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ABSTRACT

Direct generation of measurable voltages and currents is possible when a fluids flows over a variety of solids even at the modest speed of a few meters per second. In case of gases underlying mechanism is an interesting interplay of Bernoulli's principle and the Seebeck effect: Pressure differences along streamlines give rise to temperature differences across the sample; these in turn produce the measured voltage. The electrical signal is quadratically dependent on the Mach number M and proportional to the Seebeck coefficient of the solids. This discovery was made by professor Ajay sood and his student Shankar Gosh of IISC Bangalore, they had previously discovered that the flow of liquids, even at low speeds ranging from 10 -1

metre/second to 10-7 m/s (that is, over six orders of magnitude), through bundles of atomic-scale straw-like tubes of carbon known as nanotubes, generated tens of micro volts across the tubes in the direction of the flow of the liquid.

Results of experiment done by Professor Sood and Ghosh show that gas flaw sensors and energy conversion devices can be constructed based on direct generation of electrical signals. The experiment was done on single wall carbon naontubes (SWNT).These effect is not confined to naotubes alone these are also observed in doped semiconductors and metals.

The observed effect immediately suggests the following technology application, namely gas flow sensors to measure gas velocities from the electrical signal generated. Unlike the existing gas flow sensors, which are based on heat transfer mechanisms from an electrically heated sensor to the fluid, a device based on this newly discovered effect would be an active gas flow sensor that gives a direct electrical response to the gas flow. One of the possible applications can be in the field of aerodynamics; several local sensors could be mounted on the aircraft body or aerofoil to measure streamline velocities and the effect of drag forces.

Energy conversion devices can be constructed based on direct generation of electrical signals i.e. if one is able to cascade millions these tubes electric energy can be produced.

1. INTRODUCTION

As the state of art moves towards the atomic scales, sensing presents a major hurdle. The discovery of carbon nanotubes by Sujio Iijima at NEC, Japan in 1991 has provided new channels towards this end.

A carbon nanotube (CNT) is a sheet of graphene which has been rolled up and capped with fullerenes at the end. The nanotubes are exceptionally strong, have excellent thermal conductivity, are chemically inert and have interesting electronic properties which depend on its chirality.

The main reason for the popularity of the CNTs is their unique properties. Nanotubes are very strong, mechanically robust, and have a high Young’s modulus and aspect ratio. These properties have been studied experimentally as well as using

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numerical tools. Bandgap of CNTs is in the range of 0~100 meV, and hence they can behave as both metals and semiconductors. A lot of factors like the presence of a chemical species, mechanical deformation and magnetic field can cause significant changes in the band gap, which consequently affect the conductance of the CNTs. Its unique electronic properties coupled with its strong mechanical strength are exploited as various sensors. And now with the discovery of a new property of flow induced voltage exhibited by nanotubes discovered by two Indian scientists recently, has added another dimension to micro sensing devices.

2. CNT STRUCTURE AND GENERAL PROPERTIES

There are two main types of nanotubes that can have high structural perfection. Single walled nanotubes (SWNTs) consist of a single graphite sheet seamlessly wrapped into a cylindrical tube (Fig. 1, A to D). Multiwalled nanotubes (MWNTs) comprise an array of such nanotubes that are concentrically nested like rings of a tree trunk (Fig. 1, E).

Fig.1 : Schematic representation of structures of carbon nanotubes (A, A1) armchair, (B, B1) Zigzag and (C, C1) Chiral SWNTs. Projections normal to the tube axis and perspective views along the tube axis are on the top and bottom, respectively. (D) Tunneling electron microscope image. (E) Transmission electron microscope (TEM) image of a MWNT containing a concentrically nested array of nine SWNTs.

The structure of a nanotube can be defined using a roll-up vector r and/or a chiral angle θ as shown in Fig. 2. The rollup vector can be defined as a linear combination of base vectors a and b of the basic hexagon r = na + mb with m and n being integers. The roll-up vector is perpendicular to the axis of the nanotube. In Fig. 2, the shaded zone is the area which is rolled up along an axis perpendicular to the roll-up vector. Different types of nanotubes are defined by the values of m and n thus chosen. Three major categories of nanotube structures can be identified based on the values of m and n:

m = n “Armchair”

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m = 0 orn = 0 “Zigzag”m ≠ n “Chiral”

C.

Fig 2: Relation between the hexagonal carbon lattice and the chirality of Carbon Nanotubes. (A) The construction of a carbon nanotube from a single graphene sheet. By rolling up the sheet along the wrapping vector C, that is, such that the origin (0, 0) coincides with point C, nanotube is formed. Wrapping vectors along the dotted lines lead to tubes that are zigzag or armchair. All other wrapping angles lead to chiral tubes whose wrapping angle is specified relative to either the zigzag direction (q ) or to the armchair direction (F= 30 ْ - q ). Dashed lines are perpendicular to C and run in the direction of the tube axis indicated by vector T. The solid vector H is perpendicular to the armchair direction and specifies the direction of nearest-neighbor hexagon rows indicated by the black dots. The angle between T and H is the chiral angle F. ( B ) Schematic of a two-dimensional graphene sheet illustrating lattice vectors a1 and a2, and the roll-up vector Ch = na + mb. The limiting cases of (n, 0) zigzag and (n, n) armchair tubes are indicated with dashed lines. As represented here, the angle between the zigzag configuration and Ch is negative.(C) Chiral nanotube showing angle F.

