Letter pubs.acs.org/NanoLett
Fast Water Thermo-pumping Flow Across Nanotube Membranes for Desalination Kuiwen Zhao and Huiying Wu* School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China S Supporting Information *
ABSTRACT: Development of high-efficiency and low-cost seawater desalination technologies is critical to meet global water crisis. Here we report a fast water pumping method in which the water molecules in seawater are continuously pumped across nanotube membranes driven by a small temperature difference, opening the possibility of highthroughput small-scale desalination devices driven by lowgrade thermal energy. Using molecular dynamics simulations, we show that an equivalent driving pressure of 5.3 MPa is achieved with a temperature difference of only 15 K. The remarkable water pumping ability is attributed to the asymmetric thermal fluctuation of water molecules. With this method, a 10 cm2 nanotube membrane with 1.5 × 1013 pores per cm2 will produce freshwater with a flow rate of 7.77 L/h under a small temperature difference of 15 K. KEYWORDS: Water pumping, nanotube, membrane, temperature difference, desalination, molecular dynamics gradient or large electric field intensity needed to overcome the large chemical barrier makes these methods hard to be implemented for practical application in seawater desalination. Here we report a fast thermo-pumping desalination process driven by a small temperature difference. Because of the asymmetric thermal fluctuations of water molecules on two sides of nanotube membranes, water molecules in solution overcome the large chemical potential barrier, which is induced by the ionic concentration difference and the temperature difference, and move across the membranes. Without a force exerted, water molecules here spontaneously move across the nanotubes in the direction opposite to the chemical potential barrier, completely different from other thermally driven methods available in the published literature.14−16,19 This approach exhibits a powerful pumping ability and creates a unique new scheme for the reverse osmosis by utilizing a small temperature difference instead of a high driving pressure as the power source. Because no phase changes are needed, the energy requirements are low in comparison to other thermal desalination methods. To investigate the performance of this water thermopumping desalination process with molecular dynamics simulations, we choose aligned uncapped (6, 6) single-wall carbon nanotube arrays as the model of semipermeable membranes. The schematic illustration of the simulation system is shown in Figure 1. The narrow inner channels of
Water crisis is one of the most serious global challenges. Seawater desalination is anticipated to offer a seemly unlimited clean water supply. Most current desalination methods either evaporate seawater and then condense the vapors (e.g., thermal distillation) or pressurize seawater with a high-pressure pump to overcome natural osmotic pressure (e.g., reverse osmosis). Both of them are energy-intensive and expensive to maintain, and require large-scale infrastructures. Desalinating seawater efficiently without energy-intensive phase change processes or a high-pressure gradient is still a challenge.1,2 Meanwhile, the critical freshwater shortage is often accompanied by the lack of the necessary power and infrastructures in the underdeveloped areas or islands. Thus, high energy-efficiency small-scale (or even portable) seawater desalination systems, which can be used by a single person or family, will perfectly meet these needs.3−5 Nanotube or nanopore membranes have demonstrated the most potential for improving the energy efficiency and reducing the size of desalination systems due to their ultrahigh water permeability6−9 and excellent solute exclusion10−13 However, the amount of energy that can be saved only by improving the permeability of semipermeable membranes is likely to be small because current reverse osmosis desalination has already been near the thermodynamics limitation.1 Besides, the requirement of high-pressure pump is a hurdle to scale down the system for small-scale applications. More efficient driving methods are needed as alternatives to high-pressure pump. Although a small number of methods for driving fluid in nanoscale including those by capillary imbibing force,14 thermophoretic force,15,16 or electric force17,18 have been proposed, the high-temperature © XXXX American Chemical Society
Received: November 4, 2014 Revised: April 17, 2015
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DOI: 10.1021/nl504236g Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters
