Osmotic Flow through Fully Permeable Nanochannels

Osmosis across membranes is intrinsically associated with the concept of semipermeability. Here, however, we demonstrate that osmotic flow can be generated by solute gradients across nonselective, fully permeable nanochannels. Using a fluorescence imaging technique, we are able to measure the water flow rate inside single nanochannels to an unprecedented sensitivity of femtoliters per minute flow rates. Our results indicate the onset of a convective liquid motion under salinity gradients, from the higher to lower electrolyte concentration, which is attributed to diffusio-osmotic transport. To our knowledge, this is the first experimental evidence and quantitative investigation of this subtle interfacially driven transport, which need to be accounted for in nanoscale dynamics. Finally, diffusio-osmotic transport under a neutral polymer gradient is also demonstrated. The experiments highlight the entropic depletion of polymers that occurs at the nanochannel surface, resulting in convective flow in the opposite direction to that seen for electrolytes.

Figure 1

(a) Device layout. Nanochannels ($h=163\mathrm{nm}$, width $w=5\mu \mathrm{m}$, length $L=150\mu \mathrm{m}$) bridge between two microchannels, with $300\times 50\mu {\mathrm{m}}^2$ cross section, in which solutions of different solute concentrations [$n_L$ ($n_R$) in the left (right) arm] can be circulated to control the solute gradient along nanochannels. (b),(c) Steady state fluorescent probe intensity profiles along nanochannels for different solute (NaI) imbalances (b) $n_L<n_R$ (1 and $30\mathrm{m}M$) and (c) $n_R<n_L$ (30 and $1\mathrm{m}M$). Solid line (red): fit according to diffusion-convection equations (1); all profiles are seen to strongly depart from the linear diffusive-only theoretical profile.

Figure 2

Measured flow rate $\tilde{Q}$ as a function of the difference between logarithmic electrolyte concentrations $C^s$ (see text) for three different added salts: (▪) KI, (•) NaI, (▴) LiI. Inset: same data with flow rate plotted against added-salt concentration difference $n_L-n_R$.

Figure 3

Dependence of diffusio-osmotic mobility $D_{\text{DO}}$ as a function of the mobility mismatch coefficient $-\beta$: (▪) data point from Fig. 2 (see text), (solid line) linear fit. Inset: electro-osmotic characterization of nanochannel surfaces showing measured dye flow rate $\tilde{Q}$ as a function of imposed electric potential difference. (▪) data points, (dashed line) best fit according to Eq. (8) yielding $\zeta =-85\pm 2\mathrm{mV}$.

Figure 4

Water flow rate as a function of the difference between neutral polymer concentrations $n_L$ and $n_R$: (▪) PEG (MW 200), (dashed line) linear fit yielding a slope of $-173.5\pm 25\mathrm{fl}/\min /M$.