Figure 1

(a) Schematic illustration of water transporting in a double-walled carbon nanotube (DWCNT). The outer tube (black) is fixed, and the inner tube (red) is flexible and its temperature is maintained at 298 K. (b) Radial density profile of water inside DWCNT’s at various flow rates. (c) Radial velocity profiles (dots) at various flow rates, the dashed lines are the corresponding mean velocities.Reuse & Permissions

Figure 2

Sample-mean method for getting reliable data from MD simulations for the $\tau -v$ relation. (a) The decrease of deviation with the increase of sample time or sample number. (b) The dependence of deviation on the number of sample used. (c) The flow-rate independent theoretical (solid line, predicted using central limit theorem [23]) and calculated standard deviations of $\tau$ at temperature 298 K. (d) The corresponding signal-to-noise ratio (SNR) for averages based on different time intervals and sample numbers (symbols), compared with two expected levels, 5 and 10 (dashed lines).Reuse & Permissions

Figure 3

(a) Relationship between the interfacial frictional stresses $\tau$ and slip velocity $v_s$ with different water contact angles (91${}^{ˆ}$, 45${}^{ˆ}$, 135${}^{ˆ}$), diameters, and loading manners. (b) The normalized simulation values of shear stress ($\tau /{\tau }_0$) vs $v_s/v_s^0$ with respect to carbon nanotubes. The corresponding least square fits in a unified IHS function form of $\tau /{\tau }_0=\mathrm{arcsinh}(v_s/v_s^0)$. (c) A closer look at the relations in the slip speed range of 0–40 m/s. The inset shows the convergence of 10,000-sample means with a contact angle of 91${}^{ˆ}$ based on 0.25- (rightward triangles), and 0.5- ps-averaged (leftward triangles) $\tau$ for the first 2.5 ps, which correspond to the shaded area spanning from 0 to 10 m/s. (d) Comparison between the experimentally observed data (dots)[9] and the IHS relationship prediction (dashed lines). The chirality of the inner tube is (20,20) unless specified.Reuse & Permissions

Figure 4

(a) Residual probabilities of water molecules in the first layers (contact angle $=$ 91${}^{ˆ}$). The dashed lines mean the water molecules that are present in the first layer at time $t=0$ and never jump out of the first layer. The inner tube of (20,20)@(25,25) DWCNT is flexible and its temperature is maintained at 298 K unless specifically pointed out (i.e., fixed). (b) Possible distance each water molecule within the first layer can travel during a time period of 20 ps (time interval $=$ 5 ps).Reuse & Permissions