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Water mass flow rate in a finite SWCNT under electric charge: A molecular dynamic simulation
Water mass flow rate in a finite SWCNT under electric charge: A molecular dynamic simulation H.R. Abbasi, S.M.H. Karimian PII: DOI: Reference:
S0167-7322(16)30178-7 doi: 10.1016/j.molliq.2016.09.083 MOLLIQ 6360
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
21 January 2016 1 September 2016 12 September 2016
Please cite this article as: H.R. Abbasi, S.M.H. Karimian, Water mass flow rate in a finite SWCNT under electric charge: A molecular dynamic simulation, Journal of Molecular Liquids (2016), doi: 10.1016/j.molliq.2016.09.083
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Water mass flow rate in a finite SWCNT under electric charge: A molecular
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dynamic simulation
Department of Aerospace Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, 15875-4413, Iran
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H. R. Abbasi, 1 S. M. H. Karimian,1, a
In this paper, behavior of water flow in single-walled carbon nanotube (SWCNT) under electric charge is investigated using molecular dynamics simulation. It is shown that electric charging of SWCNT causes water flow to exhibit surprising
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behavior. Among water flow parameters, flow rate or flux of water molecules is of special interest. The two governing phenomena affecting flow rate in a SWCNT are resistance along the nanotube and resistance to flow at its entrance. In present study, effect of electric charging of SWCNT’s carbon molecules on these two phenomena is studied in detail in
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SWCNTs (5, 10) with 3nm, 5nm, and 7nm lengths. Charge magnitudes between zero to 1.0 e/atom are implemented along
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different lengths of nanotube. Charges are applied either constantly or stepwise. Based on the analysis of numerical results obtained in this paper, it is concluded that electric charging can be used to manipulate these two phenomena and therefore control the rate of water flow in a SWCNT very effectively.
I. INTRODUCTION*
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Keyword: carbon nanotube, water, electric charge, mass flow rate, flow control in membranes
Some investigations were concentrated on water transport through Carbon Nanotubes (CNT) due to its great applications.1-5 Many of these studies have illustrated that water transport in CNTs is considerably faster than what is expected when assuming continuum flow.3-5 Carbon nanotubes aligned in a membrane are utilized for sea water desalination, as one of their great applications.4,6 Although different techniques have been suggested to induce flow in nanotubes2 none of them use electric charging for this purpose. In this paper, molecular dynamics simulation is used to demonstrate the effect of electric charging of nanotube carbon atoms on flow of water molecules in CNTs. Numerous theoretical and experimental studies have been carried out to determine transport properties of water such as its slip length in CNTs1-3,5-18 . Inclusion of slip length effect in nano scale analysis increases velocity of water flow by 2 to 5 orders of magnitude in comparison to those predicted by continuum assumption.3,5,7 In 2001 Hummer et. al.1 showed that a)
Author to whom correspondence should be addressed. Electronic mail: [email protected].
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ACCEPTED MANUSCRIPT when a 0.81 nm diameter CNT is immersed in water, spontaneous transport of water occurs due to the high magnitude of slip velocity in CNT. However, this is if inlet and outlet effects of the CNT are not considered in the analysis. On the other hand, lower slip velocities are reported due to reduction in the channel averaged velocity for finite CNTs in comparison to the
parameter to determine whether the surface is hydrophobic or hydrophilic.9,20-25
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infinite ones.2 Other than slip velocity, contact angle of a droplet on the surface has been also reported as a governing
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Understanding properties of CNTs under electric charges are of great importance for their applications in water
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desalination6, drug delivery29, and hydrogen storage30. Studying charge effects on flow velocity and flow rate inside a CNT can play an important role in application of CNTs in new industrial fields such as electro-osmosis through CNTs31,32, and
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nano fluidic pumps33. Previous studies in this field include, charge effects in preferential ion and water intakes34, electric charge enhancements in carbon nanotubes 35, and density distribution patterns of water under charge effects 27. Also,
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Rikhtegaran et al.36 proposed a nanofilter consisting of a charged SWCNT, which can effectively remove some species from saline water. Xiao-Peng Li et al.37, have used rotating electric and magnetic field for pumping water. Some studies have used
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point charging to control and transport water molecules inside the CNT 38-41. Diannan Lu42 studied a charged CNT immersed
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in bulk water, and observed an acceleration of water molecules inside that. As reported in the literature3-5, carbon nanotubes are hydrophobic. In addition, diverse studies have shown that CNTs
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become hydrophilic by imposing electric charge on their surface.26-28 In present paper, this behavior of CNTs is studied in detail. Different magnitudes of electric charge are imposed on the surface of single-walled carbon nanotubes (SWCNT) with various lengths. Results showed that in some cases instead of reduction in flow velocity which is expected from the hydrophilic surface of a charged SWCNT, water flow rate was surprisingly increased. In this work, MD simulation is carried out to investigate how charged SWCNTs can affect velocity and mass flow rate of water molecules. Effect of parameters like charge value, length of nanotube, and the length of nanotube under electric charge are studied in this paper. Based on the present study interesting results are seen about the mass flow rate of water molecules passing through an electrically-charged finite CNT. It was observed that two main phenomena play important roles. First, the inlet effect which means that electric charging at the inlet of nanotube facilitates entering of water molecules into the nanotube. Second, resisting effect which means that electric charging along the nanotube will cause a resisting force against the flow of water molecules inside the nanotube. Knowledge about an effective technique to adjust and manipulate flow of water molecules will help us to explore its applications. Adjusting velocity and mass flow rate of water transport in SWCNTs by electric charge of nanotube is a superior approach in many aspects due to its ease of applicability.
