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A direct sensor to measure minute liquid flow rates Preeti Sharma, Jean-François Motte, Frank Fournel, Benjamin Cross, Elisabeth Charlaix, and Cyril Picard Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b02332 • Publication Date (Web): 02 Aug 2018 Downloaded from http://pubs.acs.org on August 9, 2018
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Nano Letters
A direct sensor to measure minute liquid flow rates Preeti Sharma,† Jean-François Motte,‡ Frank Fournel,¶ Benjamin Cross,† Elisabeth Charlaix,† and Cyril Picard⇤,† †Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France ‡Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France ¶Univ. Grenoble Alpes, CEA, LETI, 38000 Grenoble, France E-mail:
[email protected] Abstract
ion channel within a lipid bilayer 10 , or through an individual nanochannel or nanotube 11,12 However in nanofluidics, a central quantity is the flow rate. Despite several attempts since the 80’s to access minute flow rates, it turns out that no generic sensor exist yet to measure flow rate at the scale of an individual nanochannel. The most sensitive commercial sensor to our knowledge, based on temperature variation measurement subsequent to local heating of the flow at imposed power 13 , presents a measurement threshold of the order of 10 nL.min 1 . By comparison, the flow rate, given by the Poiseuille law, of a water pressuredriven flow through a cylindrical channel 100 nm in diameter induced by a pressure gradient of 1 bar/µm, is 15 pL.min 1 . Such a flow rate is thus 3 order of magnitude smaller than what can be measured with the best commercial sensor. During the past ten years, a few indirect strategies have been put forward to characterize precisely liquid flow rate in specific configurations. These strategies are either restricted to electrolytes solutions 14,15 , transparent nanochannels filled with a liquid supplemented with fluorescent dye 16 , or nanotubes acting as point source suspended within a liquid environment supplemented with tracers 17,18 . Minute flow rates of the order of 0.1 pL.min 1 have been measured with optical techniques, nevertheless with the prerequisite of an assumption on the theoretical velocity profile within the nanochannel. Although particularly sensitive these approaches are intrinsically linked to the nanochannel to be studied and can not be used as independent sensors. An interesting direct flow rate measurement, based on mass spectrometry, has been proposed to measure helium flow rate through single nanopore. This approach is applicable for pressure-driven flow of pure fluid 19,20 . Among the numerous strategies developed to measure flow rates it appears that the historical approach based on the accumulation of fluid over time is one of the most versatile approach. It can be used with any liquid, whatever its rheological and electrical properties, independently of the velocity profile, with any type of channel and flow generation. Such a measurement of small flow rate, though, requires to be able to collect and measure minute quantity of liquid in order to minimize the integration time. This has previously been done either by measuring the displacement of a meniscus within a calibrated transparent capillary used to collect the liquid, by weighing collected droplets of liquid 21,22 . For the study of flow in nanochannel, both approaches are hindered by capillarity effects, that are liquid dependent, but also potential evaporation, and substantial integration time. To solve this bottleneck, we show in this letter that minute flow rate can be reliably measured by the accumulation of liquid deflecting the solid-state membrane of a piezoresistive pressure transducer (figure 1A). This approach, that eliminates
Nanofluidics finds its root in the study of fluids and flows at the nanoscale. Flow rate is a quantity that is both central when dealing with flows and notoriously difficult to measure experimentally at the scale of an individual nanopore or nanochannel. We show in this letter that minute flow rate can be directly measured accumulating liquid over time within the compliant membrane of a commercial piezoresistive pressure sensor. Our flow rate sensor is versatile and can be operated independently of the nature of the liquid, the flow profile and type of nanochannel. We demonstrate this method by measuring the pressure-driven flow of silicon oil in a single nanochannel of average radius 200 nm. This approach gives reliable measurement of flow rate up to 1 pL.min 1 . Unlike other nanoscale flow measurements methods based, for instance on particle tracking, our sensor delivers a direct voltage output suitable for nano-flow control applications.
