In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order a...In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments.展开更多
Ultrasound (US)-induced cavitation is an effective way in oxidizing organic contaminants in wastewater either as the independent operation unit or in combination with other oxidation methods. In this paper, black liqu...Ultrasound (US)-induced cavitation is an effective way in oxidizing organic contaminants in wastewater either as the independent operation unit or in combination with other oxidation methods. In this paper, black liquor and filtrate after acidifying and settling were sonicated. The effect of working parameters on ultrasonic degradation of black liquor, such as different combination methods, frequency, power supply, initial concentration, pH, duration time, ionic strength and catalyst were studied. The results were as follows: (1) At the conditions of 40kHz, 100W, 4h, pH at 6 and temperature 30?℃, utilizing US/US-H2O2/US-Fenton, weak-orange filtrate turned to colloid with the increase of time and little sediment produced after settling. Especially filtrate came to be milk white collides and upper water approached to nearly achromatic by US-Fenton. Compared with the US, US-H2O2/US-Fenton COD (Chemical oxidation demand) removal ratio can increase 15%, 30% respectively. Because of more hydroxyl radicals produced in the reaction process; (2) At the condition of 100W and 4h, the degradation efficiency of black liquor was better at 40kHz over at 20kHz. Moreover black liquor can be biodegraded easily. Those based on that the big molecule of contaminants in aqueous solution can be changed into the little molecule with ultrasound (3) At the condition of 40kHz and 4h, the COD removal ratio of black liquor was more higher at 60W than at 80W, while the removal ratio of COD at 60W was nearly close to the ratio at 100W; (4) The initial concentration of black liquor influenced the effect of sonochemical degradation; (5) The variation of pH had no effect on degradation; (6) The longer the duration time, the greater the removal ratio of COD. But this ratio increased slowly after 4h; (7) Adding 0.2g/L NaCl to change the ionic strength of the black liquor, the COD removal ratio can increase 10%; (8) The degradation rates increased by the coexistent catalysts of TiO2, Co2+ and Ag+.展开更多
文摘In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments.
文摘Ultrasound (US)-induced cavitation is an effective way in oxidizing organic contaminants in wastewater either as the independent operation unit or in combination with other oxidation methods. In this paper, black liquor and filtrate after acidifying and settling were sonicated. The effect of working parameters on ultrasonic degradation of black liquor, such as different combination methods, frequency, power supply, initial concentration, pH, duration time, ionic strength and catalyst were studied. The results were as follows: (1) At the conditions of 40kHz, 100W, 4h, pH at 6 and temperature 30?℃, utilizing US/US-H2O2/US-Fenton, weak-orange filtrate turned to colloid with the increase of time and little sediment produced after settling. Especially filtrate came to be milk white collides and upper water approached to nearly achromatic by US-Fenton. Compared with the US, US-H2O2/US-Fenton COD (Chemical oxidation demand) removal ratio can increase 15%, 30% respectively. Because of more hydroxyl radicals produced in the reaction process; (2) At the condition of 100W and 4h, the degradation efficiency of black liquor was better at 40kHz over at 20kHz. Moreover black liquor can be biodegraded easily. Those based on that the big molecule of contaminants in aqueous solution can be changed into the little molecule with ultrasound (3) At the condition of 40kHz and 4h, the COD removal ratio of black liquor was more higher at 60W than at 80W, while the removal ratio of COD at 60W was nearly close to the ratio at 100W; (4) The initial concentration of black liquor influenced the effect of sonochemical degradation; (5) The variation of pH had no effect on degradation; (6) The longer the duration time, the greater the removal ratio of COD. But this ratio increased slowly after 4h; (7) Adding 0.2g/L NaCl to change the ionic strength of the black liquor, the COD removal ratio can increase 10%; (8) The degradation rates increased by the coexistent catalysts of TiO2, Co2+ and Ag+.