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ACCEPTED MANUSCRIPT In the next section simulation methodology and solution conditions will be presented. Then the impact of electric charge on accelerating and decelerating water molecules in the SWCNT is illustrated in section 3. In this section different parameters such as charge magnitude, SWCNT's length, and positioning electric charge on different length are considered. Finally, a
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summary of our findings and conclusions are presented. II. SIMULATION METHODOLOGY
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All of MD simulations presented here are carried out using LAMMPS software43 which is a parallelized open source MD
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solver. In MD simulation, motions of molecules are governed by Newton’s second law. Water flow is studied in a SWCNT with chirality of (5,10), diameter of 10Å, and different lengths of 30Å, 50Å, 70Å. Periodic boundary conditions are imposed
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in x, y, and z directions. All the simulations are performed with NVT assumption, in which the temperature of the domain is set equal to 300K. In all of the simulations, time step of 0.5fs is used to precede solution towards the equilibrium state.
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For the sake of simplicity and computational cost reduction the SPC/E water model is used, which is a tetrahedral model with an OH bond length of 0.1nm and H–O–H angle of 109.478˚. Carbon–water interaction is represented by the Lennard-
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Jones (LJ) potential of Werder et al. 19, and SHAKE algorithm44 is used to make the model rigid by constraining bond lengths
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and angles. For oxygen atoms, short-range LJ potential with a cut-off distance of 1 nm is employed. Each hydrogen of water molecule has a charge of +1q (+0.4238e) which is compensated by charge of -2q (-0.8476e) on its oxygen atom. For long-
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range electrostatic interactions, a particle–particle particle-mesh (PPPM) solver is employed which can handle long-range interactions for periodic systems with slab geometries more efficiently. In this paper, we have used LJ potential for C-C, CO, C-H, O-O, and H-H19 with LJ parameters given in table I. TableI. Molecular interaction parameters utilized.
a
Molecular pair O-O
3.166
0.1553
-0.8476
H-H
2.058
0
+0.4238
C-C
-
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0 to +1a
C-O
3.19
0.09369
0
C-H
3.19
0
0
Carbon atom charges Imposed in this study
Each test case is simulated for 25ns through 50×106 time steps which each of them are equal to 0.5fs. In each simulation, initial equilibration period includes first 10 6 time steps that are equal to 0.5ns. During this period, no external force is applied. To maintain flow of water molecules in the SWCNT, force of 67.49pN is applied upward continuously to the water molecules from the end of equilibration period. As shown in Fig. 1, simulation domain consists of a SWCNT which has
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ACCEPTED MANUSCRIPT passed through graphite sheets at its two ends. These two graphite sheets which include 1460 carbon atoms force water molecules to move only through the SWCNT. In this study, flow of 343 water molecules pass through SWCNTs with lengths of 3, 5, and 7nm with 408, 688, and 968 carbon atoms, respectively. A SWCNT is divided into 8 equal bins along the flow
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direction. Properties of molecular flow then are averaged in each of these sampling bins to obtain local values. In cases where needed, average properties over the carbon nanotube can be obtained by averaging local flow properties in these 8 bins.
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Having defined solution domain, physics of the problem, boundary conditions, and numerical specifications of the solution
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procedure, results obtained in different test cases are introduced in the next section.
(a)
(b)
(c)
Figure1. (Color online) Solution domain consists a SWCNT (5, 10) colored brown which connects two reservoirs at its two ends denoted by two graphite surfaces colored green, a) with 7nm nanotube, b) with 5nm nanotube, and c) with 3nm nanotube
III. RESULTS AND DISCUSSION As it has been reported in the literature, carbon nanotube wall becomes hydrophilic under electric charge [19]. This variation of carbon nanotube behavior can change mass flow rate of water molecules in the nanotube. In this section, we would like to investigate in detail effect of electric charge on the mass flow rate of water molecules inside a finite nanotube. Authors numerical examination of several test cases indicated that magnitude of electric charge, charge distribution or type of charging along the carbon nanotube, and the length at which charging is applied, strongly affect the rate of water flow in SWCNTs. The goal of present study is to know how flow rate is affected by these parameters and consequently how it can be controlled by electric charging of SWCNT’s carbon atoms. First, effect of charge magnitude on
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ACCEPTED MANUSCRIPT mass flow rate is investigated. Test case geometry and its specifications were given in previous section. Water flow is simulated in a 3nm, 5nm, and 7nm length SWCNT under different charge magnitudes of 0.0, 0.1, 0.25, 0.5, 0.7, and 1.0e/atoms. Note that electric charge is implemented after 2.25ns from the beginning of the simulation all along the carbon
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nanotube. Arrangements of molecules in the simulation domain are shown in Fig.2 for two solution stages of, a) initial equilibrium, and b) after implementation of force field on water molecules and electric charge on carbon atoms. As seen in
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figure 2a, water molecules are distributed in the simulation domain at the equilibrium state. Implementation of force on the
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water molecules moves them in the force direction (upward here) and causes them to accumulate on one side (lower part here). As mentioned before, atoms of SWCNT become hydrophilic under electric charge. Therefore, the interaction between
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water molecules and carbon atoms increases all along the internal surface of SWCNT. This generates kind of resistance in the carbon nanotube and therefore decelerates water flow. Hydrophilic carbon molecules of SWCNT at the inlet, however soaks
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water molecules into the nanotube. This in contrast accelerates water flow at the inlet. This contradictory effect of accelerating and decelerating has shown itself in the results plotted in Fig.3. In order to examine that if this behavior is independent of nanotube length, results of water flow in SWCNTs with 3nm and 7nm lengths are reported in Fig.3, as well.
