Introduction

Understanding liquid transport through nanoscale confinements is critical in a variety of practical applications, including energy conversion/storage1,2, water desalination1,3, phase-change thermal management4, biological and chemical separations5 and lab-on-a chip devices6. Although it has been argued that continuum assumption and classical hydrodynamics are capable of describing liquid transport at the nanoscale1,7,8,9, the differences between nanoscale and micro/macroscale liquid transport, in terms of confined liquid properties9,10,11,12,13,14,15,16,17,18, flow boundary conditions (slip/no slip)9,18,19,20,21,22,23, secondary flows24,25,26, etc, still remain elusive. In fact, a wide range of slip length and confined liquid properties with up to several orders of magnitude discrepancies between different sources have been reported, indicating that nanoscale liquid transport has remained poorly characterized and novel accurate measurement techniques for this purpose are desired. The major challenge in performing precise flow measurement in nanoscale conduits is the associated huge hydraulic resistances which result in ultra-small flow rates. For example, based on classical hydrodynamics only ~0.25 al/s water flows through a hydrophilic tube 100 micron long and 10 nm in diameter, when one atmosphere pressure is applied. The most common method to bypass this challenge is to measure liquid transport in membranes consisting of numerous similar nanoscale conduits19,20,21,22. However, analysis and verification of the data from this method is complicated by the fact that the measured flow rate constitutes an average over a large unknown number of conduits with a range of diameters and lengths. There are also concerns about possible leakage due to membrane defects and/or leakage at the membrane’s edges27. Moreover, it may not be possible to create membrane structures for certain nanoscale conduits with specific geometry and surface properties, e.g. 2-D planar nanochannels that are widely used in lab-on-a-chip devices. On the other hand, capillary flow measurement is the major method used for characterizing fluid flow in individual nanoscale conduits by tracking the location of a moving meniscus as a function of time18,28,29,30,31,32,33,34,35,36. However, in this method–which is mainly applicable to hydrophilic channels–the driving pressure in the nano-conduits is not experimentally measured, but calculated based on classical theories28,29,30,31,32,33,34,35,36 with bulk liquid properties or molecular simulations18, which can be quite different from the actual values, resulting in inaccurate calculation of the actual hydraulic resistance. Given the limitations of the current measurement techniques, it is thus necessary to develop a technique for liquid flow measurement in single nano-conduits37,38 which can be applied to both hydrophobic and hydrophilic conduits without using any theoretical estimations. Herein, we report such a technique based on capillary flow and a novel hybrid nanochannel design and use it to characterize water transport in single silica nanochannels with heights down to 7 nm.

Hybrid Nanochannel Scheme

The hybrid nanochannel design consists of a test channel (the channel under investigation) seamlessly connected to a reference channel with a different but known mass flow resistance (Fig. 1). In a typical experiment, two capillary flow measurements are conducted in the hybrid channel, one starting from the test channel side and the other starting from the reference channel side. However, the meniscus location is only recorded in one of the two channels, which we call it the “observation channel”. Without loss of generality, let’s assume the observation channel is the reference channel. In this case, the first capillary filling process starts from the reference channel side (Fig. 1b). The location of the meniscus in the reference channel X(t) is recorded and is expected to be governed by the Washburn equation, which for the case of a channel with rectangular cross-section can be written as (Supplementary information, section I)

Figure 1
figure 1

Schematic of the hybrid nanochannel scheme for nanoscale liquid transport characterization and error analysis.

(a) Channel under investigation is seamlessly connected to a reference channel of known hydraulic resistance and the data is collected from the observation channel which can be either of the channels. (b) The Observation channel is first characterized by a capillary flow experiment yielding the value of A which is a function of both hydraulic resistance and the capillary pressure only in this channel. (c) Ratio of the mass flow resistance between the two channels (η) can be found by introducing liquid from the other side and tracking the meniscus again in the observation channel. (d) Error associated with η other than the temporal and spatial dependence is a function of A and L*. Assuming δx = δX = 1 μm and the observation channel is 350 μm long, error for different values of A, L* and frame rates has been evaluated. (The square markers are the experimental data points).

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here, ΔP is the capillary pressure, R is the mass flow resistance of the channel per unit length, w and h are channel width and height and ρ is the fluid density. After the first measurement, liquid is removed from the nanochannel and is introduced from the test channel side for the second measurement (Fig. 1c). The location of the meniscus in the reference channel during the second capillary filling process x(t) is then recorded, which is expected to be described by the following equation (Supplementary information, section I):

In this equation, t = 0 corresponds to the time when the meniscus enters the reference channel (x = 0, Fig. 1c), η is the ratio of the mass flow resistance between the reference channel and the test channel per unit length, μ is the fluid viscosity, ls is the slip length and the starred variables belong to the test channel, with L* being the length of the test channel. By fitting experimental data sets X(t) and x(t) with equations (1) and (3), capillary flow constant, A, in the observation channel and the mass flow resistance ratio, η, can be extracted. Consequently, resistance of the test channel can be quantified if the resistance of the reference channel is known. It is worth noting that the test channel can be an individual channel, tube or even nanoporous media and no matter if it is hydrophobic or hydrophilic, as long as either of test or reference channels allows for spontaneous liquid filling, this technique can be applied. (Supplementary information, section IV.C).

