Dislodgement of carbon nanotube bundles under pressure driven flow

Experimental and predicted flow rates through carbon nanotubes vary considerably but generally are reported to be well in excess of that predicted by the conventional Poiseuille flow, and therefore nanotubes embedded in a matrix might provide membranes with exceptional mass transport properties. In this paper, applied mathematical modelling is undertaken to estimate the three forces acting on a nanotube bundle, namely the molecular interaction force, the viscous force, and the static pressure force. In deducing estimates of these forces we introduce a modification of the notion of the effective dead area for a carbon nanotube membrane, and we calculate the total forces necessary to push one or more of the nanotubes out of the bundle, thus creating a channel through which further enhancement of flow may take place. However, careful analysis shows that the nett dislodgement force is entirely independent on the useable flow area, but rather depends only on the total cross-sectional area perpendicular to the flow. This rather surprising result is a consequence of the flow being steady and a balance of the viscous and pressure forces.