concentration. Without an external hydrostatic pressure, water molecules tend to move from high chemical potential to low chemical potential. So an observation of a unidirectional net water flow from low-temperature reservoir to high-temperature reservoir seems to be more reasonable. We control the bulk temperatures (Tbulk) of 0.55 M NaCl solution and pure water at 325.9 and 310.8 K with the heating and cooling water temperatures of 330 and 300 K, respectively. To our surprise, despite the existence of high chemical potential barrier the water molecules in high-temperature solution reservoir move rapidly to the lower temperature pure water reservoir with nearly 500 water molecules moving across nanotubes within 32 ns, corresponding to a flux of 0.52 molecules per pore per nanosecond (Figure 2a). The flux decreases with time due to the increasing ionic concentration and the ion concentration polarization.2 To confirm this water pumping process is a perpetual behavior, we perform a long time simulation with pure water on both sides of the nanotube membrane. A robust and continuous water stream flows from high temperature reservoir to low temperature reservoir during the entire 80 ns (Figure 2b). Most of the water molecules have flowed across the nanotube membrane after 80 ns (Figure 2c). We obtain a net water flux of 0.89 molecules per pore per ns with a small bulk water temperature difference of 15 K, equivalent to the water flux created by a driving pressure of 5.3 MPa (Supporting Information 2), 221 times of the maximum driving pressure that can be obtained by the thermal transpiration effects with the same temperatures on both hot and cold sides (ΔP = (Thot/ Tcold)0.5 P).19,21 The present pumping ability is also more powerful than that driven by the capillary imbibition method, which is not effective for nanotubes with too small diameter, with almost zero flux for (7, 7) CNT (9.5 Å in diameter) under a temperature difference of 200 K.14
Figure 1. Schematic of the water thermo-pumping desalination process. The nanotube membrane (gray tubes in the middle) separates NaCl solution (bottom, transparent liquid with ions shown by cyan (Cl−) and yellow (Na+) spheres in it) and pure water (top, transparent liquid). For clarity, water molecules in bulk NaCl solution and pure water are selectively shown with red (O) and white (H) spheres. Heating (red) and cooling (blue) water are flowing through the bottom (red) and top (blue) tubes, respectively.
the nanotubes (8.1 Å in diameter) permit the passage of water molecules but reject solvated ions. Continuous nanotube membrane is formed by employing periodic boundaries. The NaCl solution and pure water reservoirs are separated by this membrane. The length of nanotubes is 1.6 nm. The number of nanotubes in one periodic simulation unit is 30. In order to avoid spurious physical phenomena caused by thermostats,20 the temperature difference is applied by heating and cooling the water in the tubes (i.e., the red and blue tubes in Figure 1) at the bottom and top of the nanotube membrane but not heating and cooling the bulk water directly in the simulations. All simulation details see Supporting Information 1. It is well-known that the chemical potential of water decreases linearly with the increase of temperature and ionic
Figure 2. Net water flow across nanotube membranes under a temperature difference. (a) The cumulative net water flow across the nanotube membrane with 0.55 M NaCl solution and pure water in −Z and +Z reservoirs, respectively. (b) The cumulative net water flow across the nanotube membrane with pure water on both sides of the membrane. (c) Snapshot of water flow across the nanotube membrane in the simulation case of panel b. B
DOI: 10.1021/nl504236g Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters
thermally driven methods where the fluid flux is proportional to the temperature gradient,15,16,19 an increase in the net water flux with the increasing nanotube length is observed (Figure 3b). Now we discuss the underlying physical mechanism. At first glance, it may be natural to ascribe the present pumping mechanism to the thermophoretic force induced by the temperature difference between two ends of nanotubes.15 However, the water thermo-pumping ability does not decline as the length of nanotube increases, which seems opposed to the fact that the movement velocity driven by thermophoretic force is proportional to the temperature gradient.16 The mechanism for the present water thermo-pumping process is also different from those for the thermal transpiration flow19,21 and the capillary imbibition flow,14 where the fluid molecules are driven from the cold side to the hot side of a channel. The analysis of force acting on water molecules allows an indepth examination of the underlying physical mechanism for the dynamic behavior of water molecules. Figure 4a shows the profile of mean force acting on a water molecule along nanotube axis, where the bulk temperature of water in −Z and +Z reservoirs are 360 and 320 K, respectively. To investigate the asymmetric interaction of water molecules along nanotubes, we have also calculated the total force acting on all the water molecules within a distance of ±D from the center of nanotube axis (Figure 4b). Though large fluctuations of the Z-direction mean force acting on a water molecule in nanotubes exist (Figure 4a), the net force acting on all the water molecules within nanotubes (D < 0.8 nm) is close to zero (small force opposite to the water flow direction is observed) (Figure 4b), which further confirms that the driving force in present thermopumping process is actually neither the thermophoretic force nor other forces exerted by the solid surface.15 Figure 4a also shows the mean force on a water molecule