An analytical model for evaluating fluid flux across carbon-based membrane

Fast Water Transport through Subnanometer Diameter Vertically Aligned Carbon Nanotube Membranes

“…Recent models for entrance resistance in graphene nanopores have sought to modify Samson's formula to account for slippage at the entrance of the CNT and the variation of the viscosity near the graphene wall. 72,73 MD simulations were used to extract the slip length 74 and the viscosity near the entrance/exit of the graphene pore and quantify the expected entrance/exit resistance. 72,73 The proposed "corrected" Sampson resistance R slip-viscosity-corrected Sampson can be expressed as the sum of two parts: slip-corrected resistance R slip-corrected Sampson and viscosity-corrected resistance R excess-viscosity Sampson (detailed expressions are given in Corrected Sampson's Entrance Resistance of the Supporting Information as eqs S10 and S11).…”

“…72,73 MD simulations were used to extract the slip length 74 and the viscosity near the entrance/exit of the graphene pore and quantify the expected entrance/exit resistance. 72,73 The proposed "corrected" Sampson resistance R slip-viscosity-corrected Sampson can be expressed as the sum of two parts: slip-corrected resistance R slip-corrected Sampson and viscosity-corrected resistance R excess-viscosity Sampson (detailed expressions are given in Corrected Sampson's Entrance Resistance of the Supporting Information as eqs S10 and S11). The slip-and viscosity-corrected Sampson resistance R slip-viscosity-corrected Sampson then depends on the diameter of the CNT.…”

“…Recent models for entrance resistance in graphene nanopores have sought to modify Samson's formula to account for slippage at the entrance of the CNT and the variation of the viscosity near the graphene wall 72,73. MD simulations were used to extract the slip length74 and the viscosity near the entrance/exit of the graphene pore and quantify the expected entrance/exit resistance 72,73. The proposed "corrected" Sampson resistance R slip-viscosity-corrected…”

“…Using this formula to calculate the theoretical upper bound for the enhancement factor, we find that the actual measured flow enhancement for the 0.8 nm SWCNTs was 6–8× higher than the classic Sampson limit in our membranes. Recent models for entrance resistance in graphene nanopores have sought to modify Samson’s formula to account for slippage at the entrance of the CNT and the variation of the viscosity near the graphene wall. , MD simulations were used to extract the slip length and the viscosity near the entrance/exit of the graphene pore and quantify the expected entrance/exit resistance. , The proposed “corrected” Sampson resistance R slip‑viscosity‑corrected Sampson can be expressed as the sum of two parts: slip-corrected resistance R slip‑corrected Sampson and viscosity-corrected resistance R excess‑viscosity Sampson (detailed expressions are given in Corrected Sampson’s Entrance Resistance of the Supporting Information as eqs S10 and S11). The slip- and viscosity-corrected Sampson resistance R slip‑viscosity‑corrected Sampson then depends on the diameter of the CNT.…”

“…Measured flow rate for our CNTs and those in the literature − ,,,− compared to the maximum flow rates expected for a flow with only entrance resistance. The limiting flow rates used for normalization are calculated from the original Sampson’s formula (filled symbols) and Heiranian et al’s “corrected” entrance resistance , (hollow symbols). The colored dashed lines visually connect data points on different diameter CNTs from the same studies, while the solid black line marks a normalized flow rate of unity.…”