_{\infty }+\left[({\eta }_{0}‒{\eta }_{\infty }){(1+{(\lambda \dot{\gamma })}^{2})}^{\frac{n‒1}{2}}\hspace{.25em}\right]
		η ∞ {\eta }_{\infty } (Pa s)	η 0 {\eta }_{0} (Pa s)	λ \lambda (s)	m	R 2	η ∞ {\eta }_{\infty } (Pa s)	η 0 {\eta }_{0} (Pa s)	λ \lambda (s)	n	R 2
SS0	4	1.967 × 10−3	1.45	11.64	1.15	1.0000	1.547 × 10−3	1.18	16.01	7.00 × 10−4	0.9906
	7	2.268 × 10−3	1.05	14.71	1.00	0.9964	2.288 × 10−3	0.69	10.10	6.84 × 10−4	0.9947
	10	2.280 × 10−3	0.59	13.16	0.95	0.9985	2.336 × 10−3	0.05	0.71	7.59 × 10−4	0.9920
	13	2.760 × 10−3	0.92	11.34	1.01	1.0000	2.760 × 10−3	0.23	2.93	7.46 × 10−4	0.9971
	15	3.310 × 10−3	0.21	3.05	0.97	1.0000	3.372 × 10−3	0.06	0.78	7.87 × 10−4	0.9976
SSA800	4	1.208 × 10−3	0.54	10.85	0.99	1.0000	1.245 × 10−3	0.10	1.95	7.49 × 10−4	0.9986
	7	1.444 × 10−3	0.66	11.49	1.03	0.9989	1.388 × 10−3	0.20	3.87	5.93 × 10−4	0.9938
	10	1.587 × 10−3	0.50	9.26	0.98	1.0000	1.552 × 10−3	0.05	0.79	7.55 × 10−4	0.9956
	13	1.982 × 10−3	0.13	1.98	0.92	1.0000	2.203 × 10−3	0.04	0.54	9.40 × 10−4	0.9985
	15	2.264 × 10−3	0.18	2.08	0.90	1.0000	2.542 × 10−3	0.07	0.72	7.56 × 10−4	0.9969
SSA850	4	1.167 × 10−3	0.16	3.49	0.96	1.0000	1.062 × 10−3	0.05	1.10	1.15 × 10−4	0.9897
	7	1.242 × 10−3	0.43	7.51	1.03	1.0000	1.241 × 10−3	0.13	2.47	5.89 × 10−4	0.9979
	10	1.267 × 10−3	0.41	6.20	1.00	0.9990	1.237 × 10−3	0.06	0.85	7.56 × 10−4	0.9881
	13	1.695 × 10−3	0.20	2.95	0.97	1.0000	1.566 × 10−3	0.05	0.69	8.01 × 10−4	0.9941
	15	2.128 × 10−3	0.11	1.49	0.90	1.0000	1.830 × 10−3	0.06	0.78	7.29 × 10−4	0.9918
SSA900	4	1.164 × 10−3	0.23	3.98	1.04	1.0000	1.250 × 10−3	0.10	1.90	7.45 × 10−4	0.9974
	7	1.237 × 10−3	0.29	4.63	1.05	1.0000	1.202 × 10−3	0.24	4.75	7.04 × 10−4	0.9984
	10	1.268 × 10−3	0.31	6.10	0.95	0.9994	1.394 × 10−3	0.05	0.87	7.47 × 10−4	0.9939
	13	1.332 × 10−3	0.25	3.99	0.96	1.0000	1.418 × 10−3	0.06	0.86	8.06 × 10−4	0.9978
	15	1.854 × 10−3	0.12	1.54	0.90	0.9992	2.480 × 10−3	0.06	0.76	1.07 × 10−3	0.9936
SSA950	4	1.162 × 10−3	0.24	3.90	1.03	1.0000	1.193 × 10−3	0.10	1.76	9.99 × 10−4	0.9941
	7	1.233 × 10−3	0.26	4.26	1.04	0.9995	1.208 × 10−3	0.24	4.69	9.76 × 10−4	0.9246
	10	1.248 × 10−3	0.17	3.96	0.93	0.9993	1.261 × 10−3	0.04	0.70	1.00 × 10−3	0.9973
	13	1.355 × 10−3	0.17	3.01	0.91	1.0000	1.608 × 10−3	0.05	0.69	1.00 × 10−3	0.9961
	15	1.361 × 10−3	0.13	1.65	1.04	0.9997	1.291 × 10−3	0.05	0.74	1.00 × 10−3	0.9986

The first step shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) and apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves of SSAs mixed with organic additives (proportion: 4% methocel + 4% amijel + 8% starch), for different TS = 4, 7, 10, 13, and 15%, at 20°C, are plotted, respectively, with the best-fit rheological model in Figures 8 and 9.

Figure 8

Shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) curves of SSAs, mixed with organic additives (4% methocel + 4% amijel + 8% starch), for different TS = 4, 7, 10, 13, and 15%, at 20°C.

Figure 9

Apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves of SSA, mixed with organic additives (4% methocel + 4% amijel + 8% starch), for different TS = 4, 7, 10, 13, and 15%, at 20°C.

Figure 8 shows that for all SSA and organic additive mixtures, the shear stress increases with increasing shear rate indicating non-Newtonian shear thickening (yield dilatant) flow behaviour at low TS (4 and 7%) and shear-thinning (pseudoplastic) flow behaviour at high TS (10, 13, and 15%). As can be clearly seen in this figure, at TS = 4%, the shear stress increases with the increase of calcination temperature. Above TS = 4%, the shear stress decreases when the calcination temperature increases from 800 to 850°C, then it increases, respectively, to reach a maximum value when the calcination temperature increases from 900 to 950°C.

The shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) experimental data were fitted to different rheological models discussed in equations (1)–(3). The several rheological parameters estimated from different models are presented with a thixotropic area (reduced hysteresis area [rHa]) in Table 4, where the Herschel–Bulkley and Ostwald–de Waele models were privileged, referring to the high values of linear correlation coefficient (R ²) and the physical meaning, as the best models fitting the experimental data. The negative value of yield stress (τ ₀), with no physical meaning, showing that the Herschel–Bulkley model was not suitable, and it was replaced in this situation by the Ostwald–de Waele model. Recently, two methods, namely, particle swarm optimization and genetic algorithm, were used as the best choice to obtain the most realistic solutions for both positive and negative yield stress values of different samples [79]. According to both models (Herschel–Bulkley and Ostwald–de Waele), the increase in TS of SSA and organic additives mixtures resulted roughly in an increase of yield stress (τ ₀), a decrease in flow behaviour index (n) and an increase in flow consistency coefficient (K).

Table 4

Sludge	TS (%)	Herschel–Bulkley model				Ostwald–de Waele model			Thixotropy
		τ = τ 0 + K γ n \tau ={\tau }_{0}+K{\gamma }^{n}				τ = K γ n \tau =K{\gamma }^{n}
		τ 0 (Pa)	K (Pa s)	n	R 2	K (Pa s)	n	R 2	rHa (Pa s−1)
SSA800 + 4% methocel + 4% amijel + 8% starch	4	0.2306	1.96 × 10−4	1.4864	0.9913	1.50 × 10−3	1.1813	0.9834	18.87
	7	0.1844	6.21 × 10−3	1.0490	0.9998	1.08 × 10−2	0.9665	0.9989	82.19
	10	−0.0500	4.39 × 10−2	0.8634	0.9998	4.15 × 10−2	0.8718	0.9998	242.35
	13	−0.7437	2.50 × 10−1	0.7275	0.9996	1.85 × 10−1	0.7707	0.9993	525.66
	15	−0.7322	3.12 × 10−1	0.7432	0.9999	2.51 × 10−1	0.7746	0.9997	NT
SSA850 + 4% methocel + 4% amijel + 8% starch	4	0.1423	9.44 × 10−4	1.2445	0.9966	2.54 × 10−3	1.0953	0.9941	41.14
	7	0.2324	4.64 × 10−3	1.0786	0.9997	1.02 × 10−2	0.9613	0.9978	69.48
	10	0.0738	3.54 × 10−2	0.8898	0.9999	3.88 × 10−2	0.8764	0.9999	175.48
	13	−0.3084	1.64 × 10−1	0.7735	0.9999	1.41 × 10−1	0.7952	0.9998	241.47
	15	−0.3487	1.73 × 10−1	0.7659	0.9999	1.47 × 10−1	0.7900	0.9998	NT
SSA900 + 4% methocel + 4% amijel + 8% starch	4	0.1372	2.29 × 10−3	1.1097	0.9987	5.10 × 10−3	0.9891	0.9968	58.18
	7	0.1416	7.57 × 10−3	1.0329	0.9999	1.11 × 10−2	0.9756	0.9994	58.77
	10	−0.2419	8.86 × 10−2	0.8036	0.9998	7.35 × 10−2	0.8310	0.9997	268.27
	13	−0.4811	2.66 × 10−1	0.7452	0.9998	2.26 × 10−1	0.7690	0.9997	233.02
	15	−0.7838	3.96 × 10−1	0.7082	0.9999	3.19 × 10−1	0.7394	0.9997	NT
SSA950 + 4% methocel + 4% amijel + 8% starch	4	0.1230	2.42 × 10−3	1.1084	0.9993	4.80 × 10−3	1.0048	0.9979	56.79
	7	0.1301	8.77 × 10−3	1.0246	0.9999	1.21 × 10−2	0.9770	0.9996	58.35
	10	−0.2068	8.23 × 10−2	0.8149	0.9998	6.99 × 10−2	0.8387	0.9997	219.88
	13	−1.4948	5.41 × 10−1	0.6644	0.9997	3.70 × 10−1	0.7185	0.9991	NT
	15	−1.4462	6.94 × 10−1	0.6836	0.9997	5.36 × 10−1	0.7205	0.9995	NT

It can also be seen that an increase in TS from 4 to 13% led to an increase in rHa. However, at a higher value of TS (15%), no thixotropic (NT) behaviour was detected. This non-thixotropy detected at TS = 15% may be due to a competition between solid interactions and viscous forces, and it seems quite logical that the stronger the viscous forces, the lower the degree of thixotropy [41].

Moreover, as can be remarked from Table 4, according to the TS, the calcination temperature significantly influences the thixotropic area (rHa). For TS = 4%, the rHa increases from 18.87 to 58.18 Pa s⁻¹ when the calcination temperature increases from 800 to 900°C, then it decreases to a value of 56.79 Pa s⁻¹ for a calcination temperature of 950°C. For TS = 7%, the rHa decreases from 82.19 to 58.35 Pa s⁻¹ when the calcination temperature increases from 800 to 950°C. For TS = 10%, the rHa decreases from 242.35 to 175.48 Pa s⁻¹ when the calcination temperature increases from 800 to 850°C, then it increases to 268.27 Pa s⁻¹ at 900°C; after that, it decreases to a value of 219.88 Pa s⁻¹ for a calcination temperature of 950°C. For TS = 13%, the rHa decreases from 525.66 to 233.02 Pa s⁻¹ when the calcination temperature increases from 800 to 900°C.