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Figure 3a demonstrates convergence of average flow velocity in a 5nm SWCNT for different electric charges. Average flow
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velocity is the average of water-molecule velocities along the nanotube. As seen, convergence has been reached after 5×107
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time steps in all of the cases. Variation of converged average velocity with charge magnitude is plotted in Fig.3b for three different lengths of nanotube. As it can be seen, flow velocity increases with charge magnitudes of 0.0 to 0.25e/atom, and then decreases with charge magnitudes of 0.25 to 1.0e/atom.
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(a (b) Figure2. Accumulation of water molecules in the 7nm SWCNT: a) solution domain equilibrium condition before imposing force field and electric charge, and b) simulation domain after imposing force field of 67.49pN on water molecules and charge of 0.25e on Carbon atoms
FIG.3a) Convergence of average velocity with time for different magnitudes of electric charge imposed to a 5nm SWCNT', and b) converged velocity versus charge magnitude for different lengths of nanotube
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molecules along the inner surface of the SWCNT. As a result, water molecules flow easily. This is why average flow velocity in an uncharged nanotube can reach values 4 to 5 times the flow velocity in a nanotube in which continuum assumption is
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made3,5,7. Hydrophobic nature of SWCNT is also the cause of a resistance at the inlet which prevents water molecules to enter
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the SWCNT easily; for more details see Ref. 2. As mentioned before, electric charging of carbon atoms makes carbon nanotube to behave hydrophilic. Due to this behavior, water molecules are pulled toward the carbon atoms of SWCNT. We
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believe that this reduces the resistance in the inlet and improves entrance condition since water molecules are pulled in by carbon atoms of SWCNT at the inlet. Inside the SWCNT, however water molecules will move along the SWCNT but more
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closer to its wall. Therefore, water molecules move with higher resistant force and consequently with lower average flow velocity.
We believe that for electric charges less than +0.25e/atom positive effect of hydrophilicity in the SWCNT’s entrance is
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dominant and consequently average flow velocity increases in the SWCNT. For electric charges more than +0.25e/atom negative effect of hydrophilicity along the SWCNT becomes stronger and therefore average flow velocity starts to decrease.
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As seen in Fig.3b, this continues until electric charge of about +0.65e/atom where two effects diffuse each other and average flow velocity becomes approximately equal to its value with zero electric charge. For electric charges more than +0.65e/atom negative effect of hydrophilicity along the SWCNT becomes dominant and therefore average flow velocity decrease notably. Having compared results of different SWCNT lengths in Fig.3b, it can be seen that due to the length increase from 3nm to 5nm average flow velocity starts a steeper decrease at a charge of 0.5e/atom. In the 7nm length SWCNT where effect of lower slip velocity or resistance type effect of hydrophilicity becomes larger, average flow velocity decreases after charges larger than 0.25e/atom. Variation of number density and mass flow rate with electric charge are analyzed as well to demonstrate that the above reasoning is acceptable. Number density is defined as the number of water molecules per volume (1/A 3). Converged values of number density versus charge magnitude is plotted in Fig.4 for different lengths of SWCNTs. As shown in this figure, number density of water molecules increases continuously with charge magnitudes of 0 to 0.25 e/atoms. We believe that this is the positive effect of electric charging of carbon nanotube on resistance reduction at the inlet. In the 7nm-length SWCNT, the so called resistance effect along the nanotube introduced earlier, becomes dominant. As a result, mass flow rate and consequently number density decreases. Such behavior is not seen in the 3nm-length SWCNT. This obviously is because the resistance along the nanotube
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ACCEPTED MANUSCRIPT is lower since its length is less than 7nm. We believe that in a 5nm-length SWCNT, the two so-called positive and negative effects of electric charge have balanced each other for electric charges more than 0.25 e/atoms. Mass flow rate is equal to multiplication of density, cross sectional area, and velocity. For SWCNTs with lengths of
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3nm, 5nm, and 7nm under different electric charges, mass flow rate is plotted in Fig.5. According to the analysis presented before regarding velocity and number density, it is not a surprise to see that maximum mass flow rate occurs at electric
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charge of 0.25e/atom in all three SWCNTs. In short, flow rate increases where the effect of electric charge at the inlet is
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dominant, and decreases where the effect of electric charge along the nanotube is dominant. For the sake of clarity, all results
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of mass flow rates here and after are presented in Tables 1 and 2, as well.