The hybrid channel scheme can be used to measure a wide range of η’s and thus a wide range of nanochannel resistance, with a relatively small error. Our linear regression based error analysis indicates that the experimental error associated with η (E = δη/η) reaches a plateau at small values of η determined by , with δx and τ being the spatial resolution and the frame interval (Fig. 1d, Supplementary information, section II). In this range, error is very small and is not a function of η and L*. At large values of η, however, error is a linear function of η () and a larger L* along with a smaller capillary flow constant A can be employed to reduce the error in this range. In fact, this method can be best utilized if η is smaller than 1. To study test channels with a very small resistance compared with the reference channel (yielding large values of η), one should possibly choose the test channel as the observation channel such that 1/η would be measured instead of η. This resolves the theoretical limit for accurate characterization of the flow and allows for measurement of very high resistance ratios with a small error. Nevertheless, by designing a long test channel and choosing a high frame rate, the hybrid nanochannel scheme is able to detect very large values of η (>104) with a small error (Fig. 1d). Therefore, this scheme is adequate for the study of enhanced liquid transport in carbon nanotubes and graphene nanochannels where a wide range of flow enhancements have been reported9,18,19,20,21.

Design, Fabrication and Measurement

In the present investigation, the proposed characterization scheme is utilized to study water transport in hydrophilic silica nanochannels with heights ranging from 7 nm to 59 nm. In our design, nanochannels with the same widths but larger heights (~110–120 nm) serve as the reference channels. This choice of the reference channel height serves several purposes: First, this depth of water in the reference channel can be very easily detected with an optical microscope. Second, this choice of height helps to avoid entrapment of air and creation of bubbles in the reference channel33,34,35,36. Finally, with this choice of heights, η would be less than 1 and the experimental error would be very small (Fig. 1d). The hybrid silica nanochannel devices are fabricated using the classic etching and bonding scheme, while the seamless connection between the test and the reference channels are achieved using double-layer photoresist coating (Fig. 2a). Briefly, five sets of stepped nanochannels were fabricated with h*/h = 7 ± 0.5 nm/117.5 ± 0.5 nm, 16.2 ± 0.4 nm/109.5 ± 1 nm, 28 ± 0.5 nm/110.5 ± 2 nm, 38 ± 0.5 nm/108 ± 1 nm and 59 ± 0.5 nm/121 ± 1 nm. Uniformity of the RIE etching throughout the entire silicon wafers allowed us to fabricate many chips of almost exact heights in each trial. The width of both test and reference channels is 3 μm, the reference channel’s length is L = 550 μm and the test channel’s length is L* = 50 μm, except for the 7 nm channel which is L* = 7.5 μm. Long test channels with very small heights impose a very large resistance before the reference channel such that the meniscus may stop at the step and the corner flows become the dominant mode of filling39,40,41 (Supplementary Figure S5). For this reason the 7 nm test channel is chosen to be 7.5 micron long to allow easy flow of water. After etching the nanochannels, two microchannels each 6 mm long, 1 mm wide and 40 μm deep were etched using DRIE on both terminals of the nanochannels to carry water from the reservoirs and the four reservoirs which are 2 mm by 2 mm through holes were later etched using DRIE (Fig. 2b). Finally, 300 nm thick dry thermal oxide layer was grown on the silicon chips and the chips were cleaned with Piranha (3:1, H2SO4:H2O2) and bonded to Borosilicate glass by using anodic bonding at 400 °C and 350 Volts. Miscroscope images of a bonded hybrid nanochannel device is shown in Fig. 2b. The test channels, reference channels, location of the steps, as well as connection of the microchannel to the nanochannels for this device (16.2 nm/109.5 nm) is shown in Fig. 2c. Heights of the test and the reference nanochannels are measured using AFM before anodic bonding. Figure 2d–g show the 3D AFM images of four representative hybrid nanochannels used for the experiments with h* = 7, 16.2, 38 and 59 nm.

Figure 2
figure 2

Device structure and characterization.