Figure 9 shows that, according to the TS, mixtures of SSA and organic additives exhibit different viscosity behaviours, where in general the apparent viscosity decreases with increasing shear rates, revealing a shear-thinning behaviour. From this figure, it could be remarked that for TS = 4%, the apparent viscosity increases with the increase of calcination temperature. Above TS = 4%, the apparent viscosity decreases when the calcination temperature increases from 800 to 850°C, then it increases respectively with a big range to reach a maximum value when the calcination temperature increases from 900 to 950°C. This last increase in viscosity is possibly due to the improvement of particle–particle interactions inside the SSA and organic additives mixtures, caused not only by a structural changing and an intensification of the crystalline phases developed at high calcination temperatures (Figure 2), but also by a competition between weak solid interactions (SSA900 and SSA950) and stronger viscous forces brought by organic additives (proportion: 4% methocel + 4% amijel + 8% starch), which in turn increases the viscosity of the dispersion. The organic additives can act physically and chemically in the system: sewage sludge ash/water, by the modification of the gradients of the chemical and electrical potentials. They formed hydrogels with their three-dimensional (3D) network chains, where the polar or charged hydrophilic parts are solvated by water molecules, but the non-polar hydrophobic parts are chemically or physically linked with each other and adsorbed on the sludge ash particles.

The apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) experimental data of the first regime were fitted to different rheological models discussed in equations (4)–(6). The various rheological parameters estimated from different models are presented in Table 5, where the Cross and Carreau models were privileged, based on the high values of linear correlation coefficient (R ²), as the best model fitting the experimental data.

Table 5

Sludge	TS (%)	Cross model					Carreau model
		η = η ∞ + ( η 0 ‒ η ∞ ) 1 + ( λ γ ̇ ) m \eta ={\eta }_{\infty }+\frac{({\eta }_{0}‒{\eta }_{\infty })}{1+{(\lambda \dot{\gamma })}^{m}}					η = η ∞ + ( η 0 ‒ η ∞ ) ( 1 + ( λ γ ̇ ) 2 ) n ‒ 1 2 \eta ={\eta }_{\infty }+\left[({\eta }_{0}‒{\eta }_{\infty }){(1+{(\lambda \dot{\gamma })}^{2})}^{\frac{n‒1}{2}}\hspace{.25em}\right]
		η ∞ {\eta }_{\infty } (Pa s)	η 0 {\eta }_{0} (Pa s)	λ \lambda (s)	M	R 2	η ∞ {\eta }_{\infty } (Pa s)	η 0 {\eta }_{0} (Pa s)	λ \lambda (s)	n	R 2
SSA800 + 4% methocel + 4% amijel + 8% starch	4	3.810 × 10−3	0.85	12.26	1.00	0.9979	3.817 × 10−3	0.16	2.31	1.79 × 10−4	0.9968
	7	8.071 × 10−3	0.86	14.64	0.84	1.0000	8.517 × 10−3	0.09	0.62	1.80 × 10−4	0.9939
	10	1.926 × 10−2	0.55	6.38	0.80	0.9960	1.891 × 10−2	0.70	12.89	2.59 × 10−1	0.9978
	13	5.496 × 10−2	0.65	2.61	0.79	1.0000	5.317 × 10−2	0.42	2.19	3.10 × 10−1	0.9987
	15	7.422 × 10−2	0.81	3.71	0.67	0.9994	8.580 × 10−2	0.24	0.31	1.80 × 10−4	0.9963
SSA850 + 4% methocel + 4% amijel + 8% starch	4	4.300 × 10−3	1.09	6.89	1.27	0.9830	3.981 × 10−3	1.02	14.38	2.89 × 10−4	0.9289
	7	7.752 × 10−3	3.35	8.90	1.15	0.9955	6.991 × 10−3	1.67	7.13	6.72 × 10−5	0.9687
	10	1.854 × 10−2	1.66	7.90	0.96	1.0000	1.862 × 10−2	1.22	5.38	1.53 × 10−4	0.9993
	13	4.781 × 10−2	0.75	4.33	0.77	1.0000	4.644 × 10−2	0.42	2.82	3.13 × 10−1	0.9996
	15	5.021 × 10−2	0.82	3.85	0.83	0.9996	4.868 × 10−2	0.55	3.29	2.55 × 10−1	0.9983
SSA900 + 4% methocel + 4% amijel + 8% starch	4	4.583 × 10−3	1.27	17.48	1.00	1.0000	4.587 × 10−3	0.23	3.22	1.01 × 10−4	0.9969
	7	9.014 × 10−3	0.25	4.63	0.83	0.9947	8.943 × 10−3	0.10	1.77	2.13 × 10−1	1.0000
	10	2.785 × 10−2	0.59	15.98	0.65	0.9971	2.743 × 10−2	0.21	3.76	3.94 × 10−1	0.9994
	13	5.656 × 10−2	0.78	24.11	0.45	0.9982	5.279 × 10−2	0.30	3.92	6.13 × 10−1	0.9973
	15	8.044 × 10−2	0.56	3.13	0.56	1.0000	7.369 × 10−2	0.30	1.68	5.63 × 10−1	0.9985
SSA950 + 4% methocel + 4% amijel + 8% starch	4	4.731 × 10−3	0.99	16.60	0.99	1.0000	4.699 × 10−3	0.96	18.22	3.79 × 10−2	0.9961
	7	9.989 × 10−3	0.30	5.34	0.85	0.9962	9.926 × 10−3	0.15	2.78	1.91 × 10−1	0.9991
	10	2.770 × 10−2	0.50	6.80	0.72	0.9983	2.831 × 10−2	0.12	0.63	2.34 × 10−1	0.9984
	13	5.708 × 10−2	0.51	6.68	0.35	1.0000	3.861 × 10−2	0.31	6.91	7.69 × 10−1	0.9988
	15	1.108 × 10−1	0.34	0.15	0.60	0.9965	6.329 × 10−2	0.30	0.67	7.64 × 10−1	0.9953

According to both models (Cross and Carreau), the increase in SSA and organic additives' TS resulted in an increase of the infinite-shear rate apparent viscosity (η _C = η _∞). This rise in viscosity is possibly due to the effective homogeneous dispersion of SSA and organic additives mixtures in water, and to the improvement of particle–particle interactions via electrostatic, steric or electrosteric mechanisms, forming a strong structural network [43,78,80]. Furthermore, for TS = 4%, the increase in calcination temperature is accompanied by an increase of the infinite-shear rate apparent viscosity (η _C = η _∞). This is probably due to the low presence of the mixture dispersed in the water. Above TS = 4%, the infinite-shear rate apparent viscosity (η _C = η _∞) decreases when the calcination temperature increases from 800 to 850°C, then it increases, respectively, with a big step to reach a maximum value when the calcination temperature increases from 900 to 950°C.

