Electroosmotic pumping of fluid through a nanopore that traverses an insulating membrane is considered. The density of surface charge on the membrane is assumed uniform, and sufficiently low for the Poisson-Boltzmann equation to be linearized. The reciprocal theorem gives the flow rate generated by an applied weak electric field, expressed as an integral over the fluid volume. For a circular hole in a membrane of zero thickness, an analytical result is possible up to quadrature. For a membrane of arbitrary thickness, the full Poisson-Nernst-Planck-Stokes system of equations is solved numerically using a finite volume method. The numerical solution agrees with the standard analytical result for electro-osmotic flux through a long cylindrical pore when the membrane thickness is large compared to the hole diameter. When the membrane thickness is small, the flow rate agrees with that calculated using the reciprocal theorem.

A theoretical model of electroosmosis through a circular pore of radius a that traverses a membrane of thickness h is investigated. Both the cylindrical surface of the pore and the outer surfaces of the membrane are charged. When h ≫ a, end effects are negligible, and the results of full numerical computations of electroosmosis in an infinite pore agree with theory. When h = 0, end effects dominate, and computations again agree with analysis. For intermediate values of h/a, an approximate analysis that combines these two limiting cases captures the main features of computational results when the Debye length κ–1 is small compared with the pore radius a. However, the approximate analysis fails when κ–1 ≫ a, when the charge cloud due to the charged cylindrical walls of the pore spills out of the ends of the pore, and the electroosmotic flow is reduced. When this spilling out is included in the analysis, agreement with computation is restored.

Electrically generated flows around a thin dielectric plate pierced by a cylindrical hole are computed numerically. The geometry represents that of a single nanopore in a membrane. When the membrane is uncharged, flow is due solely to induced charge electroosmosis, and eddies are generated by the high fields at the corners of the nanopore. These eddies meet at stagnation points. If the geometry is chosen correctly, the stagnation points merge to form a single stagnation point at which four streamlines cross at a point and eight eddies meet. C 2014 AIP Publishing LLC.

Cultivating innovative talents is an important task of colleges and universities. It is the trend of higher education development and the need of social development. Experimental teaching is an important link to develop students practice ability as well as innovative ability. The open experimental teaching is an effective way to train innovative talents. The content, conduct, effect and significance of open experimental teaching were studied in fluid mechanics.

The cooling nozzles arrangement is an important factor that affects the uniformity of the work roll temperature during hot rolling. In order to improve the work roll temperature distribution, a 2D calculation model of the unsteady temperature field of the work roll was established and the cooling nozzles arrangement was optimized based on the ANSYS finite element software. And it could be found that the temperature differences between the middle and the edge of the work roll would be reduced 7~8°C when the cooling water crowns of the work roll on F1~F7 stands were increased. Two optimization methods were adopted, one way was: the nozzle spacings of each row were the same. By changing the flow of the nozzles, the nozzles were in gradient arrangement from the middle to the edge of the roll according to the flow. The other way was: the nozzle type and flow rate of each row were the same. By changing the nozzle spacings, the nozzles were arranged from the middle to the edge of the roll according to the nozzle spacings.