Mass flow in nanoporous filtration membrane with small nanopores

The fluid flow in a small cylindrical nanotube such as occurring in the filtration membrane is essentially non-continuum, not predictable from the classical hydrodynamic flow theory. However, it has important practical applications in ultra filtration. It is shown that three factors i.e. the viscosity and density effect, the non-continuum effect and the wall slippage effect control this flow. The present paper shows that all these three effects heavily depend on the fluid-tube wall interaction, the former two effects strongly impede the flow and become more significant with the reduction of the diameter of the nanotube or with the increase of the interaction strength between the fluid and the nanotube wall, while the wall slippage effect speeds up the flow and it is more significant with the reduction of the diameter of the nanotube, with the increase of the power loss on the nanotube, or with the reduction of the interaction strength between the fluid and the nanotube wall. There is the competition between the former two effects and the wall slippage effect, determined by the power loss (POW) on the nanotube driving the flow. If POW is small enough, the viscosity and density effect and the non-continuum effect are dominant, and the mass flow rate through the nanotube is normally much lower than the classical flow theory calculation. If POW is sufficiently great, the wall slippage effect is dominant and the mass flow rate through the nanotube is much higher than the classical flow theory calculation. There are the values of POW which make the former two effects nearly equal to the wall slippage effect.