FIG.4 Converged values of number density versus charge magnitude for different lengths of nanotubes
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FIG.5 Molecular mass flow rate versus electric charge magnitude in SWCNT swith different lengths
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In order to distinguish between these two effects in SWCNTs and demonstrate each effect independently, electric charge is applied only to the first 1nm of the SWCNT in the inlet. Therefore it is expected to see only the positive effect of charging at the nanotube inlet on the mass flow rate. The mass flow rate versus charge magnitude is plotted in Fig.6, and its data are given in last row of Table 1. As seen, the mass flow rate increases continuously with charge magnitude, and reaches to at a charge of 1e/atom. Note that increase of mass flow rate up to charge of 0.25e/atom is steeper than that after charge of 0.25e/atom. In this test case carbon atoms along the remained 4nm of the SWCNT are not charged and therefore they did not become hydrophilic to cause resistance type effect. The mass flow rate for different electric charges imposed all along the SWCNT is repeated in Fig.6 for comparison purpose. Table 1: Mass flow rates in SWCNT for different charge magnitudes ( SWCNT length 3nm 5nm 7nm 5nm
type of charging all along the nanotube all along the nanotube all along the nanotube in the first 1nm from the inlet
0.0
0.10
3.41 2.56 2.96 2.56
7.66 7.17 6.86 5.47
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)
charge magnitude (e/atom) 0.25 0.50
11.32 11.16 8.58 8.5
10.62 9.94 8.57 10.45
0.70
1.0
8.57 6.91 5.22 11.63
5.03 1.97 0.92 13.02
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FIG.6 Mass flow rate of water molecules in a 5nm length SWCNT with different charge magnitudes: ▲) Imposed at the inlet on the first 1nm of the SWCNT, ■) Imposed all along the nanotube.
Since it was shown that electric charging in the 1 st 1nm of SWCNT effectively increases water mass flow rate, here we
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would like to examine the effect of length of SWCNT at which electric charge is applied. Therefore in the next test case
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charge of 0.25e/atom is applied to different lengths of the 5nm length nanotube from the inlet; i.e. along the 1nm, 2nm, 3nm,
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4nm, or 5nm from the inlet. Results are plotted in Fig.7 and its data are given in table 2. As it can be seen, implementation of 0.25e/atom electric charge along the 1nm of the nanotube from the inlet has caused mass flow rate to increase from to
, and then to
when this electric charge is applied along the first 2nm of
the nanotube. Note that extension of charge length to 3nm and 4nm do increase the mass flow rate, but not as much as it increases mass flow rate for charging along 1nm and 2nm lengths from the inlet. This is obviously because when longer length of nanotube is charged more carbon atoms cause resistance type effect in the flow field. As expected mass flow rate drops when the whole carbon nanotube is charged. In Fig.7 and table 2 same results are presented for a charge of 0.50e/atom. In this case mass flow rate increases to values higher than those in the 0.25e/atom case, but drops to a lower value when the whole carbon nanotube is charged. In comparison to the 0.25e/atom case, maximum mass flow rate occurs sooner when charge is applied along the 2nm of the SWCNT. Higher electric charging of 0.5e/atom agitates both effects of SWCNT charging introduced in this paper. Due to the positive effect of electric charging in the inlet, mass flow rate reaches to higher values, but due to the negative effect of charging along the carbon nanotube it soon starts to drop. This describes that why maximum of mass flow rate occurs at lower charge lengths for higher charge magnitudes.
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FIG.7 Mass flow rate of water molecules in a 5nm length SWCNT with charges imposed on different lengths of SWCNT from the inlet: ■) with electric charge of 0.25e/atom, ▲) with electric charge of 0.25e/atom.
Table 2: Mass flow rates in 5nm length SWCNT for different charge lengths ( 2nm
3nm
4nm
5nm Whole SWCNT
10.85 13.34
11.16 13.23 2.56
12.03 13.02
11.11 9.91
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1nm
8.5 10.45
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0.25 e/atom 0.50 e/atom 0.0 e/atom
)
charged length from the inlet
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charge magnitude (e/atom) -
0.25e/atom along first 1nm
charged magnitude and its length 0.20e/atom 0.15e/atom 0.10e/atom along 2nd along 3rd along 4th 1nm 1nm 1nm
0.05e/atom along 5th 1nm
Step-wise charging
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Results presented in this section and their analysis show that electric charging of nanotube’s carbon atoms can be used to easily manipulate flow of water molecules in SWCNTs. IV. CONCLUSION* It can be concluded that charging of a finite SWCNT affects water mass flow rate or its velocity inside the nanotube very significantly. The results which were presented here showed that electric charging up to a specific magnitude of 0.25e/atom, in cases studied here, increases mass flow rate unexpectedly but beyond this magnitude it starts to decrease the mass flow rate. Regarding this unusual behavior, we believe that this is due to the effect of two counter acting phenomena, i.e. reduction of resistance to flow at the entrance and increase of resistance to flow along the nanotube. In order to distinguish between
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the nanotube from the inlet increased mass flow rate successively, although the rate of increase was higher for charging of 1nm and 2nm lengths from the inlet. This is obviously because when longer length of nanotube is charged more carbon atoms
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along the nanotube causes resistance type effect in the flow field. Therefore, it was concluded that electric charging of a CNT
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can affect water mass flow rate through these two mechanisms. This can be used easily to manage flow rate of water in
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nanotubes and change water mass flow rate to desired one transiently.
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ACCEPTED MANUSCRIPT Highlights
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The behavior of water flow in a finite SWCNT under electric charge is investigated. The resistance along and at the entrance of the nanotube play an important role. These two phenomena can be manipulated to control the rate of water flow in a SWCNT.
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The flow rate of water in a charged SWCNT was increased 5 times the neutral one.
