Figure 1 shows the complete experimental apparatus. A stainless steel vibration plate with an attached PZT transducer (Honda Electronics Co., Ltd.) was installed in the center of a bath at its bottom. The diameter of the vibration plate was 100 mm; the diameters of 22.8 and 127 kHz transducers were 45 mm each, whereas those of 490, 940, and 1640 kHz transducers were 50 mm each. The transducers were driven by a power amplifier (1040L, E&I), which in turn was driven by a continuous sinusoidal wave produced using a signal generator (WF1974, NF Corp.). The effective electric power input to the transducer was calculated from the voltage at both ends of the transducer, and the current was

measured using both an oscilloscope (TDS3012C, Tektronix Inc.) and a current probe (TCP202, Tektronix Inc.). A glass reactor with variable vertical position was located in the center of the vibration plate. The diameter and approximate volume of the reactor were 85 mm and 10⁻³ m³, respectively. The temperature of the ultrasonic bath was maintained constant by circulating thermostat water.

Table 1 shows the experimental conditions for methylene blue degradation. Process variables were defined as follows: the ultrasonic frequency (f), ultrasound output power (P), initial methylene blue concentration (C_{0, MB}), distance between the ultrasonic transducer and bottom of the reactor (L₁), distance between the ultrasonic transducer and level of the water bath (L₂), and irradiation time (t). The volume of the sample solution (V) and temperature of the water bath (T) were maintained constant. Before ultrasonic irradiation, the sample solution and remaining space in the reactor were deoxygenated with a nitrogen gas flow for 20 min at 298 K. After de-oxygenation, the sample was irradiated with ultrasound under a continuous nitrogen gas flow (0.1 L/min).The wavelength of ultrasound depended on ultrasonic frequency, and reaction field is influenced by irradiation distance. Therefore, the reaction was carried out at the optimum condition for various frequencies. Moreover, the temperature of water bath increased by ultrasonic irradiation. Thus, the temperature of the water bath was maintained by circulation of thermostatic water.

The experiment was carried out using the same apparatus as methylene blue degradation reaction. Table 2 shows experimental conditions for KI oxidation. The initial KI concentration was defined as C_0,KI, and other process variables were the same as the above mentioned methylene blue degradation reaction.

After ultrasonic irradiation, the methylene blue concentration (C_MB) was determined by measuring absorbance of the sample at a wavelength of 665 nm using a UV-Vis spectrometer (Agilent 8453, Agilent Technologies). The measured

absorbance was converted to a concentration value using a standard curve for methylene blue.

The concentration of I 3 − ion, which was generated by oxidation reaction of I⁻ ion, was also analyzed by measuring absorbance of the sample at a wavelength of 355 nm using a UV-V is spectrometer (ε = 26303 L/mol cm).

The ultrasonic power level in the reactor was measured by a calorimeter [21] . Equation (1) gives the calculated ultra-sonic output power (P).

P = ( d T / d t ) × c p × M (1)

Here, c_p was the heat capacity of water, M was the mass of water, T was the temperature of the sample solution, and t was the ultrasonic irradiation time. Ion exchanged water was used as the sample solution (volume, 0.1 L).

From the results of our previous study, the apparent rate constant of ultrasonic degradation of methylene blue was evaluated using a pseudo-first-order reaction model [14] [15] [16] . Figure 2 shows the effect of ultrasonic power on the apparent degradation rate constant in the range of frequency of 22.8 kHz and 1640

kHz [15] . The effects of frequency on degradation rate constant have been discussed in our previous studies [14] [15] [16] . It is also observed that the degradation rate constant increases with ultrasonic power, and there is a linear relationship between degradation rate constant and power at every frequency (22.8 kHz, 127 kHz, 490 kHz, 940 kHz, and 1640 kHz). Henglein and Gutierrez have investigated the sonication of aqueous KI, and reported that the initial response of iodine yield appears to proportional to power, but this effect is reduced beyond 40 W and drops dramatically above 100 W [22] . The degradation rate constant appears to proportional to power, because the ultrasonic power in this study is less than 20 W. In addition, a threshold power is existed for degradation reaction to progress, and it is found that the threshold power is not affected by ultrasonic frequency.

When ultrasound was irradiated into an aqueous KI solution, I⁻ ions were oxidized to give I₂. When excess I⁻ ions were present in solutions, I₂ reacts with the excess I⁻ ion to form I 3 − ion. Figure 3 shows the effect of ultra-sonic power on the generation rate of I 3 − ion at the frequencies of 127, 490, and 1640 kHz. The generation rate of I 3 − ion was influenced by ultrasonic frequency, and the generation rate at 127 and 490 kHz was higher than that at 1640 kHz. These phenomena also agree with previous reported results [18] . It is also observed that the generation rate increases with ultrasonic power, and there is a linear relationship between generation rate and power at every frequency. Moreover, a threshold power is also existed for oxidation reaction to progress, and it is found that the threshold power is affected by ultrasonic frequency.

Figure 4 shows the effect of ultrasonic frequency on the threshold power of methylene blue degradation and KI oxidation reaction. In the KI oxidation reaction

process, the ultrasonic frequency affects the threshold power, and the threshold power increases with increasing frequency. This phenomenon well agrees with previous study [1] . Thus, it is clarified that the generation of I 3 − ion was caused by oxidation reaction of I⁻ ions with hydroxyl radicals.

On the other hand, in the methylene blue degradation reaction process, it is observed that the threshold power is not affected by frequency, and the threshold power is almost same value in every frequency, and it is about 2 W. When the frequency is lower than 130 kHz, the values of threshold power of KI oxidation reaction and methylene blue degradation reaction are almost same. However, when the frequency is higher than 500 kHz, the value of threshold power of KI oxidation is higher than that of methylene blue degradation, and the difference becomes large with increasing frequency. In our previous study, there is a relationship between SE_KI value and degradation rate constant of methylene blue [14] [15] [16] . In addition, it has been reported that the ultrasonic degradation of methylene blue is enhanced by TiO₂ particle addition under dark condition [23] [24] [25] , and the presence of TiO₂ particle accelerates the generation of hydroxyl radicals during ultrasonic irradiation even in the absence of UV irradiation [26] . Moreover, it has been also reported that the ultrasound and TiO₂ particle exhibit synergistic effects in the degradation of azo dye of acid orange 8, and the origin of the synergistic effect is considered to be the formation of additional hydroxyl radicals by TiO₂ particle from the extra hydrogen peroxide produced by ultrasound [27] . From the results of these studies, it is suggested that the degradation of methylene blue by ultrasound is caused by hydroxyl radicals, and the threshold power in the ultrasonic degradation of methylene blue increases with increasing frequency. However, the threshold power did not increase with increasing frequency. Therefore, it is guessed that the mechanism of degradation of methylene blue changes with frequency. When the frequency is lower than 130 kHz, the degradation of methylene blue is mainly occurred around cavitation bubbles by hydroxyl radicals. On the other hand, when the frequency is higher than 500 kHz, it is guessed that the degradation of methylene blue is occurred inside cavitation bubble by pyrolysis. However, this hypothesis has not been clarified yet. It is necessary to divide the degradation mechanism into hydroxyl radical decomposition and pyrolysis. Therefore, the effect of radical scavenger addition on the ultrasonic degradation of methylene blue will be investigated for various frequencies in the future.