Fast flow through nanotubes and tube blow-out

Abstract

© Springer Science+Business Media Dordrecht 2013. Both observed and theoretical predictions of flows through carbon nanotube membranes are known to vary greatly, but generally they are believed to be well in excess of that predicted by conventional pipe flow. For Newtonian fluid flow in a nanotube, with a linear Navier slip boundary, we show that a second flow field arises which is different to conventional Poiseuille flow in the sense that the corresponding pressure is quadratic in its dependence on the length along the tube, rather than the linear dependence which applies for conventional Poiseuille flow. However, assuming that the quadratic pressure is determined, say from known experimental data, then the new solution only exists for a precisely prescribed permeability along the boundary. While this cannot occur for conventional pipe flow, for fluid flow through nanotubes embedded in a porous matrix, it may well be an entirely realistic possibility, and perhaps could well explain some of the high flow rates which have been reported in the literature. The maximum flow rate possible for the new solution is precisely twice that for the conventional Poiseuille flow, which occurs for a constant inward directed flow across the boundary. The three major forces acting on a nanotube bundle, namely the molecular interaction force, the viscous force, and the static pressure force, are examined with a view to the determination of conditions under which a nanotube or a nanotube bundle could be blown out. In deducing estimates of these forces we formulate a novel modification of the notion of the effective dead area for a carbon nanotube membrane, and we.