Physical and rheological properties of the Chorfa dam mud: dependency on solids concentration
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Abstract
The main purpose of this study is to determine the mud rheological properties of the Chorfa dam (region of Mascara, Algeria) and to propose a rheological model that describes mud flow behavior. This study helps on one hand to give a better understanding of fine sediment transport dynamics in the dam, as well as contributing to reduce the dredging costs, and on other hand to valorize dredged sediments in road construction. Rheological measurements were conducted using an Engler viscometer and a Haake RS 600 rheometer. Mud samples were prepared with purified water at a range of solids concentration varying between 5.0 and 32.5%. Besides, the physical, chemical and mineralogical characteristics of the Chorfa dam’s mud and the rheological tests were presented and the effect of solids concentration on mud viscosity was studied. The results indicate that the Chorfa dam’s mud showed a nonNewtonian behavior for solids concentration higher than the critical solids concentration, and the apparent viscosity increases with increasing solid concentration at different shear rates. In addition, for a fixed concentration, the apparent viscosity decreases with increasing shear rates, which approves the shear thinning behavior of the Chorfa dam’s mud. Fitting results of four rheological models (Bingham Plastic Model, Ostwald–de Waele (power law), Herschel–Bulkley and Casson) to the experimental data were presented. Hence, the Ostwald–de Waele model was the best fitting model for mud samples.
Keywords
Mud Solids concentration Apparent viscosity Rheometer Rheological modelIntroduction
 The model of Ostwald–de Waele (Reiner 1926) is expressed as follows:where k is the flow consistency index, n is the flow behavior index;$$\tau = k \cdot \dot{\gamma }^{n}$$(1)
 The Bingham model (Bingham 1922) is expressed as follows:where τ_{0} is the yield stress, \(\eta_{\text{B}}\) is the plastic viscosity independent of the shear rate, n is the flow behavior index.$$\tau = \tau_{0} + \eta_{B} .\dot{\gamma }^{n}$$(2)
 The Herschel–Bulkley model corrects this failure by replacing the term plastic viscosity in the Bingham model with a power law expression (Herschel and Bulkley 1926) as follows:$$\tau = \tau_{0} + k.\dot{\gamma }^{n}$$(3)
 Moreover, Casson equation is generally used to express the nonNewtonian behavior of sediments and activated sludges (Casson 1959):$$\tau^{1/2} = \tau_{0}^{1/2} + \eta_{\infty }^{1/2} \dot{\gamma }^{1/2}$$(4)
 The Sisko model is another model which includes three parameters to describe the fluid flow at low and high shear rates (Sisko 1958):$$\eta = \eta_{\infty } + k \cdot \dot{\gamma }^{n}$$(5)
 There are also models with four parameters, who can be used over the full range of shear rates, like the Carreau model. These models are mainly used for food and beverages (Steffe 1996) and blood flow (Shibeshi and Collins 2005).a is the index that describes the transition between low shear rate as a Newtonian fluid and high shear rate as a powerlaw fluid; \(\lambda\) is a time constant.$$\frac{{\eta  \eta_{\infty } }}{{\eta_{0}  \eta_{\infty } }} = \left( {1 + \left( {\lambda \gamma } \right)^{a} } \right)^{{\frac{n  1}{a}}}$$(6)
But on the other hand, the models with four parameters can be difficult to apply because there is not enough data to get the best fit between model and experimental data. Guibaud et al. (2004) and Baudez et al. (2004) found that the Herschel–Bulkley model could be suitable for describing the viscosity of activated sludge at high concentrations. Furthermore, Bingham’s model was used for characterizing low concentrated sludge. Hasar et al. (2004), Laera et al. (2007) and Pollice et al. (2007) showed that the power law model was the best to describe the viscosity of activated sludge for a low shear rate range. Many studies have been developed to establish a rheological model suitable for all parameters of sludge (Seyssiecq et al. 2008). But so far, there is not a best rheological model having the exactitude to describe the complex properties of all fine sediments and sludge. All these previous models remain empirical.
The main objective of this study was to define the rheological properties of samples taken upstream of the Chorfa dam, to estimate the best rheological model adapted to experimental data, and to determine the correlation between rheological parameters and sludge solids concentration.
Materials and Methods
Characteristics of the site
Identification of mud characteristics
Physical characterization
Physical characteristics of the mud
Parameters  Value 