Keywords nanofluidic, flow rate, sensor, nanopore
Flow and transport phenomena in nanometric confinement are peculiar due to enhanced surface effects mediated by fluid/wall interactions. Biology gives fascinating examples of such transport phenomena controlled at the molecular scale and leveraged at a full organ scale such as kidney 1 . Transmembrane channel for instance present excellent sieving properties with both large permeability to specific chemicals for instance water in Aquaporin 2 and exclusion of others such as ions 3 . Mastering such a filtering capability intrinsically bound to the nanoscale would benefit to various large scale applications from water desalination 4,5 to reversely renewable electricity production from the so called blue energy 6,7 to mention only these two examples. Appealing both from a fundamental and applicative point of view, fluid behavior at the nanoscale has motivated numerous studies that contributed to the maturation of nanofluidics 8 in particular through the development of sensitive instruments to measure physical quantities related to transport at the vicinity of interfaces or within nano-confinement 9 . The characterization of ion transport, for instance, can now be addressed with commercial apparatus enabling the measurement of electrical current with a sensitivity better than the pA, allowing one to probe ionic exchanges through a single
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free surfaces and capillarity issues, is reminiscent of the accumulation technique developed for measuring the flow rate of rarefied gas within microcapillaries. This latter technique relies on the pressure variation within a container mounted downstream of the flow, and within which the gas molecules accumulate 23,24 . The measurement is then similar to electrical current measurements using the charge of a capacitance: the flow rate q, equal to the time derivative of the accumulated volume V, is related to the pressure p by: q=
can also be used to measure the accumulated volume of liquid. More specifically, in order to measure the targeted flow rate mentioned above of 15 pL/min in a time shorter or equal to 1 min, one needs to be able to measure volumes as small as 10 pL. The volume accommodated in the deflection of a membrane of size a is of order of a3 e where e is the deformation. As the smallest (and typical) membranes in piezoresistive pressure sensors are of millimeter size, this requires measuring deformations as small as 10 5 . This is achieved in commercial piezoresistive sensors, thanks to the high piezoresistive properties of silicon and on a push-pull mounting of the strain gauges in a Wheastone bridge (see figure 1B) whose diagonals undergo an opposite variation under deformation (the gauges on one diagonal are extended while the ones on the other diagonal are compressed) 27,28 . Another requirement in this measurement method is that the pressure built by the volume accumulation should not disturb the flow significantly. This is important in particular for electro-osmotic or diffusio-osmotic flows, which should not be perturbed by an unwanted pressure-driven flow. The typical pressure resolution of the most sensitive commercial piezoresistive sensors is of the order of the Pascal, which meets fully this requirement. For instance considering an electro-osmotic flow of 10 pL.min 1 in a nanochannel of 100 nm in diameter and length, a pressure difference of 1 Pa would lead to a spurious pressure-driven flow rate of 1 fL.min 1 which is largely negligible, and the effect becomes even smaller for smaller pore sizes. A pressure resolution dp = 1 Pa associated to a volume smaller than 10 pL, corresponds to a targeted value of the hydraulic capacitance Ch < 10 pL/Pa. Note that, assuming that the sensor membrane behaves like a spring of stiffness k ⇠ E⇤ e3 /a2 with E⇤ ⇡ 60 GPa the reduced Young modulus of silicon, the required membrane thickness e for obtaining a deformation e ⇠ 10 5 at applied pressure dp = 1 Pa is of order e ⇠ (dp a/k)1/3 ⇠ a(dp/eE⇤ )1/3 which is about 10 µm. We demonstrate here our flow rate measurement method using the commercial piezoresistive sensor PX170 from Omega Engineering. Further developments are however presented in the see Supplementary Information section 1 in order to design membranes for specific use as flow rate sensors. The PX170 Omega Engineering is made of a glass cuvette closed on its base by a silicon square membrane approximately 2.5 mm wide and 13 µm thick, which corresponds to a calculated hydraulic capacitance of the order of 3 pL.Pa 1 . To convert this standard pressure sensor into an ultra sensitive flow rate sensor, we milled the upper part of the sensor in order to connect it to a non-deformable cell made out of peek, used to collect the liquid issued from the studied