near the interface of the hot side is smaller than that near the interface of the cold side, yielding a negative net force opposite to the net water flow direction. Figure 4b indicates that the net force is mainly created by the force acting on the water molecules within 0.5 nm to the interfaces, no more than two water molecule layers (one water molecule layer ∼0.39 nm). The negative net force is due to the chemical potential barrier,22 which is induced by the temperature difference. Considering that the above force analysis is only for the situation where both −Z and +Z reservoirs are filled with pure water, it is anticipated that the negative net force for the situation where −Z reservoir is filled with NaCl solution and +Z reservoir is filled with pure water is more powerful due to the combination effect of temperature difference and ionic concentration difference. As analyzed above, the negative net force between two sides of nanotube membrane is powerful. Under such a powerful negative force, however, the water molecules flow rapidly across the nanotube membrane, moreover, this flow is not decayed with the increasing nanotube length. Considering that no force acts on the water molecules in flow direction within nanotubes, there must exist another mechanism that can account for this counterintuitive phenomenon. We attribute this driving mechanism to the asymmetric thermal fluctuations of water molecules on two sides of the nanotube membrane. The transport of water molecules across a nanotube is subject to two factors: the frequency of collision of water molecules with the entrances of nanotube induced by thermal fluctuation and the energy barrier induced by the chemical potential difference. As shown in Figure 4c, water molecules are continually colliding
To thoroughly investigate the performance of the water thermo-pumping process, we further perform a series of molecular dynamics simulations. The results obtained for different heating/cooling temperatures and NaCl concentrations in −Z reservoir are summarized in Figure 3a. Upon
Figure 3. Water thermo-pumping performance under different operating conditions. (a) Net water flux for various heating temperatures and concentrations of NaCl solution in −Z reservoir. The cooling temperature of all the simulations is 300 K. The NaCl concentration is the initial concentration at the start of the simulations. +Z reservoir is filled with pure water. (b) Net water flux for various nanotube lengths with pure water in both reservoirs. The heating and cooling temperatures are 370 and 300 K, respectively.
controlling the bulk temperature of NaCl solution and pure water at 325.2 and 310.4 K, respectively, 0.55 M NaCl solution can be concentrated to about 1 M, the maximum concentration value. As the concentration increases further to 1.01 M while keeping the bulk temperatures on both sides unvaried, the water in pure water side will flow to the solution side with a small flux due to the increased chemical potential barrier (Figure 3a). Thus, with the thermo-pumping desalination scheme implemented, it is anticipated that up to 41% of the seawater with a typical salinity of about 0.59 M can be recovered as freshwater with a bulk temperature difference of only 15 K, leaving less remainder discharged as wastewater. Increasing the bulk temperature difference from 15 to 40 K, the freshwater throughput rate increases up to 3.6 times, and the percent of water recovery will be remarkably improved accordingly. A much higher freshwater throughput rate can be obtained for the desalination of brackish groundwater with a relatively lower salinity (0.08−0.5 M) than seawater. With the same temperature difference between two sides of the nanotube membranes, the temperature gradient decreases with the increase of nanotube length. Thus, it is reasonable to question whether the water pumping ability declines as the nanotube length increases. For this purpose, we test the water pumping performances for different nanotube lengths (1.6− 24.5 nm) while with the same heating and cooling temperatures of 370 and 300 K, respectively (Figure 3b). Contrary to other C
DOI: 10.1021/nl504236g Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters
Figure 4. Mechanism for water thermo-pumping flow induced by asymmetric thermal fluctuation. (a) Profiles of mean force acting on a water molecule, density, and temperature of water along nanotube axis. The size of analysis slices is 0.1 nm in Z direction, and 1 nm in both X and Y directions. The data is averaged over 10 ns. The average statistical uncertainties in Fx, Fy, and Fz are ±0.0042, ± 0.0040, and ±0.086 kcal·mol−1·Å−1, respectively. (b) Profile of the total force acting on all the water molecules within a distance of ±D from the center of the nanotube axis (Z = 0). The negative force near interface is due to the chemical potential barrier induced by the temperature difference. (c) Schematic illustration of the asymmetric thermal fluctuation of water molecules on two sides of the nanotube membrane. More water molecules successfully escape from hot bulk water and move across the nanotube as compared to those from cold bulk water, yielding a net water flow from the hot side to the cold side.