Figures 10 and 11, respectively, illustrate the first step shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) and apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves with the best-fit rheological model of sewage sludge ash SSA850, mixed with organic additives (4% amijel + 8% starch) and various percentages of methocel: 3, 4, 5, and 6%, for different TS = 4, 7, 10, 13, and 15%, at 20°C.

Figure 10

Shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) curves of sewage sludge ash SSA850, mixed with organic additives (4% amijel + 8% starch) and various percentages of methocel: 3, 4, 5, and 6%, for different TS, at 20°C.

Figure 11

Apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves of sewage sludge ash SSA850, mixed with organic additives (4% amijel + 8% starch) and various percentages of methocel: 3, 4, 5, and 6%, for different TS, at 20°C.

Figure 10 highlights that for SSA850 and organic additives mixtures, the shear stress increases with increasing shear rate indicating non-Newtonian shear thickening (yield dilatant) flow behaviour at low TS (4 and 7%) for all methocel percentages and shear-thinning (pseudoplastic) flow behaviour at high TS (10, 13, and 15%) for methocel percentages of 4, 5, and 6%. It can be remarked from this figure that the shear stress increases significantly when the percentage of methocel increases from 2 to 6%. This means that the increase in organic additives percentage enhances the shear-thinning behaviour and leads to higher shear-stress magnitudes [59,81].

The shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) experimental data were fitted to different rheological models discussed in equations (1)–(3). Several rheological parameters estimated from different models are presented with a thixotropic area (rHa) in Table 6, where the Herschel–Bulkley and Ostwald–de Waele models were preferred, referring to the high values of linear correlation coefficient (R ²) and the physical meaning, as the best models fitting the experimental data. According to Herschel–Bulkley and Ostwald–de Waele models, for each TS, the increase in the methocel percentage caused roughly a decrease in flow behaviour index (n) and an increase in flow consistency coefficient (K).

Table 6

Sludge	TS (%)	Herschel–Bulkley model				Ostwald–de Waele model			Thixotropy
		τ = τ 0 + K γ n \tau ={\tau }_{0}+K{\gamma }^{n}				τ = K γ n \tau =K{\gamma }^{n}
		τ 0 (Pa)	K (Pa s)	n	R 2	K (Pa s)	n	R 2	rHa (Pa s−1)
SSA850 + 3% methocel + 4% amijel + 8% starch	4	0.1117	7.97 × 10−6	1.9683	0.9993	3.97 × 10−5	1.7211	0.9949	NT
	7	0.3205	6.56 × 10−6	2.0215	0.9956	3.06 × 10−4	1.4294	0.9728	NT
	10	0.2465	1.42 × 10−4	1.6243	0.9990	5.79 × 10−4	1.4091	0.9950	NT
	13	0.5263	5.27 × 10−4	1.4941	0.9991	2.69 × 10−3	1.2460	0.9932	NT
	15	0.7269	1.54 × 10−3	1.3971	0.9993	5.78 × 10−3	1.1968	0.9951	NT
SSA850 + 4% methocel + 4% amijel + 8% starch	4	0.1423	9.44 × 10−4	1.2445	0.9966	2.54 × 10−3	1.0953	0.9941	41.14
	7	0.2324	4.64 × 10−3	1.0786	0.9997	1.02 × 10−2	0.9613	0.9978	69.48
	10	0.0738	3.54 × 10−2	0.8898	0.9999	3.88 × 10−2	0.8764	0.9999	175.48
	13	−0.3084	1.64 × 10−1	0.7735	0.9999	1.41 × 10−1	0.7952	0.9998	241.47
	15	−0.3487	1.73 × 10−1	0.7659	0.9999	1.47 × 10−1	0.7900	0.9998	NT
SSA850 + 5% methocel + 4% amijel + 8% starch	4	0.1618	2.10 × 10−3	1.1285	0.9990	5.31 × 10−3	0.9897	0.9966	NT
	7	0.1035	1.47 × 10−2	0.9779	1.0000	1.79 × 10−2	0.9491	0.9998	NT
	10	−0.2135	8.02 × 10−2	0.8297	0.9998	6.83 × 10−2	0.8531	0.9997	NT
	13	−0.5515	2.97 × 10−1	0.7552	0.9999	2.53 × 10−1	0.7786	0.9998	NT
	15	−0.9060	6.48 × 10−1	0.7163	0.9997	5.60 × 10−1	0.7374	0.9996	NT
SSA850 + 6% methocel + 4% amijel + 8% starch	4	0.1208	2.15 × 10−3	1.1360	0.9993	4.42 × 10−3	1.0284	0.9979	NT
	7	0.1226	1.78 × 10−2	0.9539	0.9999	2.21 × 10−2	0.9220	0.9997	NT
	10	−0.0702	1.20 × 10−1	0.8106	0.9999	1.05 × 10−1	0.8304	0.9999	NT
	13	−0.2255	8.35 × 10−1	0.6900	0.9993	6.70 × 10−1	0.7215	0.9991	NT
	15	−0.7781	8.19 × 10−1	0.7039	0.9985	8.26 × 10−1	0.7025	0.9985	NT

As expected from Table 6, SSA850 and organic additives mixtures containing 3, 5, and 6% of methocel exhibit a non-thixotropic behaviour. This alteration in behaviour (non-thixotropy) occurs at the cross-over point of the shear-rate-rising (continuous ramp step 1) and shear-rate-falling (continuous ramp step 2) for methocel percentages of 3 and 5%. However, for a methocel percentage of 6%, the non-thixotropy occurs while the shear-rate-falling is greater than the shear-rate-rising.