nano system, as shown in figure 1A. This cell is also used to connect two micro-electrovalves (FLV- 2-N1G and EXAAK-NC Takasago fluidic systems) to the PX170 sensor in order to relax the membrane when it has reached its maximum deflection and to be able to change the nature of the liquid when needed. The choice of the valves is critical for operating the transducer as a flow sensor (see SI section 2). On one hand, the valves should not displace a large volume of liquid when they operate, so as to not overcome the pressure limit of the sensor or even break its membrane. Second, one of them should be bistable, to be able to either accumulate or release the liquid without any production of heat and thermal dilatation which could change the value of the accumulated volume. Finally, the cell is closed on its upper part by a pierced cover equipped with an o-ring (figure 2A) to obtain a leak-free connection with the nanofluidic system, in this paper we present the benchmark case of a single nanochannel pierced in a silicon wafer (figure
dV dp = Ch dt dt
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Figure 1: (A) Schematic of the flow rate sensor based on a volume measurement by means of (B) a silicon deformable membrane equipped with four strain gauges (C) electrically connected in a Wheatstone bridge. tional to the volume of the container collecting the flow. In our nanofluidic application the liquid is essentially incompressible, and the largest part of the flow volume is accommodated in the deformation of the membrane of a piezoresistive pressure transducer itself. The hydraulic capacitance Ch thus depends only on the characteristics of the transducer membrane and is independent of the nature of the liquid as long as it does not contain any bubble. Since the early paper of Mason and Thurston 25 in 1957, piezoresistive pressure sensors have become among the most reported micromachined devices 26 . They are based on a membrane of piezoresistive material (usually silicon) on which piezoresistive strain gauges are directly implemented, and whose edges are clamped on a small container. When a pressure difference is applied on the opposite sides of the membrane, it bulges, and in the linear regime its deformation is proportional to the pressure (see figure 1C). However in this linear regime the membrane deflection is also proportional to the volume it can accommodate, and thus the strain gauges
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4A). To eliminate thermal dilatation perturbations, the sensor has been tested in a home made thermally regulated chamber that limits the thermal drift to a maximum value of 5 mK/h. The set up details are given in SI section 3. In replacement of the DC power supply recommended by the supplier, the Wheatstone bridge is fed with the source of a lock-in amplifier (HF2LI Zurich Instruments) which is used to measure the voltage imbalance of the bridge. The sensitivity of our sensor is thus optimized with a power supply less than 1 µW. The pressure calibration, by means of a column of liquid of controlled height, gives a linear behavior in the range 0-1000 Pa with a sensitivity of 0.88 Pa/µV for a 100 mV supply, in agreement with the sensitivity provided by the supplier (figure 2B ). The resolution on the pressure signal is limited to ±0.2 Pa (inset of the figure 2B). In order to measure the exact capacitance Ch of the sensor, we feed it with a capillary behaving as a known hydraulic conductance Gh , apply a pressure jump, and measure the time constant t = Ch /Gh that characterizes the pressure response of the sensor (figure 2C). This calibration is carried out with V20 silicon oil of viscosity h = 20.3 mPa.s at 22.4°C for which the capillary, approximately 27 mm long, 50 µm in diameter, presents a conductance Gh = 11.5 ± 0.3 pL.min 1 .Pa 1 . This conductance, ratio of flow rate over pressure difference between inlet ant outlet of the capillary, was carefully determined before the calibration from pressure-driven flow rate measurement by means of the meniscus displacement method (see SI section 4). The sensor calibration leads to a time constant t = 0.339 ± 10 3 min, extracted from a first order relaxation fit, which is, as expected, independent on the amplitude of the jump of pressure and the same during charge and discharge. The resulting capacitance is Ch = 3.9 ± 0.1 pL/Pa with an uncertainty mainly related to the uncertainty on Gh . This capacitance value is consistent with the theoretical order of magnitude of 3 pL/Pa. The resolutions on the volume is estimated while closing all inlets of the sensor and found to be of the order of ±1 pL as shown in the inset of the figure 3A. To give an order of magnitude, this volume resolution corresponds to a resolution on the deflection at the center of the membrane of ±5 Å.