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S0167-7322(16)30178-7 doi: 10.1016/j.molliq.2016.09.083 MOLLIQ 6360
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
21 January 2016 1 September 2016 12 September 2016
Please cite this article as: H.R. Abbasi, S.M.H. Karimian, Water mass flow rate in a finite SWCNT under electric charge: A molecular dynamic simulation, Journal of Molecular Liquids (2016), doi: 10.1016/j.molliq.2016.09.083
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Water mass flow rate in a finite SWCNT under electric charge: A molecular
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dynamic simulation
Department of Aerospace Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, 15875-4413, Iran
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H. R. Abbasi, 1 S. M. H. Karimian,1, a
In this paper, behavior of water flow in single-walled carbon nanotube (SWCNT) under electric charge is investigated using molecular dynamics simulation. It is shown that electric charging of SWCNT causes water flow to exhibit surprising
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behavior. Among water flow parameters, flow rate or flux of water molecules is of special interest. The two governing phenomena affecting flow rate in a SWCNT are resistance along the nanotube and resistance to flow at its entrance. In present study, effect of electric charging of SWCNT’s carbon molecules on these two phenomena is studied in detail in
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SWCNTs (5, 10) with 3nm, 5nm, and 7nm lengths. Charge magnitudes between zero to 1.0 e/atom are implemented along
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different lengths of nanotube. Charges are applied either constantly or stepwise. Based on the analysis of numerical results obtained in this paper, it is concluded that electric charging can be used to manipulate these two phenomena and therefore control the rate of water flow in a SWCNT very effectively.
I. INTRODUCTION*
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Keyword: carbon nanotube, water, electric charge, mass flow rate, flow control in membranes
Some investigations were concentrated on water transport through Carbon Nanotubes (CNT) due to its great applications.1-5 Many of these studies have illustrated that water transport in CNTs is considerably faster than what is expected when assuming continuum flow.3-5 Carbon nanotubes aligned in a membrane are utilized for sea water desalination, as one of their great applications.4,6 Although different techniques have been suggested to induce flow in nanotubes2 none of them use electric charging for this purpose. In this paper, molecular dynamics simulation is used to demonstrate the effect of electric charging of nanotube carbon atoms on flow of water molecules in CNTs. Numerous theoretical and experimental studies have been carried out to determine transport properties of water such as its slip length in CNTs1-3,5-18 . Inclusion of slip length effect in nano scale analysis increases velocity of water flow by 2 to 5 orders of magnitude in comparison to those predicted by continuum assumption.3,5,7 In 2001 Hummer et. al.1 showed that a)
Author to whom correspondence should be addressed. Electronic mail: [email protected].
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ACCEPTED MANUSCRIPT when a 0.81 nm diameter CNT is immersed in water, spontaneous transport of water occurs due to the high magnitude of slip velocity in CNT. However, this is if inlet and outlet effects of the CNT are not considered in the analysis. On the other hand, lower slip velocities are reported due to reduction in the channel averaged velocity for finite CNTs in comparison to the
parameter to determine whether the surface is hydrophobic or hydrophilic.9,20-25
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infinite ones.2 Other than slip velocity, contact angle of a droplet on the surface has been also reported as a governing
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Understanding properties of CNTs under electric charges are of great importance for their applications in water
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desalination6, drug delivery29, and hydrogen storage30. Studying charge effects on flow velocity and flow rate inside a CNT can play an important role in application of CNTs in new industrial fields such as electro-osmosis through CNTs31,32, and
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nano fluidic pumps33. Previous studies in this field include, charge effects in preferential ion and water intakes34, electric charge enhancements in carbon nanotubes 35, and density distribution patterns of water under charge effects 27. Also,
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Rikhtegaran et al.36 proposed a nanofilter consisting of a charged SWCNT, which can effectively remove some species from saline water. Xiao-Peng Li et al.37, have used rotating electric and magnetic field for pumping water. Some studies have used
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point charging to control and transport water molecules inside the CNT 38-41. Diannan Lu42 studied a charged CNT immersed
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in bulk water, and observed an acceleration of water molecules inside that. As reported in the literature3-5, carbon nanotubes are hydrophobic. In addition, diverse studies have shown that CNTs
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become hydrophilic by imposing electric charge on their surface.26-28 In present paper, this behavior of CNTs is studied in detail. Different magnitudes of electric charge are imposed on the surface of single-walled carbon nanotubes (SWCNT) with various lengths. Results showed that in some cases instead of reduction in flow velocity which is expected from the hydrophilic surface of a charged SWCNT, water flow rate was surprisingly increased. In this work, MD simulation is carried out to investigate how charged SWCNTs can affect velocity and mass flow rate of water molecules. Effect of parameters like charge value, length of nanotube, and the length of nanotube under electric charge are studied in this paper. Based on the present study interesting results are seen about the mass flow rate of water molecules passing through an electrically-charged finite CNT. It was observed that two main phenomena play important roles. First, the inlet effect which means that electric charging at the inlet of nanotube facilitates entering of water molecules into the nanotube. Second, resisting effect which means that electric charging along the nanotube will cause a resisting force against the flow of water molecules inside the nanotube. Knowledge about an effective technique to adjust and manipulate flow of water molecules will help us to explore its applications. Adjusting velocity and mass flow rate of water transport in SWCNTs by electric charge of nanotube is a superior approach in many aspects due to its ease of applicability.