Figure 11 compares different TS, the viscosity behaviour of SSA850 and organic additives mixtures, as the methocel percentage varies from 3 to 6%, and an applied shear rate increases from 0 to 600 s⁻¹. For a low methocel percentage (3%), the apparent viscosity exhibits similar behaviours as that detected for SS0 and SSA (shear-thinning laminar and shear-thickening turbulent behaviours, Figure 6). However, for methocel percentages above 3% (4–6%), the shear rate dependence of the apparent viscosity reveals a shear-thinning flow behaviour. As also reported in Figure 11, it could be stated that for all TS, the apparent viscosity increases with the increase of the methocel percentage. The viscosity rheological parameters estimated from different models are presented in Table 7, where the Cross model was preferred as the best model fitting the experimental data.

Table 7

Sludge	TS (%)	Cross model					Carreau model
		η = η ∞ + ( η 0 ‒ η ∞ ) 1 + ( λ γ ̇ ) m \eta ={\eta }_{\infty }+\frac{({\eta }_{0}‒{\eta }_{\infty })}{1+{(\lambda \dot{\gamma })}^{m}}					η = η ∞ + ( η 0 ‒ η ∞ ) ( 1 + ( λ γ ̇ ) 2 ) n ‒ 1 2 \eta ={\eta }_{\infty }+\left[({\eta }_{0}‒{\eta }_{\infty }){(1+{(\lambda \dot{\gamma })}^{2})}^{\frac{n‒1}{2}}\hspace{.25em}\right]
		η ∞ {\eta }_{\infty } (Pa s)	η 0 {\eta }_{0} (Pa s)	λ \lambda (s)	m	R 2	η ∞ {\eta }_{\infty } (Pa s)	η 0 {\eta }_{0} (Pa s)	λ \lambda (s)	n	R 2
SSA850 + 3% methocel + 4% amijel + 8% starch	4	1.246 × 10−3	0.06	0.43	1.24	0.9992	8.456 × 10−4	0.05	0.56	7.58 × 10−4	0.9987
	7	2.807 × 10−3	0.12	0.45	1.16	0.9978	2.461 × 10−3	0.09	0.49	7.48 × 10−4	0.9976
	10	4.982 × 10−3	0.06	0.22	1.55	0.9977	4.184 × 10−3	0.06	0.44	7.60 × 10−4	0.9910
	13	8.075 × 10−3	0.20	0.59	1.00	0.9998	8.489 × 10−3	0.12	0.40	7.59 × 10−4	0.9982
	15	1.126 × 10−2	0.49	1.35	0.87	1.0000	1.359 × 10−2	0.21	0.46	7.60 × 10−4	0.9986
SSA850 + 4% methocel + 4% amijel + 8% starch	4	4.300 × 10−3	1.09	6.89	1.27	0.9830	3.981 × 10−3	1.02	14.38	2.89 × 10−4	0.9289
	7	7.752 × 10−3	3.35	8.90	1.15	0.9955	6.991 × 10−3	1.67	7.13	6.72 × 10−5	0.9687
	10	1.854 × 10−2	1.66	7.90	0.96	1.0000	1.862 × 10−2	1.22	5.38	1.53 × 10−4	0.9993
	13	4.781 × 10−2	0.75	4.33	0.77	1.0000	4.644 × 10−2	0.42	2.82	3.13 × 10−1	0.9996
	15	5.021 × 10−2	0.82	3.85	0.83	0.9996	4.868 × 10−2	0.55	3.29	2.55 × 10−1	0.9983
SSA850 + 5% methocel + 4% amijel + 8% starch	4	4.855 × 10−3	0.97	9.13	1.06	0.9921	4.746 × 10−3	3.09	37.33	4.51 × 10−4	0.9909
	7	1.260 × 10−2	1.15	29.54	0.81	0.9985	1.306 × 10−2	0.08	0.65	1.50 × 10−4	0.9894
	10	2.762 × 10−2	0.79	28.88	0.62	0.9974	3.043 × 10−2	0.09	0.29	5.00 × 10−4	0.9701
	13	7.697 × 10−2	0.42	1.32	0.65	1.0000	6.880 × 10−2	0.64	13.86	5.48 × 10−1	0.9983
	15	1.231 × 10−1	0.71	1.39	0.49	0.9995	1.732 × 10−1	0.36	0.21	1.01 × 10−4	0.9817
SSA850 + 6% methocel + 4% amijel + 8% starch	4	4.993 × 10−3	0.47	8.62	0.98	0.9944	5.025 × 10−3	0.08	1.36	7.45 × 10−4	0.9923
	7	1.284 × 10−2	0.86	42.80	0.69	1.0000	1.278 × 10−2	0.20	5.28	3.29 × 10−1	0.9979
	10	3.261 × 10−2	0.63	44.98	0.45	0.9968	3.190 × 10−2	0.19	3.67	5.89 × 10−1	0.9916
	13	1.637 × 10−1	0.68	3.48	0.46	0.9991	1.466 × 10−1	0.42	2.20	6.86 × 10−1	0.9988
	15	2.536 × 10−1	1.82	0.26	2.99	0.9937	1.771 × 10−1	2.75	0.80	4.43 × 10−4	0.9915

According to the Cross model, the increase in the methocel percentage resulted in an increase of the infinite-shear rate apparent viscosity (η _C = η _∞). This interesting increase in viscosity is due to the primordial role of the plasticizer (methocel), which makes it possible to extend the pseudoplastic plateau by reducing the migration of the liquid phase [82,83,84]. Plasticizers are adsorbed on the surface of SSA particles and, depending on their chemistry, create surface charges participating in the electrostatic repulsion of the SSA particles [85] or form deposits covering the particles' morphology and allowing better relative sliding of these last ones. In addition, plasticizers can also attach water molecules to their chains, thus creating a water-saturated network which in turn facilitates the sliding of particles over each other [82,86].