Dry density ɣ_{d} (g/cm^{3})  2.65 
Water content natural (%)  52.33 
Liquid limit W_{L} (%)  58.93 
Plastic limit W_{P} (%)  35.86 
Plasticity index I_{P} (%)  23.07 
Consistency index I_{c} (%)  0.28 
Methylene blue value MBV (g/100 g of soil)  5.41 
Organic matter OM (%)  7 
Depending on results obtained from the physical analyzes, the sediments of the Chorfa dam are found to be fine grained soil composed mainly of clay, fine sand and silt. According to Casagrande’s abacus, the samples are classified as a clay loam soil. All the physical and geotechnical analysis were carried out at the materials, soil and thermal laboratory at the University of Science and Technology of Oran, “Algeria.”
Mineralogical characterization
The Xray diffraction analysis of the mud in its natural state (Fig. 4) shows the existence of high quantity of silica (SiO_{2}) and calcite (CaCO_{3}), a small amount of kaolinite (Al_{2}O_{3} 2SiO_{2} 2H_{2}O), illite and also dolomite CaMg (CO_{3})_{2}.
Chemical characterization
Chemical composition of the mud
Elements  SiO_{2}  Al_{2}O_{3}  CaO  Cl  Fe_{2}O_{3}  MgO  K_{2}O  Na_{2}O  (LOI) 

Quantity (%)  45.64  11.08  12.67  0.18  6.38  2.33  2.76  0.37  18.23 
Results of chemical analysis (Table 2) show that the Chorfa dam mud contained a large percent of silica in order of 45.64%, and alumina in order of 43.77%. These two oxides confirm the mineralogical analysis of the mud and the existence of kaolinite and illite with the presence of potassium oxide in order of 2.76%. The percent of loss on ignition is significant, in order of 18.23% which confirms the presence of organic matter in sediments. The percent of CaO (12.67%) and MgO (2.33) confirms the presence of carbonates such as calcite CaCo_{3} and dolomite CaMg (Co_{3})_{2}.
Rheological characterization
Materials
All rheological tests were carried out in the Rheology of Complex Fluids Laboratory at the University of Science and Technology of Oran “Algeria.” In this experiment, every sample was diluted with purified water to total solids concentration of 5%, 10.5%, 15.6%, 22.7%, 26.8% and 32.5%. The concentrations were empirically chosen to get the same range of solids concentration used during dam dredging. Then, all mixtures were stirred thoroughly for 24 h until a sufficiently homogeneous material was obtained. Further, the resulting mixture was left standing for 1 h, then stirred lightly for 5 min before placing the sample under the measurement geometry.
Rheological measurements
The Engler viscometer was used in this work to determine the critical solids concentration (C _{s} ^{*} ) of the Chorfa dam mud. The rheological analysis was carried out using a coaxial cylinder rheometer (Haake RS600) which was equipped with a measuring rotor system and with an inner diameter of 22.80 mm and an outer diameter of 24.80 mm. A shear rate range was 0–160 s^{−1}, and temperature was fixed at 20 °C.
Results and discussion
Determination of critical solids concentration of mud
Effect of solids concentration on mud rheology
As depicted in Fig. 6, the relationship between shear stress and shear rate is linear for sample which has solids concentration of 5% and mud behaves as a Newtonian fluid. On the other hand, shear stress–shear rate relationship is nonlinear for all.
Other samples certified that mud samples behave as nonNewtonian fluid, for solids concentration (C_{s}) greater than the critical solids concentration (C _{s} ^{*} ). Moreover, the shear stress increased with the increase in solids concentration, and the increment in shear stress was higher with higher mud solids concentration. This is probably due to a smaller distance between particles in a denser sample which produces a large attraction of particles to each other. A shearing force has to be exerted on the mud to decrease the internal friction among the particles forming flocs and to make it flow again. Once the mud flows, the flocs are broken down and the water blended within them is progressively released with increasing shear rate, which facilitates the mud flow and leads to decrease in the viscosity of fluid. This is similar to previous research (Seyssiecq et al. 2008; Baroutian et al. 2013; Liu et al. 2012). According to Seyssiecq et al. (2008), who stated that, a strong interaction between particles got closer to each other and form flocs. This is also interpreted by Baroutian et al. (2013) that the content of polysaccharide and protein increased with increasing solid contents sludge, which was significant for rheological behavior.
Effect of solids concentration on viscosity
The viscosity decreased with increase in the shear rate, and the increment in viscosity was higher with higher mud solids concentration. This was also interpreted by Cheng who stated that the increase in apparent viscosity with the increase in solids concentration can be attributed to the increase in the interactions between particles in the fluid, and the low attraction between a large particle leads to forming flocs and aggregates (Cheng 1980).
It is noted in Fig. 9 that for a given solids concentration, in the first zone, the viscosity decreases rapidly at low shear rates (\(\dot{\gamma }\, < \,1.2 \,{\text{s}}^{  1}\)), and in the second zone, the viscosity reaches a stable phase at high shear rates. The first zone dominated by the yield shear stress is a phase in which the material flowed before reaching the second zone and dominated by plastic viscosity (Slatter 2006). The viscosity becomes lower at the high shear rates which corresponds to the infinite viscosity of Sisko (\(\eta_{\infty }\)). It is 1 Pa s at 5% and 20 Pa s at 32.5%. Furthermore, it was observed that the samples have been a shear thinning behavior in the region of low shear rate. This is similar to results obtained by Olhero and Ferreira from the experiments carried out on fine silica powder of average size 19 μm (Olhero and Ferreira 2004).
Modeling and correlation of parameters
Parameters of different rheological models with different solids concentrations and coefficient of determination
Model  Parameters  