(a) Fabrication procedure of the hybrid channels, using double layer photoresist coating and RIE etching. (b,c) structure of a chip used for experiments; water is carried from one of the reservoirs to the nanochannels through a microchannel. Nanochannels 600 micron long are located between two microchannels, each consisting of a shallow side and a deep side creating a step in the nanochannels. (scale bars of (b,c) are 2 mm and 20 micron) (d–g) Representative AFM images of four hybrid channels used for the experiments with h*/h = 7 nm/117.5 nm, 16.2 nm/109.5 nm, 38 nm/108 nm and 59 nm/121 nm.

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All the experiments were performed with DI water (electrical resistivity >18 MΩ-cm) at 22 ± 1 °C (pH = 7), before each experiment oxygen plasma was applied to the chips for 15 minutes to make the surfaces super hydrophilic and prevent formation of bubbles in the nanochannels. The water Meniscus in nanochannels were tracked by an Olympus inverted microscope model IX81 equipped with a monochromatic HAMAMATSU CMOS FLASH 4.0 C11440 camera recording at up to 900 fps (or at lower rates when not necessary). Position of the meniscus as a function of time was extracted from the recorded frames using a MATLAB image processing code.

Results and Discussion

The capillary flow constant, A, is found by introducing water from the reference channel side, tracking the location of meniscus as a function of time and curve fitting to the experimental data (Fig. 3a,b). This quantity is known to be smaller than theoretical predictions for the nanochannels and different reasons have been proposed to explain the discrepancies between theory and experiments24,25,26,28,29,30,31,32,34,35. (Supplementary information, section IV.A) Here, for the reference channels of similar height (110 nm to 120 nm), the measured correction factors defined as C = Atheory/Aactual ranged from 1 to 1.35 with the average of C = 1.22. Moreover, we observed that this correction factor increases over time, which is mainly attributed to deterioration of surface properties and creation of hydrophobic sites along the channels. (Supplementary information, section IV.B) After measuring the capillary flow constant, in the second experiment water is introduced from the test channel side. (Figure 3c,d, h* = 16.2 nm) It was observed that meniscus moves with a constant speed (linear dependence of x on t, instead of ), consistent with equation (3) in case of η ≪ 1:

Figure 3
figure 3

Capillary filling of a hybrid nanochannel.

(a) Microscope image of capillary filling of the reference channel starting from the reference channel side. Image processing of the recorded frames allows for extraction of X − t curve of the meniscus. (b) Meniscus location in the reference channel recorded at 500 fps, showing a clear square root time dependence. (c,d) Capillary filling of the reference channel starting from the test side (h* = 16.2 nm). Meniscus moves with a constant speed and the filling rate is 2 orders of magnitude slower than the first experiment.

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In fact, when η ≪ 1, most of the resistance originates from the test channels and as a result, ΔP at the meniscus has to overcome an almost constant resistance throughout the entire filling process and thus travels with a constant velocity. This velocity is much slower than the first experiment which allows for easy measurement of the x − t data at low frame rates.

