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... samples were collected from various stratigraphic levels of the bentonite deposits between the Mihalgazi and Sarıcakaya districts in Eski s° ehir (Western Turkey) ( Figure 2). Bentonite deposits in this region were formed by alteration of andesitic and dacitic volcanic rocks. The bentonites are classified in three groups based on their geologic features; bentonite deposits in andesitic and dacitic lavas, bentonite deposits in andesitic agglomerate, and bentonite deposits in tuff (Yıldız et al. , 2008). Characterization test results of the three samples are given in Table 1. Here, the CEC values of each bentonite group were determined by the methylene blue (MB) standard method (Rytwo et al ., 1991; O ̈ nal, 2007) and viscosity values were measured with 5, 7.5, or 10% solids at 600 rpm using a Fann viscosimeter at Turkish General Directorate of Mineral Research & Exploration. The swelling of each sample was measured as the total volume of a gel formed from a 2 g sample in 100 mL of water (ASTM D 5890-95). The CEC, viscosity, and swelling volume of the raw bentonites were relatively small (Table 1). The second group of bentonites had the best physical properties. Chemical analyses of major oxides were obtained by inductively coupled plasma- mass spectrometry (ICP-MS) at the ACME analytical laboratory, Canada (Table 2), and chemical analyses revealed that the CaO+Na 2 O totals of all three bentonites were in the range 4.28 À 7.00%. Mineralogical investigations were carried out on processed and random powder samples by means of X-ray diffraction (XRD) analysis, using a Rigaku Geiger Flex Diffractometer with Ni-filtered CuK a radiation. The scanning speed for all samples was 2 o 2 y /min. Smectite and the other mineral contents of the samples were determined by semi- quantitative interpretation of the XRD data (without standards). The reflections, peak intensity, and Reference Intensity Ratio (RIR) of minerals were analyzed by the formulae of Chung (1974), which enabled calculation of mineral abundances as weight percentages. This method was chosen because it yields reproducible results and has been used by other researchers (Biscaye, 1965; Johns et al. , 1954; G ̈ ndo ̆ du, 1982), thus giving the mineral contents of the present samples. Morphological and mineralogical studies were carried out using a LEO VP-1431 (Korea) scanning electron microscope (SEM) with EDS equip- ment. The XRD patterns indicated that smectite was the major mineral phase in the bulk samples (Table 3; Figure 3) (Grim, 1962; Brown and Brindley, 1980; Brown, 1972). Illite and chlorite were minor constitu- ents. Non-clay minerals in the samples included cristobalite/opal-CT, quartz, feldspar, calcite, and dolomite. The smectite content, which affects the performance of the bentonites in various industrial applications, was 54%, 55%, and 40% in Groups 1, 2, and 3, respectively. Feldspar was a major impurity in all groups and the amount of feldspar was 40%, 32%, and 30% in Groups 1, 2, and 3, respectively. The cristobalite/ opal-CT contents of the bentonites in Groups 1, 2, and 3 were 0 wt.%, 5 wt.%, and 7 wt.%, respectively (Table 3). Cristobalite/opal-CT minerals are somewhat similar to smectites with respect to their physical properties such as density, crystal size, etc. The XRD investigations revealed that the bentonites in Groups 1 and 2 consisted of mixed (Na-Ca) smectites; Group 3 included Na- smectites. The Na 2 O contents of bentonites were determined as 1.52 wt.% (Group 1), 3.24 wt.% (Group 2), and 2.52 wt.% (Group 3) in EDS studies (Figure 4). The XRD and EDS studies show that the Na + is the primary exchangeable cation in smectites of Groups 2 and 3. The swelling properties of the Na- smectite are commonly more developed than those of Ca-smectite (Luckham and Rossi, 1999). The Box–Behnken design (Box et al. , 1978; Box and Wilson, 1951; Box and Behnken, 1960; Montgomery, 2001; Ferreira et al. , 2004; Souza Anderson et al. , 2005; Aslan and Cebeci, 2007) is a rotatable second-order design based on three-level incomplete factorial designs. The special arrangement of the Box–Behnken design levels allows the number of design points to increase at the same rate as the number of polynomial coefficients. For three factors, for example, the design can be constructed as three blocks of four experiments consisting of a full two-factor factorial design with the level of the third factor set at zero (Souza Anderson et al. , 2005; Aslan and Cebeci, 2007). In the present study, the Box–Behnken factorial design was chosen to discover the relationship between the response functions (smectite concentration and swelling of the bentonite concentrate) and four variables of the hydrocyclone (feed solid, inlet pressure, vortex diameter, and apex diameter), while