C_{s} (%)  5  10.5  15.6  22.7  26.8  32.5  
Power law  k  0.0144  0.0849  0.1273  0.8199  0.7994  1.4715 
n  0.9737  0.2695  0.1354  0.1914  0.2262  0.2358  
R ^{2}  0.9628  0.8664  0.8665  0.8879  0.8855  0.8703  
Herschel–Bulkley  τ _{0}  0.0194  0.0406  0.0442  0.1218  − 0.7642  0.1656 
k  0.0032  0.0167  0.031  0.7578  0.8722  16,741  
n  0.9281  0.6586  0.4278  0.188  0.1743  0.17  
R ^{2}  0.9639  0.8664  0.8709  0.8898  0.913  0.9014  
Bingham  τ _{0}  0.0196  0.082  0.151  14,224  16,171  29,388 
η _{B}  0.0008  0.0012  0.001  0.0042  0.0164  0.0079  
R ^{2}  0.9736  0.8664  0.6739  0.4737  0.4988  0.4708  
Casson  τ _{0}  0.0111  0.0717  0.1217  11,686  10,141  23,195 
\(\eta_{\infty }\)  0.00042  0.00021  0.00022  0.00082  0.00452  0.00182  
R ^{2}  0.9782  0.847  0.8411  0.8316  0.7518  0.6788 
Thus, the Herschel–Bulkley model present a good fitting with experimental data and in this model, the value of (R^{2}) was greater. But on the other hand, the value of \(\tau_{0}\) using Herschel–Bulkley model for C_{s} = 26.8% was negative (τ_{0} = − 0.7642 Pa for C_{s} = 26.8%), which is physically impossible. As a result, the Herschel–Bulkley model is not suitable for all solids concentrations. Therefore, the power law model was the best fitting for all range of solids concentration of mud, followed by the Herschel–Bulkley model. The Bingham and Casson models were also suitable but with less precision.
Using power law model, the fitting results revealed that Chorfa dam mud showed shear thinning behavior because the flow behavior index values (n) were less than 1 (Table 3) for all range of solids concentrations (using power law model, n = 0.97 for C_{s} = 5% and n = 0.23 for C_{s} = 32.5%), and the consistency index (k) increased with the increasing solids concentration. This suggested that, with the decrease in solids concentration, mud samples performed more like a Newtonian fluid and the coefficient of determination coefficients (R^{2}) reduced with decline in solids concentration.
Conclusion

The geotechnical study showed that the samples studied composed a large proportion of clay and silt and were classified as a clay loam soil.

Both chemical and mineralogical analyses indicated that mud samples are composed of a clay phase, mostly silica, calcite and other minerals.

The rheological characteristics were investigated for mud samples from Chorfa dam with solids concentration of 5%, 10.5%, 15.6%, 22.7%, 26.8% and 32.5% at an ambient temperature of 20 °C.
First, it is found that for a solids concentrations (C_{s}) less than the critical solids concentrations (C _{s} ^{*} = 8.46%), the mud samples showed the Newtonian behavior and the variation of the shear stress with the shear rate are linear. On the other hand, the mud samples showed the shear thinning behavior for solids concentrations (C_{s}) greater than the critical solids concentrations (C _{s} ^{*} ) and the shear stress–shear rate relationship is nonlinear. In addition to this, the apparent viscosity increases with the increase in the solids concentration, but for a given solids concentration, the apparent viscosity decreases with increasing shear rate, which explains the shear thinning behavior of the Chorfa dam mud.
Finally, fitting results of four rheological models (Bingham Plastic Model, Ostwald–de Waele (power law), Herschel–Bulkley and Casson) to the experimental rheological data of mud samples revealed that the Ostwald–de Waele (power law) model was the best fitting for all range of solids concentration.
Notes
Acknowledgements
The authors gratefully thank the Vice Chancellor and Research Coordinator of University of Science and Technology of Oran, “Algeria,” for their unfailing support of research and their encouragement of collaboration between laboratories of the university to develop the scientific research.
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