The effect of temperature on rheological properties of different sludge systems (SS0, SSA850, SSA850 mixed with 4% methocel + 4% amijel + 8% starch, and SSA850 mixed with 5% methocel + 4% amijel + 8% starch) has been studied at different testing temperatures of 20, 30, 40, 50, and 60°C for a TS of 10%. As shown in Figures 12 and 13, experimental results show that temperature exerted a significant impact on the shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) and apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves over the entire temperature range (20–60°C).

Figure 12

Shear stress (τ)−shear rate ( γ ̇ \dot{\gamma } ) curves of sludge systems (SS0, SSA850, SSA850 + 4% methocel + 4% amijel + 8% starch, and SSA850 + 5% methocel + 4% amijel + 8% starch) for a TS = 10%, at different testing temperatures (20, 30, 40, 50, and 60°C).

Figure 13

Apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves of sludge systems (SS0, SSA850, SSA850 + 4% methocel + 4% amijel + 8% starch, and SSA850 + 5% methocel + 4% amijel + 8% starch) for a TS = 10%, at different testing temperatures (20, 30, 40, 50, and 60°C).

Figure 12 reports that for all testing temperatures, the shear stress increases with increasing shear rate, indicating non-Newtonian shear thickening (yield dilatant) flow behaviour for SS0 and SSA850 and shear-thinning (pseudoplastic) for SSA850 mixed with 4% methocel + 4% amijel + 8% starch, and SSA850 mixed with 5% methocel + 4% amijel + 8% starch. As can be obviously observed in this figure, the shear stress decreases meaningfully when the testing temperature increases from 20 to 60°C. This decrease is the result of the thermal destruction of sludge systems, which manifests itself in the reduction of the mutual interaction between particles [42,52,58,85,87].

As also mentioned in Table 8, only the sludge system composed of SSA850 mixed with 4% methocel + 4% amijel + 8% starch exhibited a thixotropic response at testing temperatures of 20, 30 and 40°C. With the increase of temperature from 20 to 40°C, the rHa decreased gradually from 175.48 to 59.04 Pa s⁻¹. This indicates that the thixotropic behaviour of the sludge system was distinctly weakened during the heating testing. Thus highlighting that temperature negatively impacts the network strength between the particles and breaking some chemical bonds of macromolecules. The more aggregated particles can be fractured, the size and fraction of particles be reduced, and solid matter dissolves into liquid [81].

Table 8

Sludge system	T (°C)	Herschel–Bulkley model				Ostwald–de Waele model			Thixotropy
		τ = τ 0 + K γ n \tau ={\tau }_{0}+K{\gamma }^{n}				τ = K γ n \tau =K{\gamma }^{n}
		τ 0 (Pa)	K (Pa s)	n	R 2	K (Pa s)	n	R 2	rHa (Pa s−1)
SS0	20	0.1628	2.15 × 10−5	1.8161	0.9976	1.61 × 10−4	1.5076	0.9900	NT
	30	0.1128	1.63 × 10−5	1.8572	0.9994	7.16 × 10−5	1.6296	0.9953	NT
	40	0.0846	2.03 × 10−5	1.8243	0.9992	6.01 × 10−5	1.6581	0.9969	NT
	50	0.0836	1.29 × 10−5	1.8677	0.9994	4.85 × 10−5	1.6638	0.9962	NT
	60	0.0661	2.64 × 10−5	1.7487	0.9993	7.23 × 10−5	1.5945	0.9972	NT
SSA850	20	0.0698	5.63 × 10−5	1.6359	0.9992	1.44 × 10−4	1.4926	0.9972	NT
	30	0.0609	3.92 × 10−5	1.6861	0.9993	9.55 × 10−5	1.5501	0.9976	NT
	40	0.0397	1.04 × 10−4	1.5204	0.9986	1.81 × 10−4	1.4354	0.9979	NT
	50	0.0275	1.96 × 10−4	1.3989	0.9973	2.93 × 10−4	1.3383	0.9969	NT
	60	0.0409	1.75 × 10−4	1.3898	0.9986	3.52 × 10−4	1.2838	0.9973	NT
SSA850 + 4% methocel + 4% amijel + 8% starch	20	0.0738	3.54 × 10−2	0.8898	0.9999	3.88 × 10−2	0.8764	0.9999	175.48
	30	0.2021	1.60 × 10−2	0.9644	0.9998	2.31 × 10−2	0.9095	0.9994	111.92
	40	0.2005	6.94 × 10−3	1.0533	0.9996	1.18 × 10−2	0.9743	0.9988	59.04
	50	0.1598	3.74 × 10−3	1.1101	0.9997	1.57 × 10−4	0.0039	0.9987	NT
	60	0.1398	1.31 × 10−3	1.2387	0.9997	2.72 × 10−3	1.1293	0.9983	NT
SSA850 + 5% methocel + 4% amijel + 8% starch	20	−0.2135	8.02 × 10−2	0.8297	0.9998	6.83 × 10−2	0.8531	0.9997	NT
	30	0.0962	4.32 × 10−2	0.8711	1.0000	4.81 × 10−2	0.8554	0.9999	NT
	40	0.1929	1.61 × 10−2	0.9813	0.9998	2.23 × 10−2	0.9333	0.9995	NT
	50	0.1875	8.13 × 10−3	1.0435	0.9998	1.27 × 10−2	0.9767	0.9991	NT
	60	0.2102	2.52 × 10−3	1.1967	0.9995	5.15 × 10−3	1.0893	0.9981	NT

The shear stress–shear rate rheograms were found to best fit the Herschel–Bulkley model. The several rheological parameters extracted from different models are collected with the thixotropic area (rHa) in Table 8. For all sludge systems, conforming to the Herschel–Bulkley model, an increase in testing temperature usually brings about a decrease in yield stress (τ ₀).

