Schematic diagram of a hydrocyclone. 

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... Sarıkaya et al ., 2000; O ̈ nal et al ., 2002; Varma, 2002; Komadel, 2003; Tan et al ., 2004; Kahraman et al ., 2005; O ̈ nal, 2007). The physical state of a bentonite can be changed from a dry solid to a hydrated solid, a semi-rigid plastic, a gel, and a suspension, respectively, with increasing water content (Low, 1979; Sharmm and Kwak, 1982; G ̈ ven and Pollastro, 1992; Malfoy et al ., 2003; O ̈ nal, 2007). Bentonite-water systems are of vital importance for agricultural, industrial, environmental, and civil engineering applications such as preparation of desiccants, sealants, ceramics, cat litter, iron ore pellets, molding sand for foundry use, drilling mud for oil recovery, and subsurface barriers for water and nuclear waste (Grim and G ̈ ven, 1978; Kahr et al ., 1990; Push, 1992; Komine and Ogata, 1999; Yong, 1999; Neaman et al ., 2003; Wersin et al ., 2004; O ̈ nal, 2007). Bentonite contains not only swelling clay minerals such as montmorillonite but also non-swelling minerals such as quartz, calcite, etc. The swelling clay minerals expand by adsorbing water and filling the voids in the compacted bentonite (Komine and Ogata, 1994, 1996). The non-clay minerals in bentonite have a negative effect on the swelling properties (Christidis and Scott, 1993; Allo and Murray, 2004; Yıldız and Kuscu, 2007). Most studies on the swelling of bentonites have focused on the increase in basal spacing which depends on the bentonite mineralogy, the degree to which water is taken up, and also size, valence, electronegativity, and hydration energy of the exchangeable cations. As higher-quality bentonite reserves have diminished the use of lower-grade materials has become necessary. Enrichment of bentonites is very important in the production of bentonite-based products such as bleaching earth, material for cosmetics, and for use in medicine (Boylu et al ., 2007). When clay systems with impurities are resettled or dispersed in water, they reveal two different size groups. Impurities and clays form clusters of different sizes when submerged and kept in water for a certain amount of time. Different clay minerals have similar particle densities but can be separated according to their particle size (Boylu et al ., 2007). Non-clay mineral impurities in bentonite, such as quartz, calcite, etc., can also be removed through beneficiation processes to separate the smectite (Hassan and Abdel-Khalek 1998). Although enrichment of bentonites is relatively easy, costs are a consideration. Small solid:liquid ratios are adopted in some wet-processing methods, such as the hydrocyclone. Because viscosity is a function of the solids rate, the increase in viscosity that results from mixing bentonite with water limits the ability of the hydrocyclone to remove non-clay particles by increasing the centrifugal force required to achieve separation. The hydrocyclone does, however, still have advantages over beneficiation by decantation in the enhancement of bentonites. Mineral processes use hydrocyclone separators to perform separations on the basis of size and/or density differences between the dispersed particulate phases (Williams et al ., 1994; Rickwood et al. , 1992). A hydrocyclone consists of two main parts (Figure 1). The first is a cylindrical part, with an inlet through which the feed enters tangentially. This part also includes an outlet, located at the top of the cylinder, extends into the cylinder and is known as the vortex finder. The second main part is conical and is connected to the cylindrical section at the top and to the underflow at the bottom end. The latter part is known as the spigot. The centrifugation forces exerted by the vortex cause larger particles to migrate to the cyclone wall where they are discharged through the underflow orifice. Small particles move to the central axis of the cyclone and are carried out by the overflow stream (Habibian et al. , 2008). The parameters that affect the performance of the hydrocyclone are the feed solid ratio (%), inlet pressure (bar), vortex diameter (mm), apex diameter (mm), viscosity of the feed stock (cP), and cyclone diameter (mm). The success of the hydrocyclone depends on the selection of suitable parameter levels and minerals. Optimization of the parameters requires many tests. The total number of experiments required can be reduced by careful choice of the experimental design technique (O ̈ zbayo ̆ lu and Atalay, 2000; Aslan, 2007a). Experimental design is a systematic, rigorous approach to engineering problem solving that applies principles and techniques at the data-collection stage so as to ensure the generation of valid, precise, and accurate engineering conclusions (Xiao and Vien, 2004; Aslan, 2007b; O ̈ zgen et al. , 2009). Experimental design is a very economical means of extracting the maximum amount of complex information, while saving significant experimental time and material (Kincl et al. , 2005; Aslan, 2007b; O ̈ zgen et al. , 2009). Furthermore, analysis of the results is easy and experimental errors are minimized. A statistical method measures the effects of change in the operating variables and their combined interactions on the processes (Box et al. , 1978). The design of experiments leads to unique response surface methodologies using mathematical and statistical techniques, with important applications not only for new products but also in the improvement of the design of existing products. With this aim in mind, one must first select the appropriate mixtures from which the response surface might be calculated; then the property value can be predicted for any design, depending on changes in the proportions of its components (Box and Behnken, 1960; Ragonese et al. , 2002, Correia et al. , 2004; Aslan, 2007b; O ̈ zgen et al. , 2009). Experimental design methods and response surface methodologies are used widely for modeling process parameters, especially in chemical processes and phar- maceutical systems. To date, experimental design has not, however, been applied widely to mineral-processing systems. The central composite design here has been used successfully to design an experimental program to provide data to model the effects of inlet pressure, feed density, and length and diameter of the inner vortex finder on the operational performance of a 150 mm three-product cyclone (Obeng et al. , 2005). The Box– Wilson statistical experimental design method was employed to evaluate the effects of important variables such as bridging liquid (oil) concentration, salt (CaCl 2 .2H 2 O) concentration, and stirring speed on the agglomeration of bituminous coal (Cebeci and So ̈ nmez, 2006). The response surface methodology and Box À Behnken design have been discussed for possible modeling of bond-work indexes for some Turkish coals by Aslan and Cebeci (2007). A study of flotation tests of synthetic mixtures of celestite (SrSO 4 ) and calcite (CaCO 3 ) minerals using a factorial experimental design was carried out by Martinez et al. (2003). Aslan (2007a) discussed the application of response surface methodology and central composite rotatable design for modeling the influence of some operating variables on the performance of a Multi-Gravity Separator (Mozley, Gloucester, UK) for coal cleaning. Finally, ...