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ACCEPTED MANUSCRIPT In the next section simulation methodology and solution conditions will be presented. Then the impact of electric charge on accelerating and decelerating water molecules in the SWCNT is illustrated in section 3. In this section different parameters such as charge magnitude, SWCNT's length, and positioning electric charge on different length are considered. Finally, a
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summary of our findings and conclusions are presented. II. SIMULATION METHODOLOGY
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All of MD simulations presented here are carried out using LAMMPS software43 which is a parallelized open source MD
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solver. In MD simulation, motions of molecules are governed by Newton’s second law. Water flow is studied in a SWCNT with chirality of (5,10), diameter of 10Å, and different lengths of 30Å, 50Å, 70Å. Periodic boundary conditions are imposed
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in x, y, and z directions. All the simulations are performed with NVT assumption, in which the temperature of the domain is set equal to 300K. In all of the simulations, time step of 0.5fs is used to precede solution towards the equilibrium state.
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For the sake of simplicity and computational cost reduction the SPC/E water model is used, which is a tetrahedral model with an OH bond length of 0.1nm and H–O–H angle of 109.478˚. Carbon–water interaction is represented by the Lennard-
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Jones (LJ) potential of Werder et al. 19, and SHAKE algorithm44 is used to make the model rigid by constraining bond lengths
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and angles. For oxygen atoms, short-range LJ potential with a cut-off distance of 1 nm is employed. Each hydrogen of water molecule has a charge of +1q (+0.4238e) which is compensated by charge of -2q (-0.8476e) on its oxygen atom. For long-
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range electrostatic interactions, a particle–particle particle-mesh (PPPM) solver is employed which can handle long-range interactions for periodic systems with slab geometries more efficiently. In this paper, we have used LJ potential for C-C, CO, C-H, O-O, and H-H19 with LJ parameters given in table I. TableI. Molecular interaction parameters utilized.
a
Molecular pair O-O
3.166
0.1553
-0.8476
H-H
2.058
0
+0.4238
C-C
-
-
0 to +1a
C-O
3.19
0.09369
0
C-H
3.19
0
0
Carbon atom charges Imposed in this study
Each test case is simulated for 25ns through 50×106 time steps which each of them are equal to 0.5fs. In each simulation, initial equilibration period includes first 10 6 time steps that are equal to 0.5ns. During this period, no external force is applied. To maintain flow of water molecules in the SWCNT, force of 67.49pN is applied upward continuously to the water molecules from the end of equilibration period. As shown in Fig. 1, simulation domain consists of a SWCNT which has
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ACCEPTED MANUSCRIPT passed through graphite sheets at its two ends. These two graphite sheets which include 1460 carbon atoms force water molecules to move only through the SWCNT. In this study, flow of 343 water molecules pass through SWCNTs with lengths of 3, 5, and 7nm with 408, 688, and 968 carbon atoms, respectively. A SWCNT is divided into 8 equal bins along the flow
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direction. Properties of molecular flow then are averaged in each of these sampling bins to obtain local values. In cases where needed, average properties over the carbon nanotube can be obtained by averaging local flow properties in these 8 bins.
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Having defined solution domain, physics of the problem, boundary conditions, and numerical specifications of the solution
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procedure, results obtained in different test cases are introduced in the next section.
(a)
(b)
(c)
Figure1. (Color online) Solution domain consists a SWCNT (5, 10) colored brown which connects two reservoirs at its two ends denoted by two graphite surfaces colored green, a) with 7nm nanotube, b) with 5nm nanotube, and c) with 3nm nanotube
III. RESULTS AND DISCUSSION As it has been reported in the literature, carbon nanotube wall becomes hydrophilic under electric charge [19]. This variation of carbon nanotube behavior can change mass flow rate of water molecules in the nanotube. In this section, we would like to investigate in detail effect of electric charge on the mass flow rate of water molecules inside a finite nanotube. Authors numerical examination of several test cases indicated that magnitude of electric charge, charge distribution or type of charging along the carbon nanotube, and the length at which charging is applied, strongly affect the rate of water flow in SWCNTs. The goal of present study is to know how flow rate is affected by these parameters and consequently how it can be controlled by electric charging of SWCNT’s carbon atoms. First, effect of charge magnitude on
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ACCEPTED MANUSCRIPT mass flow rate is investigated. Test case geometry and its specifications were given in previous section. Water flow is simulated in a 3nm, 5nm, and 7nm length SWCNT under different charge magnitudes of 0.0, 0.1, 0.25, 0.5, 0.7, and 1.0e/atoms. Note that electric charge is implemented after 2.25ns from the beginning of the simulation all along the carbon
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nanotube. Arrangements of molecules in the simulation domain are shown in Fig.2 for two solution stages of, a) initial equilibrium, and b) after implementation of force field on water molecules and electric charge on carbon atoms. As seen in
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figure 2a, water molecules are distributed in the simulation domain at the equilibrium state. Implementation of force on the
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water molecules moves them in the force direction (upward here) and causes them to accumulate on one side (lower part here). As mentioned before, atoms of SWCNT become hydrophilic under electric charge. Therefore, the interaction between
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water molecules and carbon atoms increases all along the internal surface of SWCNT. This generates kind of resistance in the carbon nanotube and therefore decelerates water flow. Hydrophilic carbon molecules of SWCNT at the inlet, however soaks
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water molecules into the nanotube. This in contrast accelerates water flow at the inlet. This contradictory effect of accelerating and decelerating has shown itself in the results plotted in Fig.3. In order to examine that if this behavior is independent of nanotube length, results of water flow in SWCNTs with 3nm and 7nm lengths are reported in Fig.3, as well.
