Figure 2. Measurement of Landau-Squire flows driven from nanotubes.

(a) Maps of the velocity field near a CNT with (R_t, L_t) =(33, 900) nm for various ΔP (C_s=10^-2 M and pH 6). (b) Magnitude of mean particle velocity as a function of $r^{\prime }(\theta )=r\times 2/\sqrt{1+3{\cos }^2\theta }$ for ΔP=0.5, 1, and 1.5 bar (from bottom to top). Dashed lines are fits of the Landau-Squire prediction. Inset: Particle velocity along the jet axis (θ = 0) versus distance from the nanotube for ΔP=0.75 bar (green) and ΔP=1.7 bar (orange). The dashed line is a 1/r fit. (c) ΔP -dependence of $\frac{F_P}{4\pi \eta }$ for CNTs (green symbols) and BNNTs (blue symbols). CNT dimensions were, from top to bottom, (R_t, L_t) = (50,1000) nm, (33,900) nm, (38,800) nm, (15,700) nm, and (17,450) nm and BNNT (R_t, L_t) = (26,700) nm and (23,600) nm. The salt concentration is C_s=10^-3 M, except for the 33 nm CNT which was studied at both C_s=10^-3 M and C_s=10^-2 M without a detectable difference. Dashed green lines are linear fits from which the permeability was calculated. The orange line indicates the lowest detectable flow strength. The black dashed line corresponds to the results of a control experiment using a nanocapillary without a nanotube (see Supplementary Method 5). Error bars correspond to the uncertainty in the slope in panel (b), estimated from at least 3 measurement replicates at each ΔP.