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Figure 3: Pressure-driven flow within cylindrical micro capillaries.(A) Direct measures of accumulated volume over time for several minute flow rate. (B) Flow rate according to pressure difference measured (filled symbol) with our sensor and (open symbol) with meniscus displacement method. (blue dots) Flow of V20 silicon oil through a 27 mm long 10 µm in diameter PEEK capillary. (orange dots) Flow of water through a 3 mm long 5 ± 2 µm in diameter silica capillary. silica capillary (TSP005375 Polymicro). From the slope of the flow-rate (orange dots in the figure 3B) with respect to the pressure difference, a conductance of 0.254 pL.min 1 .Pa 1 is measured. This conductance corresponds to an effective diameter of 4.67 µm in agreement with the supplier value. The third example adresses the study of a pressure-driven flow of V20 silicon oil through an individual nanochannel pierced within a silica membrane of thickness L = 1.35 µm. The membrane is made from an oxide layer grown thermally at the surface of a silicon wafer. By local chemical etching of the anisotropic silicon crystal one obtains the spontaneous formation of a truncated pyramidal well closed at its end by a square free-standing silica membrane. This membrane is pierced at it center by focused ion beam in order to create a single nanochannel (LEO 1530 SEM FIB cross beam) 29,30 . In the end, the nanochannel seats at the center of piece of wafer that is easily handable (figure 4A). The so obtained nanochannel is slightly conical as shown in the figure 4A from the cut of a similarly prepared nanochannel. The aperture radii of the nanochannel used in the experiment, measured from in plane scanning electron microscopy, are r1 = 102 ± 10 nm and r2 = 315 ± 10 nm (inset of figure 4B). The piece of wafer holding the single nanochannel is connected to the flow sensor cell in order to collect the liquid flowing out from the nanochannel (see SI section 5). Flow rate measurement are carried out at 24.5°C. As previously, a linear behavior between flow rate and pressure is obtained with a significantly smaller conductance of 1.32 ⇥ 10 3 pL.min 1 .Pa 1 . As a comparison purpose, using the Poiseuille law, a cylindrical nanochannel of same length L = 1.35 µm that would have the same conductance, would have a radius of 195 nm which seats within the measured value r1 and r2 . In summary, we demonstrate in this letter a flow-rate sensor based on an accumulation approach using the deformation of a membrane. This sensor enables for the first time the direct measurement of flow rate with a detection threshold of 1 pL.min 1 with an integration time of a few minutes. The sensor works independently of the nature of the liquid and the origin of the flow. The measurement approach is completely
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image analysis and the method provides a voltage output suitable for standard data acquisition and flow control applications. Finally, an important requirement when using this technique with a commercial piezoresistive sensor is the temperature control to avoid unwanted volume drifts of the accumulation chamber. The design of home-made membranes directly implemented on nanofluidic circuits could contribute to relax this constraint minimizing dead volume. The most sensitive instruments devoted to the study of transport and organization of fluid in confinement are dynamical surface force apparatus 31 and atomic force microscopy 32 . These approaches are well suited for the characterization of dynamical phenomena in linear regime only. During the past decades, numerous studies revealed, intriguing non linear nanofluidic effects, such as electrical current rectification in nanofluidics diode 33,34 . In this framework most of theses studies about non linear regime rely on electrical current characterization while flow rate has remained out of reach experimentally 18 . To go beyond the study of linear regime, our flow rate sensor would offer the possibility to characterize in permanent regime the flow related to non linear transport phenomena in individual model nano confinement.
(11) Siria, A.; Poncharal, P.; Biance, A.-l.; Fulcrand, R.; Blase, X.; Purcell, S.; Bocquet, L. Nature 2013, 494, 455– 458.
Acknowledgement The authors thanks Mickael Betton, Jérome Giraud, Bruno Travers for their help in building the sensor. This work was supported by the ANR Blue Energy 15-CE06- 0005-02 and the ARC Energies Region Rhône-Alpes.
(18) Laohakunakorn, N.; Gollnick, B.; Moreno-Herrero, F.; Aarts, D. G. A. L.; Dullens, R. P. A.; Ghosal, S.; Keyser, U. F. Nano Lett. 2013, 13, 5141–5146.
(12) Davenport, M.; Rodriguez, A.; Shea, K. J.; Siwy, Z. S. Nano Lett. 2009, 9, 2125–2128. (13) Schöler, L.; Lange, B.; Seibel, K.; Schäfer, H.; Walder, M.; Friedrich, N.; Ehrhardt, D.; Schönfeld, F.; Zech, G.; Böhm, M. Microelectron. Eng. 2005, 78-79, 164–170. (14) Mathwig, K.; Mampallil, D.; Kang, S.; Lemay, S. G. Phys. Rev. Lett. 2012, 109, 1–5. (15) Siria, A.; Biance, A.-L.; Ybert, C.; Bocquet, L. Lab Chip 2012, 12, 872–5. (16) Lee, C.; Cottin-Bizonne, C.; Biance, A. L.; Joseph, P.; Bocquet, L.; Ybert, C. Phys. Rev. Lett. 2014, 112, 1–5. (17) Secchi, E.; Marbach, S.; Niguès, A.; Stein, D.; Siria, A.; Bocquet, L. Nature 2016, 537, 210–213.
Supporting Information Available
(19) Velasco, A. E.; Friedman, S. G.; Pevarnik, M.; Siwy, Z. S.; Taborek, P. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 2012, 86, 1–5.
The following files are available free of charge. The Supplemental information covers material and methods.
(20) Savard, M.; Dauphinais, G.; Gervais, G. Phys. Rev. Lett. 2011, 107, 1–4.
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