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Figure 3a demonstrates convergence of average flow velocity in a 5nm SWCNT for different electric charges. Average flow
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velocity is the average of water-molecule velocities along the nanotube. As seen, convergence has been reached after 5×107
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time steps in all of the cases. Variation of converged average velocity with charge magnitude is plotted in Fig.3b for three different lengths of nanotube. As it can be seen, flow velocity increases with charge magnitudes of 0.0 to 0.25e/atom, and then decreases with charge magnitudes of 0.25 to 1.0e/atom.
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(a (b) Figure2. Accumulation of water molecules in the 7nm SWCNT: a) solution domain equilibrium condition before imposing force field and electric charge, and b) simulation domain after imposing force field of 67.49pN on water molecules and charge of 0.25e on Carbon atoms
FIG.3a) Convergence of average velocity with time for different magnitudes of electric charge imposed to a 5nm SWCNT', and b) converged velocity versus charge magnitude for different lengths of nanotube
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ACCEPTED MANUSCRIPT As seen in Fig.3b, highest average velocity of flow occurs with electric charge of 0.25e/atom. In addition, at electric charge of 0.65e/atom average velocity becomes approximately equal to its value with zero electric charging. We know that hydrophobic nature of an uncharged SWCNT causes water molecules to move with lower resistant force in front of the water
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molecules along the inner surface of the SWCNT. As a result, water molecules flow easily. This is why average flow velocity in an uncharged nanotube can reach values 4 to 5 times the flow velocity in a nanotube in which continuum assumption is
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made3,5,7. Hydrophobic nature of SWCNT is also the cause of a resistance at the inlet which prevents water molecules to enter
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the SWCNT easily; for more details see Ref. 2. As mentioned before, electric charging of carbon atoms makes carbon nanotube to behave hydrophilic. Due to this behavior, water molecules are pulled toward the carbon atoms of SWCNT. We
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believe that this reduces the resistance in the inlet and improves entrance condition since water molecules are pulled in by carbon atoms of SWCNT at the inlet. Inside the SWCNT, however water molecules will move along the SWCNT but more
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closer to its wall. Therefore, water molecules move with higher resistant force and consequently with lower average flow velocity.
We believe that for electric charges less than +0.25e/atom positive effect of hydrophilicity in the SWCNT’s entrance is
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dominant and consequently average flow velocity increases in the SWCNT. For electric charges more than +0.25e/atom negative effect of hydrophilicity along the SWCNT becomes stronger and therefore average flow velocity starts to decrease.
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As seen in Fig.3b, this continues until electric charge of about +0.65e/atom where two effects diffuse each other and average flow velocity becomes approximately equal to its value with zero electric charge. For electric charges more than +0.65e/atom negative effect of hydrophilicity along the SWCNT becomes dominant and therefore average flow velocity decrease notably. Having compared results of different SWCNT lengths in Fig.3b, it can be seen that due to the length increase from 3nm to 5nm average flow velocity starts a steeper decrease at a charge of 0.5e/atom. In the 7nm length SWCNT where effect of lower slip velocity or resistance type effect of hydrophilicity becomes larger, average flow velocity decreases after charges larger than 0.25e/atom. Variation of number density and mass flow rate with electric charge are analyzed as well to demonstrate that the above reasoning is acceptable. Number density is defined as the number of water molecules per volume (1/A 3). Converged values of number density versus charge magnitude is plotted in Fig.4 for different lengths of SWCNTs. As shown in this figure, number density of water molecules increases continuously with charge magnitudes of 0 to 0.25 e/atoms. We believe that this is the positive effect of electric charging of carbon nanotube on resistance reduction at the inlet. In the 7nm-length SWCNT, the so called resistance effect along the nanotube introduced earlier, becomes dominant. As a result, mass flow rate and consequently number density decreases. Such behavior is not seen in the 3nm-length SWCNT. This obviously is because the resistance along the nanotube
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ACCEPTED MANUSCRIPT is lower since its length is less than 7nm. We believe that in a 5nm-length SWCNT, the two so-called positive and negative effects of electric charge have balanced each other for electric charges more than 0.25 e/atoms. Mass flow rate is equal to multiplication of density, cross sectional area, and velocity. For SWCNTs with lengths of
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3nm, 5nm, and 7nm under different electric charges, mass flow rate is plotted in Fig.5. According to the analysis presented before regarding velocity and number density, it is not a surprise to see that maximum mass flow rate occurs at electric
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charge of 0.25e/atom in all three SWCNTs. In short, flow rate increases where the effect of electric charge at the inlet is
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dominant, and decreases where the effect of electric charge along the nanotube is dominant. For the sake of clarity, all results
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of mass flow rates here and after are presented in Tables 1 and 2, as well.