Representative measured x − t curves for each of the five tested hybrid nanochannel sets along with the experimental η’s are presented in Fig. 4a. Our experimental results measure η’s spanning over three orders of magnitude with a small error predicted by our error analysis (Figs 1d and 4a). Theoretical values of η normalized by the experimental η yield the increase in the resistance as a function of height: α = ηtheoretical/ηactual = Rtest,actual/Rtest,theoretical. An implicit assumption here is that resistance of ~120 nm reference channels can be approximated by the classical equation for R, otherwise a slight increase in the measured α can be expected. Our results indicate that for the 59 nm channels the actual resistance is very close to the theoretical prediction and as the test channel height becomes smaller, difference between the actual and the theoretical resistance becomes more pronounced, with the ratio reaching α = 1.45 ± 0.31 in case of 7 nm channels (Fig. 4b). As it’s clear from the definition of R, within the realm of hydrodynamics the liquid-surface interaction can manifest itself in the boundary conditions, i.e., slip/no-slip boundary condition, and/or in the form of an altered liquid property (i.e., density and viscosity). In terms of the boundary condition, slip boundary condition has been reported for the hydrophilic channels22,23. However, any non-zero slip lengths could only reduce the resistance and hence can not serve as an explanation for our results (here Rtheoretical is calculated with ls = 0). In terms of liquid properties, several of previous studies have employed long-range electrostatic forces to explain the slow capillary filling in hydrophilic nanochannels through the Debye-layer correction for the hydraulic resistance. However, this effect known as electroviscosity has been proven insignificant for realistic estimates of central parameters24,25,26. On the other hand, change in the interfacial liquid properties due to short-range interaction forces can be another way to explain the increased resistance32,37. When water is in contact with a polar surface, water dipoles reorient making formation of stagnant/tenacious hydration layers at the interface favorable. Experimental studies concerning fluidity of confined water between hydrophilic surfaces less than a few nanometers apart have demonstrated 1 to 6 orders of magnitude increase in water viscosity due to ordering of the water structure at the hydrophilic surfaces10,11,12,13,14, although there are other studies indicating this increase is not more than three-folds15,16,17. Moreover, MD simulations indicate a three to five fold increase in water density near hydrophilic surfaces10,15,17. Such changes in interfacial liquid properties, or formation of an ice-like network of water adsorbed on silica42, can reduce the effective flow cross-sectional area and hence be a possible explanation for our measurements. According to our measurements, a stagnant layer of water on the silica surfaces with thickness of angstroms corresponding to two to three layers of water molecules can explain the observed increase in the mass flow resistance. However, since the fabrication method we have used involves anodic bonding, there is a concern about decrease in channel height after bonding. (Supplementary information, section III) Of course if any reduction in the channel height is going to happen after bonding, it must be subtracted from the measured thickness of the hydration layer. When comparing our results with previously reported hydration layer thickness of 5 angstroms43 or 4 angstroms37 in capillary filling studies one may argue that heights of our channels might have decreased by a few angstroms after bonding. However, it is worth noting that our measured value is in agreement with infrared reflection spectroscopy of water adsorbed on hydrophilic silicon oxide surfaces, which revealed that the first three adsorbed water layers (~8.4 angstroms thick) have an ice-like configuration42. Haneveld et al. also reported a thickness of δ = 9 ± 5 angstroms for the hydration layer in sub-10 nm nanochannels in their capillary filling study31, although their results may have overestimated the thickness of the hydration layer as they attribute deviations of both capillary pressure and hydraulic resistance from theory to the increase in hydraulic resistance. Additional possible sources of error for such measurements include capillary pressure induced channel wall deflection and dissolution of silica in water over time44. Nevertheless, the capillarity-induced channel wall deflection during water filling32,45,46,47 can be safely ignored for our nanochannels because of the thick cover layers (i.e., 0.5 mm thick glass/silicon). Moreover, the effect of channel wall dissolution (dissolution rate ~45 pm/hr44), a phenomenon observed when water flows in nanochannels over a long period, e.g. 48 hrs, is negligible as it only takes 1~2 minutes to perform multiple experiments in each nanochannel.

Figure 4
figure 4

Location of the meniscus versus time, α versus channel height and decoupling of α from C.

(a) Representative curves of the location of meniscus versus time for hybrid nanochannels with different η’s. Solid lines are fitted curves to the experimental results (markers). For η ≪ 1, the linear relation between x and t signifies the hydraulic resistance is almost entirely caused by the shallow test nanochannels. (b) Ratio of the actual resistance of the nanochannels to the theoretical resistance (α) vs nanochannel height. Formation of a stagnant layer of water on the silica surface with the thickness of δ = 4.3, 7.1, 8.9, 8 and 7 angstroms (from shallow to deep) can explain the increased resistance. (c) Characterizing the increased hydraulic resistance for a 28 nm channel measured with two chips of different hydrophilicity. Decrease in the capillary pressure due to change in hydrophilicity of the surfaces does not impact the measured hydraulic resistance.

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The hybrid channel design decouples two unknown parameters in conventional capillary flow measurements, i.e., driving capillary pressure and hydraulic resistance, holding promise to be the standard for nanofluidic flow characterization. The pressure-resistance decoupling in this method is further explored by testing hybrid channels with deteriorated surface properties which demonstrated correction factors C of up to 2 in the reference channels (Supplementary information, Figure S4a). In the deteriorated channels, while C was measured to be ~50% larger than a fresh chip, α maintained its value within 10% of the fresh chips, verifying that hybrid nanochannel scheme can avoid a large error arising from any changes in the pressure term (Fig. 4c).

In summary, our experimental results characterize water transport in sub-10 nm hydrophilic nanochannels and lends more validity to the use of classical hydrodynamics at the nanoscale. The proposed hybrid nanochannel scheme provides insight into collective effects of the boundary condition as well as the properties of a nanoscale confined liquid and can open the prospect for accurate characterization of liquid transport through 2-D nanochannels, 1-D nanotubes, as well as nanoporous media. In particular, characterization of water transport in hydrophobics CNTs and graphene nanochannels can be improved through their integration with hydrophilic channels in the form of hydrophobic-hydrophilic hybrid channels. This method has the potential to be standard for nanofluidic flow characterization and can serve to advance studies of many nanofluidics-involved disciplines, including membrane separation, soil science, colloid chemistry, biology and physiology.

Additional Information

How to cite this article: Alibakhshi, M. A. et al. Accurate measurement of liquid transport through nanoscale conduits. Sci. Rep. 6, 24936; doi: 10.1038/srep24936 (2016).