The relationship between sludge systems’ apparent viscosity and temperature is exposed in Figure 13. On the whole testing temperature range (20–60°C), the viscosity decreased with the increasing temperature due to the weakening of inter-molecular cohesive forces within the sludge systems. For all testing temperatures, the apparent viscosity of SS0 and SSA850 systems exhibit shear-thinning laminar and shear-thickening turbulent behaviours. Furthermore, for the systems composed of SSA850 mixed with 4% methocel + 4% amijel + 8% starch, and SSA850 mixed with 5% methocel + 4% amijel + 8% starch, the shear rate dependence of the apparent viscosity discloses a shear-thinning flow behaviour.

Moreover, different rheological models were fitted to the apparent viscosity (η)−shear rate ( γ ̇ \dot{\gamma } ) curves, and the obtained rheological parameters are tabulated in Table 9. According to Cross and Carreau models, the increase in testing temperature induced a decrease of the infinite-shear rate apparent viscosity (η _C = η _∞). This decrease in infinite-rate viscosity is due to some restructuring in the sludge systems network, which resulted in the weakening of the network strength [42,52,58,81,85,87].

Table 9

Sludge	T (°C)	Cross model					Carreau model
		η = η ∞ + ( η 0 ‒ η ∞ ) 1 + ( λ γ ̇ ) m \eta ={\eta }_{\infty }+\frac{({\eta }_{0}‒{\eta }_{\infty })}{1+{(\lambda \dot{\gamma })}^{m}}					η = η ∞ + ( η 0 ‒ η ∞ ) ( 1 + ( λ γ ̇ ) 2 ) n ‒ 1 2 \eta ={\eta }_{\infty }+\left[({\eta }_{0}‒{\eta }_{\infty }){(1+{(\lambda \dot{\gamma })}^{2})}^{\frac{n‒1}{2}}\hspace{.25em}\right]
		η ∞ {\eta }_{\infty } (Pa s)	η 0 {\eta }_{0} (Pa s)	λ \lambda (s)	m	R 2	η ∞ {\eta }_{\infty } (Pa s)	η 0 {\eta }_{0} (Pa s)	λ \lambda (s)	n	R 2
SS0	20	2.28 × 10−3	0.59	13.16	0.95	0.9985	2.336 × 10−3	0.05	0.71	7.59 × 10−4	0.9920
	30	1.556 × 10−3	0.43	5.33	1.03	0.9987	1.510 × 10−3	0.39	5.68	6.91 × 10−4	0.9982
	40	1.258 × 10−3	0.20	3.57	0.97	1.0000	1.353 × 10−3	0.06	0.95	1.00 × 10−3	0.9988
	50	1.006 × 10−3	0.09	1.43	1.03	1.0000	1.010 × 10−3	0.04	0.73	7.47 × 10−4	0.9980
	60	1.017 × 10−3	0.10	1.51	1.07	0.9982	7.905 × 10−4	0.06	1.07	1.79 × 10−4	0.9989
SSA850	20	1.267 × 10−3	0.41	6.20	1.00	0.9990	1.237 × 10−3	0.06	0.85	7.56 × 10−4	0.9881
	30	1.175 × 10−3	0.09	1.38	1.07	0.9994	1.105 × 10−3	0.05	0.87	7.53 × 10−4	0.9969
	40	1.126 × 10−3	0.15	2.01	1.11	1.0000	9.833 × 10−4	0.23	4.52	6.65 × 10−4	0.9979
	50	1.030 × 10−3	0.26	3.78	1.09	1.0000	8.731 × 10−4	0.46	9.00	4.63 × 10−4	0.9927
	60	9.888 × 10−4	0.14	1.87	1.13	0.9987	7.800 × 10−4	0.31	5.91	1.77 × 10−4	0.9973
SSA850 + 4% methocel + 4% amijel + 8% starch	20	1.854 × 10−2	1.66	7.90	0.96	1.0000	1.862 × 10−2	1.22	5.38	1.53 × 10−4	0.9993
	30	1.230 × 10−2	0.25	2.25	0.78	1.0000	1.208 × 10−2	0.11	1.01	2.80 × 10−1	0.9997
	40	9.526 × 10−3	0.16	1.86	0.86	0.9967	9.319 × 10−3	0.18	3.96	2.47 × 10−1	0.9961
	50	7.444 × 10−3	0.08	0.55	1.16	0.9933	7.328 × 10−3	0.06	0.61	7.49 × 10−4	0.9923
	60	5.679 × 10−3	0.05	0.38	1.44	0.9782	5.494 × 10−3	0.36	6.30	1.74 × 10−4	0.9592
SSA850 + 5% methocel + 4% amijel + 8% starch	20	2.762 × 10−2	0.79	28.88	0.62	0.9974	3.043 × 10−2	0.09	0.29	5.00 × 10−4	0.9701
	30	2.092 × 10−2	0.26	2.33	0.75	1.0000	2.019 × 10−2	0.13	1.19	3.44 × 10−1	1.0028
	40	1.357 × 10−2	0.28	7.17	0.67	0.9999	1.334 × 10−2	0.22	7.68	3.90 × 10−1	0.9963
	50	1.048 × 10−2	0.20	3.12	0.83	0.9950	1.043 × 10−2	0.08	1.04	2.12 × 10−1	0.9930
	60	8.577 × 10−3	0.06	0.35	1.37	0.9766	8.378 × 10−3	0.07	0.82	1.79 × 10−4	0.9700

In general, the activation energy signifies the strength of the inter-particle forces that preserve the cohesion of the sludge system network. An increase in activation energy reveals higher resistance to flow and greater sludge network strength [56,57,58,81].

