**3. Results and discussion**

The quartz sand in the three different mono-size intervals were grinding linearly with increasing grinding times. At the end of each milling period, the fractions of material remaining in the top particle size range were plotted against milling times. The graphs of the first-order breakage lines obtained for five different ball sizes are given in **Figures 2**–**4**. The region where the graph decreases linearly represents the first-order breakage region. The slope of the line in the first-order breakage region gives the specific rate of breakage based on the particle size range of the quartz sand. *The Effects of Mill Conditions on Breakage Parameters of Quartz Sand in the District… DOI: http://dx.doi.org/10.5772/intechopen.102554*

After determining the specific rate of breakage for the three mono-size intervals fractions exhibiting first-order breakage kinetics behavior, *Si* values were plotted against particle size fraction. The rate of breakage parameters of these lines was determined as *aT* and *α*. The results are given in **Figure 5**.

aT and α values, which are parameters of specific rates of breakage, were obtained by non-linear regression (from Eq. (1) and **Figure 5**), and are 0.15, 0.85 for 6.35 mm and 0.14, 0.78 for 7.94 mm and 0.14, 0.76 for 9.52 mm and 0.24, 0.95 for 12.70 mm and 0.26, 0.96 for 19.05 mm, respectively. In **Figure 5**, specific breakage rates also decreased based on the decrease in alloy steel ball size in general. Moreover, when the graphics in **Figure 5** are evaluated based on the particle size, the breakage rates

**Figure 2.** *First-order plots for alloy steel balls with different diameters of quartz sand as well as* �*0.063 + 0.053.*

**Figure 3.** *First-order plots for alloy steel balls with different diameters of quartz sand as well as* �*0.075 + 0.063.*

**Figure 4.** *First-order plots for alloy steel balls with different diameters of quartz sand as well as* �*0.090 + 0.075.*

**Figure 5.**

*Variation of the specific rate of breakage as a function of the maximum feed size for quartz sand ground with different alloy steel balls.*

decrease as the particle size intervals decrease. The presence of a maximum is quite logical because large lumps obviously will be too strong to be broken in the mill. Austin et al. (1984) explain that "[t]he theory of fracture implies that smaller particles are relatively stronger because larger Griffith flaws exist in larger particles and they are broken out as size is reduced. The fact that the specific rates of breakage are a simple power function of size has not been adequately explained on a theoretical basis, but it has been amply demonstrated by many experiments [21]."

In ball mills, large balls are known to be responsible for the breakage of coarse particles, and small balls are supposed to grind the fine ones. Austin et al. (1984)

*The Effects of Mill Conditions on Breakage Parameters of Quartz Sand in the District… DOI: http://dx.doi.org/10.5772/intechopen.102554*

#### **Figure 6.**

*Variation of ball diameter with first order breakage constant.*

stated the effect of ball diameter on breakage rate as "considering a representative unit volume of the mill, the rate of ball-on-ball contacts per unit time will increase as ball diameter decreases since the number of balls in the mill increases as 1/d<sup>3</sup> . Thus, the rates of breakage of smaller sizes are higher for smaller ball diameters [21]." However, balls in the range of 20 mm–50 mm were used for grinding the raw material with a particle size of 30x40 mesh here. The grinding conditions in this study are not the same. According to <sup>4</sup> √2 sieve series, 3 mono-sized fractions in the range of �0.090 + 0.053 were used. The grinding process was performed with alloy steel balls in the range of 6.35–19.05 mm. It is understood from the results that the grinding was difficult due to working in too small particle size ranges. In **Figure 6**, it can be said that the grinding energy that large-sized balls transferred on the quartz sand particles is high and therefore, high specific rates of breakage values were obtained in the grinding works carried out with large-sized balls. It can be seen that the grinding process is carried out faster by using large-sized balls compared to small-sized balls. This study was shown that d = 19.05 mm was the optimum balls size for the maximum breakage rates.

### **4. Conclusions**

Quartz and quartz sand consumption in the traditional ceramics industry in Turkey is approximately 600.000 tons per year. The quartz sand, which has the features that can meet the needs of Turkey's ceramics industry in terms of cost and chemical content, is produced in Şile, İstanbul. Glass quality quartz sand beds have decreased around İstanbul. The quartz sand beds in Turkey are suitable for casting and ceramics industries except for glass. Quartz sands separated by washing in some clay deposits are being evaluated. In addition, as a result of the evaluation of side products in the ore dressing facilities in some raw material quarries that are not economically operable, the operation of these quarries will be possible. It is essential to keep the energy consumed in downscaling processes at an optimum level in order to ensure the economy in raw material production. When the literature is examined, it is seen that many raw materials used for different purposes do not have breakage values under different milling conditions. Breakage values of raw materials belonging to any region differentiate according to their properties such as mineral rates in the raw material, its structural features, chemical impurities, and physical fractures. Therefore, in order for the ore dressing facilities to keep the energy consumed in grinding processes at an optimum level, the grinding kinetics of the raw material must be taken into account.

Accordingly, in this study, the impact of ball size on the grinding characteristic of quartz sand in the district of Şile on the Black Sea Coast of İstanbul in the laboratory ball mill was examined. These quartz sands are rather used in the production of traditional ceramics materials. However, if it is enriched by flotation, it can also be used in different industries. Grinding and classification processes must definitely be applied in order for the quartz sands to be used in any other area of the industry. That is, it is desired that the particle size is in a certain range. The grinding process in the traditional ceramic industry is carried out with ball mills and generally uses alumina balls. A large part of the energy consumed in grinding processes carried out in rod and ball mills turns into sound and heat energy. The grinding efficiency decreases due to this situation. It is very important to choose balls with the appropriate size to reduce the inefficiency of grinding.

In this study, it was found that very small ball sizes could not play an effective role in grinding quartz sand and that their impact and attrition effect on the particles was low. The energy transferred by the steel balls to the quartz sand particles during grinding increased with the increase in ball size. In this study carried out with different ball sizes, it was found that the most effective breakage was achieved with d = 19.05 mm alloy steel ball.
