In a microfluidic system, the flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in the microchannel. The flow-electricity interaction in a complex microfluidic system subjec...In a microfluidic system, the flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in the microchannel. The flow-electricity interaction in a complex microfluidic system subjected to a joint action of wall slip and electro-viscosity is an important topic. An analytical solution for the periodical pressure-driven flow in a two-dimensional uniform microchannel, with consideration of wall slip and electro-viscous effect is obtained based on the Poisson-Boltzmann equation for the Electric Double Layer （EDL） and the Navier-Stokes equations for the liquid flow. The analytic solutions agree well with the numerical solutions. The analytical results indicate that the periodical flow velocity and the Flow-Induced Electric Field （FIEF） strongly depend on the frequency Reynolds number （Re = （wh2/v ）, that is a function of the frequency, the channel size and the kinetic viscosity of fluids. For Re 〈 1, the flow velocity and the FIEF behave similarly to those in a steady flow, whereas they decrease rapidly with Re as Re 〉 1. In addition, the electro-viscous effect greatly influences the periodical flow velocity and the FIEF, particularly, when the electrokinetic radius kH is small. Furthermore, the wall slip velocity amplifies the FIEF and enhances the electro-viscous effect on the flow.展开更多
In the early Middle Ages the Europe was a chaotic social environment.The empire was so vast that no king could build a centralized government,so the king depended on counts to administrate the regions.There were confl...In the early Middle Ages the Europe was a chaotic social environment.The empire was so vast that no king could build a centralized government,so the king depended on counts to administrate the regions.There were conflicts,wars,invasion and famine at that time.The decentralized government could not protect people from these sufferings,so the people just could search for the strong to secure them.The lord could provide protection to his vassals and grant fiefs to his vassals,and in turn vassals needed to perform their obligation to the lord.These obligation included loyalty,military service,assistance,offering material and counsel which stabilized the area that the lord ruled.The feudalism in the administration of Merovingian and Carolingian even after the breakup of Carolingian could illustrate the stable units of the empire.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 50805059)
文摘In a microfluidic system, the flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in the microchannel. The flow-electricity interaction in a complex microfluidic system subjected to a joint action of wall slip and electro-viscosity is an important topic. An analytical solution for the periodical pressure-driven flow in a two-dimensional uniform microchannel, with consideration of wall slip and electro-viscous effect is obtained based on the Poisson-Boltzmann equation for the Electric Double Layer （EDL） and the Navier-Stokes equations for the liquid flow. The analytic solutions agree well with the numerical solutions. The analytical results indicate that the periodical flow velocity and the Flow-Induced Electric Field （FIEF） strongly depend on the frequency Reynolds number （Re = （wh2/v ）, that is a function of the frequency, the channel size and the kinetic viscosity of fluids. For Re 〈 1, the flow velocity and the FIEF behave similarly to those in a steady flow, whereas they decrease rapidly with Re as Re 〉 1. In addition, the electro-viscous effect greatly influences the periodical flow velocity and the FIEF, particularly, when the electrokinetic radius kH is small. Furthermore, the wall slip velocity amplifies the FIEF and enhances the electro-viscous effect on the flow.
文摘In the early Middle Ages the Europe was a chaotic social environment.The empire was so vast that no king could build a centralized government,so the king depended on counts to administrate the regions.There were conflicts,wars,invasion and famine at that time.The decentralized government could not protect people from these sufferings,so the people just could search for the strong to secure them.The lord could provide protection to his vassals and grant fiefs to his vassals,and in turn vassals needed to perform their obligation to the lord.These obligation included loyalty,military service,assistance,offering material and counsel which stabilized the area that the lord ruled.The feudalism in the administration of Merovingian and Carolingian even after the breakup of Carolingian could illustrate the stable units of the empire.
