Issue34

Q. Like et alii, Frattura ed Integrità Strutturale, 34 (2015) 543-553; DOI: 10.3221/IGF-ESIS.34.60 544 difference may form between the gangue and mineral, and a temperature stress may form, producing micro cracks on the mineral boundary and contributing to mineral liberation [9, 10]. Testing and numerical methods nowadays are chiefly adopted in microwave-assisted grinding and crushing studies. The test method is primarily used for determining the mineral temperature rising curve and the effect of auxiliary grinding. Some scholars have adopted the test method to examine the temperature rising characteristics of titanium concentrate and ilmenite in a microwave field using thermocouple [11, 12]. Xiaojuan Pan [13] investigated the temperature rising characteristics of manganese ore powder in a microwave field. Mamdouh Omranet et al. [14] placed the iron ore under microwave irradiation and scanned it via electron microscope (see Fig. 1). Their test results confirm that micro cracking occurs more easily between mineral and gangue through microwave heating than traditional heating. Shenghui Guo et al. [15] placed ilmenite under microwave irradiation and revealed that micro cracking occurs between useful mineral and gangue through microwave irradiation, which can effectively promote liberation between mineral and gangue. Figure 1 : BSE image of micro crack distribution after microwave irradiation [14]. At present, measuring via tests the internal temperature and the stress and strain distribution of rocks under microwave irradiation is difficult. Qualitative analysis can be performed through scanning electron microscope for the generation and development of micro cracks in minerals under microwave irradiation. However, conducting quantitative research in this manner is difficult. Therefore, numerical methods have been primarily used for research in this field. Huijun Cui et al. [16] simulated the characteristic curve of the increasing temperature of carbon chrome ore powder in a microwave field using the finite element method. Some scholars have studied the internal temperature and the stress and strain distribution characteristics of a single crystal mineral through the finite difference method and finite element method, respectively [17- 19]. A.Y. Ali et al. [20] confirmed the existence of micro cracks between mineral and gangue via the numerical method. Whittles et al. [21] analyzed the change of rock strength under microwave irradiation using the finite difference method. Although studies on microwave-assisted mineral liberation have achieved certain results, research on the characteristics and influencing factors of mineral liberation cracks remains scarce. Thus, this study takes rock grains with galena and calcite as the research object to investigate the distribution and evolution characteristics of mineral boundary failure under microwave irradiation using the finite difference method. It seeks to ascertain the mineral liberation mechanism under microwave irradiation, and to provide a theoretical basis for the selection of microwave source and optimized design of microwave equipment. C ALCULATION M ODEL Calculation Principal he heat energy produced by microwave irradiation primarily depends on the microwave frequency and the electric field intensity. The quantity of heat produced by a material of unit volume can be calculated by the following formula: " 2 2 d o r o P f E     (1) where P d denotes the power density of microwave (W/m 3 ), that is, the power of microwave transforming heat energy; f is the microwave divergence frequency (Hz); " r  is the dielectric coefficient in a vacuum (8.854×10 -12 F/m); o  is the medium dielectric loss factor; and E o is the effective value of the electric field (V/m). Given that the dielectric loss factor of calcite is 4×10 -4 and that of galena is 13, under the irradiation by microwave, calcite absorbs little energy from the microwaves, and the non-production of heat by calcite in the calculation may be assumed [22]. T