The dependence between temperature and apparent viscosity of different sludge systems (SS0, SSA850, SSA850 + 4% methocel + 4% amijel + 8% starch, and SSA850 + 5% methocel + 4% amijel + 8% starch), at a TS of 10%, can be commonly expressed by the Arrhenius model equation: (7) ln η ∞ = ln η 0 + E a R T , \mathrm{ln}\hspace{.25em}{\eta }_{\infty }=\hspace{.25em}\mathrm{ln}\hspace{.5em}{\eta }_{0}+\frac{{E}_{\text{a}}}{RT}, where η _∞ is the infinite-shear rate apparent viscosity (Pa s), η ₀ is the zero-shear rate apparent viscosity (Pa s) (generally termed the frequency factor: pre-exponent coefficient), E _a is the activation energy (J mol⁻¹), R is the universal gas constant (8.314 J mol⁻¹ K⁻¹), and T is the absolute temperature (K).

The activation energies and the zero-shear rate apparent viscosities of the flow process were calculated, respectively, from the slope and the intercept of the Arrhenius-type plots (ln η _∞ against 1/T) as shown in Figure 14, and the obtained values are presented in Table 10.

Figure 14

Arrhenius plots of ln(η) versus 1/T for sludge systems (SS0, SSA850, SSA850 mixed with 4% methocel + 4% amijel + 8% starch, and SSA850 mixed with 5% methocel + 4% amijel + 8% starch), at TS = 10%.

It shows that the sludge system composed of SSA850 mixed with 5% methocel + 4% amijel + 8% starch exhibits the highest activation energy (24.67 kJ mol⁻¹) followed by the system consisting of SSA850 mixed with 4% methocel + 4% amijel + 8% starch (23.35 kJ mol⁻¹), then the SS0 system (20.80 kJ mol⁻¹) and lastly the SSA850 system (5.10 kJ mol⁻¹). The activation energies obtained for SS0 and SSA850 mixed with organic additive systems are in the same order of magnitude and compared to those obtained by Hong et al. [56], Gienau et al. [57], and Liu et al. [88], respectively, for municipal TEAS (13.10–24.80 kJ mol⁻¹), for anaerobic sludge obtained from agricultural and bio-waste biogas plants (13.00–20.00 kJ mol⁻¹), and for swine manure (composed of protein, polysaccharide, volatile fatty acids, lignin, etc.)/sewage sludge systems (13.91–25.91 kJ mol⁻¹). The activation energies are also found to be significantly higher than those obtained by Trávníček and Junga [89] for non-diluted (8.87 kJ mol⁻¹) and diluted (9.41–11.56 kJ mol⁻¹) sewage sludge. The activation energy measured for the SSA850 system was proven to be lower than that reported by Lopez et al. [90] for the activated sludge in MBR (17.69 kJ mol⁻¹).

Through the results presented in Table 10, it can be deduced that, on the one side, the increase of calcination temperature to 850°C induces a sharp decrease in the activation energy from SS0 to SSA850 suspensions, where the apparent viscosity curves shifted to lower levels of viscosity (Figure 7 and Table 9). The reduction of sludge viscosity can be achieved by reduction of its interfacial tension [91]. The observed decrease in the activation energy is due to a combination of devolatilization of organic matter and the transformation of inorganic matter. Indeed, due to the effect of thermal calcination, the overall organic matter content is removed, the oxygen is consumed during the oxidation to form vacancies, and the SSA850 structure underwent modifications such as the transformation of calcite (CaCO₃) into lime (CaO). Therefore, the gases generated by the decomposition of minerals and organic additives must pass through the very fine and tortuous porosity to escape from the aggregate [92]. These synergistic effects can be manifested in the increase of the average pore diameter and nanoscale surface roughness of SSA850 particles [93].

On the other side, the addition of organic additives and the increase of methocel percentage to 5% lead to an increase in activation energy caused by the modification of the interaction mechanisms/pathways. This increase can be related to the strong solubilization of organic additives during the thermal treatment, which induced a transfer of the organic matter from the solid compounds to the dissolved constituents, and this transfer is proportional to the evolutions of the yield stress and viscosity [87]. The colloidal sludge suspensions (CSS) are generally stabilized by adsorption of organic compounds on their surface [94,95,96,97]. The enhanced stability of CSS with organic coatings has stereotypically been attributed to steric hindrance effects when compressed or deformed adsorbed organic layers overlap and exhibit nonuniform or incomplete surface coverage [94,98]. Molecular organic coatings can either enhance or inhibit colloid aggregation and retention behaviour. Enhanced colloid interactions have been linked to charge neutralization or bridging of macromolecules [94,96]. Contrarily, inhibited aggregation or retention has been elucidated by an increase in repulsive electrostatic, steric hindrance, or electrosteric interactions [94,99,100,101]. The case of inhibited aggregation or retention effect can be applied to compare the colloidal suspension systems (SSA850; SSA850 + meth4% + ami4% + star8%; SSA850 + meth5% + ami4% + star8%), where the increase of activation energy is attributed to the increase of apparent viscosity and interfacial tension. This last physical parameter strongly dependent on the interaction energy remains to be confirmed by the use of different methods of measuring surface and interfacial tension. So, in this sense, it can be categorically stated that to envisage situations that are promising or unpromising for colloid aggregation and/or retention mechanism, it is necessary to calculate the interaction energy taking into account the van der Waals and electrostatic double-layer interactions; the particle sizes, shapes and orientation; the curvature and nanoscale surface roughness; and finally the steric or electrosteric barrier energies [94,95,96,97,98,99,100,101]. This last one is considered the vital parameter tuning sludge rheology. Because the electrical characteristics follow the same temperature-dependence relationships as the rheological characteristics with the same activation energies, the same interactions are most likely involved in both the rheological and electrical properties [85].