research on nanotube membranes with high thermal resistance is required to improve the energy efficiency. Given the water thermo-pumping ability does not decline as the length of nanotube increases, the selection of long nanotubes is a potential effective method. Admittedly, the minimum energy demand for the thermo-pumping process is larger than that for traditional pressure-driven reverse osmosis process (3.8 J/g1). However, the low-grade thermal energy, which can be obtained easily, is used instead of the high-grade electrical energy during this process, and no high-pressure pump is needed, which is beneficial to small-scale applications. Also, note that no net pressure exerted on the nanotube membrane by water is observed in the present water thermopumping process (Supporting Information Figure S4). So a high mechanical strength is not needed for the membranes to withstand a high external pressure, which is required in the traditional pressure-driven reverse osmosis desalination method. In summary, we propose a novel thermo-pumping desalination process driven by a small temperature difference. Owing to the asymmetric thermal fluctuations of water molecules on two sides of nanotube membranes, water molecules in NaCl solution overcome the chemical potential barrier and move across the membranes. This water thermopumping method provides a promising step toward the development of thermally driven reverse osmosis desalination as an alternative to the traditional pressure-driven reverse osmosis desalination. Assuming nanotube membranes with a pore density of 1.5 × 1013 pores per cm2,23 a thermo-pumping desalination system with a membrane area of 10 cm2 will produce freshwater with a flow rate of 7.77 L/h under a temperature difference of 15 K (according to the simulation result in Figure 2a). The water thermo-pumping mechanism proposed here also can be applied to other fields, including
with the membrane pores from both sides. The frequency of collision is remarkably larger on the high-temperature side (left) than that on the low-temperature side (right) owing to the asymmetric thermal fluctuations of water molecules. Once the asymmetric thermal fluctuations of water molecules predominates over the negative net force induced by the chemical potential barrier between two sides of the membrane, more water molecules on the hot side successfully escape from the bulk water and move across the nanotube when compared with those on the cold side, yielding a net water flow in +Z direction. It is not a paradox that water flows in the direction opposite to the force. Though a powerful negative force exists at the interface, the water molecules have an initial momentum in +Z direction when they enter the nanotube from hot side, which is sufficient for them to overcome the negative force induced by the chemical potential barrier. It is worth noting that the temperature of nanotube is constant along the axial direction during the simulations due to the high thermal conductivity of the nanotube. The temperature decrease of water inside nanotube along the axial direction (Figure 4a) is due to the energy exchange between water molecules. The temperature of water inside the nanotube is not the same with that of nanotube because water molecules move very fast inside nanotube and thus the thermal energy cannot fully exchange with nanotube in such a short time. The theoretical minimum energy demand for the thermopumping process is the chemical potential difference induced by the temperature difference and the ionic concentration difference (60.6 J/g for Figure 2a). It is very small compared to the theoretical minimum energy demand for other thermal desalination processes based on phase changes (2400 J/g). However, because the short nanotube membranes, which are excellent heat conductors, are selected to simplify the simulations in this work, most thermal energy transfers across nanotube membranes (Supporting Information 3). Further D
DOI: 10.1021/nl504236g Nano Lett. XXXX, XXX, XXX−XXX
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(19) Thekkethala, J. F.; Sathian, S. P. J. Chem. Phys. 2013, 139 (17), 174712. (20) Page, A. J.; Isomoto, T.; Knaup, J. M.; Irle, S.; Morokuma, K. J. Chem. Theory Comput. 2012, 8 (11), 4019−4028. (21) Miller, G. A.; Buice, R. L. J. Phys. Chem. 1966, 70 (12), 3874− 3880. (22) Raghunathan, A. V.; Aluru, N. R. Phys. Rev. Lett. 2006, 97 (2), 024501. (23) Zhong, G.; Warner, J. H.; Fouquet, M.; Robertson, A. W.; Chen, B.; Robertson, J. ACS Nano 2012, 6 (4), 2893−2903.
thermal energy harvesting devices, pumps, and molecular motors.
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ASSOCIATED CONTENT
S Supporting Information *
(1) Methods; (2) water flux under a driving pressure; (3) thermal energy demand for water thermo-pumping process; and (4) net pressure exerted on the nanotube membrane. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/nl504236g.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China through Grants 51376130 and 50925624, National Basic Research Program of China (973 Program) through Grant 2012CB720404, Science and Technology Commission of Shanghai Municipality through Grant 12JC1405100.
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REFERENCES
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DOI: 10.1021/nl504236g Nano Lett. XXXX, XXX, XXX−XXX