FIG.4 Converged values of number density versus charge magnitude for different lengths of nanotubes
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FIG.5 Molecular mass flow rate versus electric charge magnitude in SWCNT swith different lengths
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In order to distinguish between these two effects in SWCNTs and demonstrate each effect independently, electric charge is applied only to the first 1nm of the SWCNT in the inlet. Therefore it is expected to see only the positive effect of charging at the nanotube inlet on the mass flow rate. The mass flow rate versus charge magnitude is plotted in Fig.6, and its data are given in last row of Table 1. As seen, the mass flow rate increases continuously with charge magnitude, and reaches to at a charge of 1e/atom. Note that increase of mass flow rate up to charge of 0.25e/atom is steeper than that after charge of 0.25e/atom. In this test case carbon atoms along the remained 4nm of the SWCNT are not charged and therefore they did not become hydrophilic to cause resistance type effect. The mass flow rate for different electric charges imposed all along the SWCNT is repeated in Fig.6 for comparison purpose. Table 1: Mass flow rates in SWCNT for different charge magnitudes ( SWCNT length 3nm 5nm 7nm 5nm
type of charging all along the nanotube all along the nanotube all along the nanotube in the first 1nm from the inlet
0.0
0.10
3.41 2.56 2.96 2.56
7.66 7.17 6.86 5.47
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)
charge magnitude (e/atom) 0.25 0.50
11.32 11.16 8.58 8.5
10.62 9.94 8.57 10.45
0.70
1.0
8.57 6.91 5.22 11.63
5.03 1.97 0.92 13.02
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FIG.6 Mass flow rate of water molecules in a 5nm length SWCNT with different charge magnitudes: ▲) Imposed at the inlet on the first 1nm of the SWCNT, ■) Imposed all along the nanotube.
Since it was shown that electric charging in the 1 st 1nm of SWCNT effectively increases water mass flow rate, here we
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would like to examine the effect of length of SWCNT at which electric charge is applied. Therefore in the next test case
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charge of 0.25e/atom is applied to different lengths of the 5nm length nanotube from the inlet; i.e. along the 1nm, 2nm, 3nm,
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4nm, or 5nm from the inlet. Results are plotted in Fig.7 and its data are given in table 2. As it can be seen, implementation of 0.25e/atom electric charge along the 1nm of the nanotube from the inlet has caused mass flow rate to increase from to
, and then to
when this electric charge is applied along the first 2nm of
the nanotube. Note that extension of charge length to 3nm and 4nm do increase the mass flow rate, but not as much as it increases mass flow rate for charging along 1nm and 2nm lengths from the inlet. This is obviously because when longer length of nanotube is charged more carbon atoms cause resistance type effect in the flow field. As expected mass flow rate drops when the whole carbon nanotube is charged. In Fig.7 and table 2 same results are presented for a charge of 0.50e/atom. In this case mass flow rate increases to values higher than those in the 0.25e/atom case, but drops to a lower value when the whole carbon nanotube is charged. In comparison to the 0.25e/atom case, maximum mass flow rate occurs sooner when charge is applied along the 2nm of the SWCNT. Higher electric charging of 0.5e/atom agitates both effects of SWCNT charging introduced in this paper. Due to the positive effect of electric charging in the inlet, mass flow rate reaches to higher values, but due to the negative effect of charging along the carbon nanotube it soon starts to drop. This describes that why maximum of mass flow rate occurs at lower charge lengths for higher charge magnitudes.
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FIG.7 Mass flow rate of water molecules in a 5nm length SWCNT with charges imposed on different lengths of SWCNT from the inlet: ■) with electric charge of 0.25e/atom, ▲) with electric charge of 0.25e/atom.
Table 2: Mass flow rates in 5nm length SWCNT for different charge lengths ( 2nm
3nm
4nm
5nm Whole SWCNT
10.85 13.34
11.16 13.23 2.56
12.03 13.02
11.11 9.91
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1nm
8.5 10.45
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0.25 e/atom 0.50 e/atom 0.0 e/atom
)
charged length from the inlet
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charge magnitude (e/atom) -
0.25e/atom along first 1nm
charged magnitude and its length 0.20e/atom 0.15e/atom 0.10e/atom along 2nd along 3rd along 4th 1nm 1nm 1nm
0.05e/atom along 5th 1nm
Step-wise charging
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Results presented in this section and their analysis show that electric charging of nanotube’s carbon atoms can be used to easily manipulate flow of water molecules in SWCNTs. IV. CONCLUSION* It can be concluded that charging of a finite SWCNT affects water mass flow rate or its velocity inside the nanotube very significantly. The results which were presented here showed that electric charging up to a specific magnitude of 0.25e/atom, in cases studied here, increases mass flow rate unexpectedly but beyond this magnitude it starts to decrease the mass flow rate. Regarding this unusual behavior, we believe that this is due to the effect of two counter acting phenomena, i.e. reduction of resistance to flow at the entrance and increase of resistance to flow along the nanotube. In order to distinguish between
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the nanotube from the inlet increased mass flow rate successively, although the rate of increase was higher for charging of 1nm and 2nm lengths from the inlet. This is obviously because when longer length of nanotube is charged more carbon atoms
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along the nanotube causes resistance type effect in the flow field. Therefore, it was concluded that electric charging of a CNT
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can affect water mass flow rate through these two mechanisms. This can be used easily to manage flow rate of water in
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nanotubes and change water mass flow rate to desired one transiently.
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ACCEPTED MANUSCRIPT Highlights
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The behavior of water flow in a finite SWCNT under electric charge is investigated. The resistance along and at the entrance of the nanotube play an important role. These two phenomena can be manipulated to control the rate of water flow in a SWCNT.
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The flow rate of water in a charged SWCNT was increased 5 times the neutral one.
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