holding other operational parameters of the hydrocyclone constant (cyclone diameter of 44 mm, feed suspension of 30 L, pre-feed mixture in mixer for 5 min). Batch hydrocyclone tests were conducted at the mineral processing laboratory of Afyon Kocatepe University, Turkey. Samples were dried at 60 o C and then added to water (10% solids); the suspension was settled for 24 h and stirred for 2 À 3 h by a propeller agitator. The suspension was passed through a 500 m m sieve and then fed into the hydrocyclone. The solid:liquid ratio was regulated by addition of water. The suspension was stirred using a centrifugal pump (with by-pass valve) for 5 min to achieve homogeneity (in the system). Later, material was fed into the hydrocyclone by closing the by-pass valve, and two discrete overflow and underflow products were obtained. The samples were filtered, dried, and analyzed for smectite content and swelling (Figure 5). Response surface methodology is a collection of statistical and mathematical methods that are useful for modeling and analyzing engineering problems. The main objective is to optimize the response surface that is influenced by various process parameters. Response surface methodology also quantifies the relationship between the controllable input parameters and the response surfaces obtained (Kwak, 2005; Aslan and Cebeci, 2007; Aslan, 2007a, 2007b). The design of the response surface methodology consisted of the following (Gunaraj and Murugan, 1999; Kwak, 2005; Aslan and Cebeci, 2007; Aslan, 2007a, 2007b): (1) designing a series of experiments for adequate and reliable measurement of the response of interest; (2) developing a mathematical model of the second-order response surface with the best fittings; (3) finding the optimal set of experimental parameters to produce a maximum or minimum value of response; and (4) representing the direct and interactive effects of process parameters through two-dimensional (3D) and three-dimensional (3D) plots. If all variables are assumed to be measurable, the response surface can be expressed as follows (equation 1): where y is the response variable, and x i = x 1 , x 2 , x 3 , or x k are the controlling variables referred to as factors. The goal of this aspect of the study was to optimize the response variable y . The independent variables are assumed to be continuous and controllable by the experiments with negligible errors. A reasonable approx- imation for the true functional relationship between independent variables and the response surface is desired. A second-order model is usually used in response surface methodology (Gunaraj and Murugan, 1999; Kwak, 2005; Aslan and Cebeci, 2007; Aslan, 2007a, 2007b): where x 1 , x 2 ,..., x k are the input factors which influence the response y ; b 0 , b ii ( i = 1, 2,..., k ), b ij ( i = 1,2,..., k ; j = 1,2,. . . ,k ) are unknown parameters, and e is a random error term. The b coefficients, which should be determined in the second-order model, are obtained by the least-squares method. In general equation 2 can be written in matrix form (Kincl et al. , 2005; Kwak, 2005; Aslan and Cebeci, 2007; Aslan, 2007a, 2007b): where Y is a matrix of measured values and X is a matrix of independent variables. The matrices b and e consist of coefficients and errors, respectively. The solution of equation 3 can be obtained by the matrix approach (Gunaraj and Murugan, 1999; Kwak, 2005; Aslan and Cebeci, 2007; Aslan, 2007a, 2007b). where X is the transpose of the matrix X and ( X X ) is the inverse of the matrix X T X (Kwak, 2005; Aslan and Cebeci, 2007; Aslan, 2007a, 2007b). The coefficients, i.e. the main effect ( b i ) and the two- factor interactions ( b ij ), can be estimated from the experimental results by computer-simulation programming applying the least-squares method using Minitab 15 (Minitab Inc., 2007). Box À Behnken design requires an experiment number according to N = k 2 + k + c p , where k is the factor number and c p is the replicate number of the mid-point (Massart et al. , 1997; Neto et al. , 2001; Ferreira et al. , 2004; Souza Anderson et al. , 2005; Aslan, 2007b;). Box À Behnken is a spherical, revolving design. Viewed as a cube (Figure 6a) (Souza Anderson et al. , 2005; Massart et al. , 1997; Aslan and Cebeci, 2007), the Box– Behnken design consists of a central point and the middle points of the edges. However, it can also be viewed as consisting of three interlocking 2 2 factorial designs and a central point (Figure 6b) (Souza Anderson et al. , 2005; Massart et al. , 1997; Aslan and Cebeci, 2007). For the three-level, four-factorial Box À Behnken experimental 8 9 design, 27 experimental runs in total ( : 4 2 ; 4 þ 3 centerpoints), were needed (Table 4). Considering the effects of the main factors and also the interactions between two-factor sets, equation 2 takes the ...