To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
The wall wettability of microchannels plays an important role in the gas-liquid mass transfer dynamics under Taylor flow.In this study,we regulated the contact angle of the wall surface through surface chemical grafti...The wall wettability of microchannels plays an important role in the gas-liquid mass transfer dynamics under Taylor flow.In this study,we regulated the contact angle of the wall surface through surface chemical grafting polymerization under controlled experimental conditions.The dynamic changes of CO_(2)bubbles flowing along the microchannel were captured by a high-speed video camera mounted on a stereo microscope,whilst a unit cell model was employed to theoretically investigate the gas-liquid mass transfer dynamics.We quantitatively characterized the effects of wall wettability,specifically the contact angle,on the formation mechanism of gas bubbles and mass transfer process experimentally.The results revealed that the gas bubble velocity,the overall volumetric liquid phase mass transfer coefficients(kLa),and the specific interfacial area(a)all increased with the increase of the contact angle.Conversely,gas bubble length and leakage flow decreased.Furthermore,we proposed a new modified model to predict the gas-liquid two-phase mass transfer performance,based on van Baten’s and Yao’s models.Our proposed model was observed to agree reasonably well with experimental observations.展开更多
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
基金the financial supports from National Natural Science Foundation of China(21978250,22208278)Natural Science Foundation of Shandong Province(ZR2020KB013,ZR2020QE211,2019KJC012).
文摘The wall wettability of microchannels plays an important role in the gas-liquid mass transfer dynamics under Taylor flow.In this study,we regulated the contact angle of the wall surface through surface chemical grafting polymerization under controlled experimental conditions.The dynamic changes of CO_(2)bubbles flowing along the microchannel were captured by a high-speed video camera mounted on a stereo microscope,whilst a unit cell model was employed to theoretically investigate the gas-liquid mass transfer dynamics.We quantitatively characterized the effects of wall wettability,specifically the contact angle,on the formation mechanism of gas bubbles and mass transfer process experimentally.The results revealed that the gas bubble velocity,the overall volumetric liquid phase mass transfer coefficients(kLa),and the specific interfacial area(a)all increased with the increase of the contact angle.Conversely,gas bubble length and leakage flow decreased.Furthermore,we proposed a new modified model to predict the gas-liquid two-phase mass transfer performance,based on van Baten’s and Yao’s models.Our proposed model was observed to agree reasonably well with experimental observations.
