Water Flow in Carbon Nanotubes: Transition to Subcontinuum Transport

The structure and flow of water inside 75 and 150 nm-long carbon nanotubes with diameters ranging from 0.83 to 1.66 nm are examined using molecular dynamics simulation. The flow rate enhancement, defined as the ratio of the observed flow rate to that predicted from the no-slip Poiseuille relation, is calculated for each tube and the liquid structure is examined using an axial distribution function. The relationship between the intermolecular water structure and water flow is quantified and differences between continuum and subcontinuum flow are discussed.

Figure 1

Snapshot from a typical flow simulation for the 0.83 nm-diameter CNT. A constant pressure difference is established between the reservoirs using a reflecting particle membrane. After a 0.25 ns initialization period, the mean pressure in each reservoir remains constant over the duration of the ensuing data collection period and flow through the tube is steady. Periodic boundary conditions are imposed in the flow direction. The number of molecules inside the CNT ranges from $310\pm 5$ for the 75 nm-long, 0.83 nm-diameter CNT to $3676\pm 20$ for the 150 nm-long, 1.66 nm-diameter CNT.

Figure 2

(a) Water structures inside the 0.83–1.66 nm-diameter CNTs. Carbon atoms are removed for clarity and the chirality vector for each CNT is provided. (b) Axial distribution function (ADF), structure relaxation time $\tau$, and extent of the ADF, $L_t$, for each CNT. (c) $P(n,t_c)$, the probability that $n$ molecules cross the system midplane over the characteristic flow time $t_c$. The CNT permeability $\alpha$ is provided for $\Delta P/L=4\times {10}^{14}\mathrm{Pa}/\mathrm{m}$.

Figure 3

(a) Relationship between average flow velocity $\overline{v}$ and applied pressure gradient $\Delta P/L$ for the 75 nm-long CNTs. A similar relationship exists for the 150 nm-long CNTs. We note that $\overline{v}$ is well below the molecular thermal velocity ($340\mathrm{m}/\mathrm{s}$ at $T=298\mathrm{K}$). For each data point, the standard deviation in $\overline{v}$ and $\Delta P/L$ is $0.5\mathrm{m}/\mathrm{s}$ and $2\times {10}^{13}\mathrm{Pa}/\mathrm{m}$, leading to a $\pm 25\%$ uncertainty in $\epsilon$. Guide lines are added to highlight the trends. (b) Variation in flow enhancement factor $\epsilon$ with CNT diameter $D$. The dashed line between $D=1.25\mathrm{nm}$ and $D=1.39\mathrm{nm}$ delineates continuum and subcontinuum flow regimes. The line in the continuum regime is a model we developed previously [3].