Dislodgement of carbon nanotube bundles under pressure driven flow

Abstract

Experimental and predicted flow rates through carbon nanotubes vary considerably butgenerally are reported to be well in excess of that predicted by the conventionalPoiseuille flow, and therefore nanotubes embedded in a matrix might providemembranes with exceptional mass transport properties. In this paper, appliedmathematical modelling is undertaken to estimate the three forces acting on a nanotubebundle, namely the molecular interaction force, the viscous force, and the staticpressure force. In deducing estimates of these forces we introduce a modification ofthe notion of the effective dead area for a carbon nanotube membrane, and wecalculate the total forces necessary to push one or more of the nanotubes out of thebundle, thus creating a channel through which further enhancement of flow maytake place. However, careful analysis shows that the nett dislodgement force isentirely independent on the useable flow area, but rather depends only on the totalcross-sectional area perpendicular to the flow. This rather surprising result is aconsequence of the flow being steady and a balance of the viscous and pressure forces.