The electronic properties of perfect MWNTs are rather similar to those of perfect SWNTs, because the coupling between the cylinders is weak in MWNTs. Because of the nearly one-dimensional electronic structure, electronic transport in

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metallic SWNTs and MWNTs occurs ballistically (i.e., without scattering) over long nanotube lengths, enabling them to carry high currents with essentially no heating. Phonons also propagate easily along the nanotube: The measured room temperature thermal conductivity for an individual MWNT (3000 W/m K) is greater than that of natural diamond and the basal plane of graphite (both 2000 W/m K). Superconductivity has also been observed, but only at low temperatures, with transition temperatures of 0.55 K for 1.4-nm-diameter SWNTs and 5 K for 0.5-nm-diameter SWNTs grown in zeolites. Small-diameter SWNTs are quite stiff and exceptionally strong, meaning that they have a high Young’s modulus and high tensile strength. With the total area per nanotube in a nanotube bundle for normalizing the applied force to obtain the applied stress, the calculated Young’s modulus for an individual nanotube is 0.64 TPa, which is consistent with measurements. Because small-diameter nanotube ropes have been extended elastically by5.8% before breaking, the SWNT strength calculated from the product of this strain and modulus is 37 GPa, which is close to the maximum strength of silicon carbide nanorods (53 GPa) This modulus of 0.64 TPa is about the same as that of silicon carbide nanofibers (0.66 TPa) but lower than that of highly oriented pyrolytic graphite (1.06 TPa).

More impressive and important for applications needing light structural materials, the density-normalized modulus and strength of this typical SWNT are, respectively,19 and 56 times that of steel wire, respectively, and 1.7 times that of silicon carbide nanorods. The challenge is to achieve these properties of individual SWNTs in nanotube assemblies found in sheets and continuous fibers.

3. CNT ELECTRONIC PROPERTIES

Electrically CNTs are both semiconductor and metallic in nature which is determined by the type of nanotube, its chiral angle, diameter, relation between the tube indices etc. The electronic properties structure and properties is based on the two dimensional structure of Graphene. For instance if the tube indices, n and m, satisfies the condition n-m=3q where q is and integer it behaves as a metal. Metal, in the sense that it has zero band gap energy. But in case of armchair (where n=m) the Fermi level crosses i.e. the band gap energy merges. Otherwise it is expected the properties of tube will be that of semiconductor. The table below (Table 1) is the observations of experiments done on nanotubes by Scanning tunneling microscope (STM) and Scanning tunneling spectroscopes (STS). The dependency of energy gap or band gap energy on chiral angle and diameter is clear from the observation below.

Table 1. Here d is the nanotube diameter; F is the chiral angle; E gap is the apparent band gap in the STS I–V spectra and dE is the shift of the Fermi energy due to doping of the tube by the substrate. Note that a chiral angle 0 ْ denotes armchair nanotube and an angle of 30 ْ a zigzag tube. The flat Au surface allowed the diameter

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d of the nanotubes to be determined with an accuracy of 0.1nm by measuring the tube heights relative to the surface. A possible systematic uncertainty in determining the diameter is due to a difference in barrier heights for the gold substrate and the tubes. The wrapping angle F can be determined with an accuracy of 1 ْ. Accuracy in F is limited by the curvature of the tubes. A combination of high accuracy in both F and d (0.05 nm) is required for an unambiguous identification of the n, m indices. Accuracy in Egap and dE is 0.05–0.1 eV. For this sample a shift in the Fermi energy towards the conduction band was observed, instead of a shift towards the valence band as observed in the other samples.

From the table above, two categories can be distinguished: one with gap values around 0.5–0.6 eV, the other with significantly larger gap values. The first category of tubes is identified as the semi conducting type, the second as metallic tubes. Another noted property of nanotube is that oscillation of Band Gap energy when magnetic field is applied parallel to the tube axis. It has been showed theoretically that the band gap energy would oscillate with increasing magnetic field, so a metallic tube is converted to a semiconductor and then metallic again, with a period depending on the magnetic field strength.

Fig 3 : Electronic properties of single-walled carbon nanotubes. (A). Current–voltage curves obtained by tunneling spectroscopy on various individual nanotubes is shown here. Tubes no. 1 to 6 are chiral, no. 7 is zigzag and no. 8 is armchair. The bias voltage is applied to the sample, which means that the sign of Vbias corresponds to that of the energy relative to the tube Fermi level. Curves no. 1–7 show a low conductance at low bias, followed by several kinks at larger bias voltages. The armchair tube does not show clear kinks in the range 1 to 1V(B) Energy gap Egap versus diameter d for semiconducting chiral tubes. The data points correspond quite well to the theoretical predicted values. The solid line denotes a fit of:

Egap = 2g0aC–C /d with g0 = 2:7 eV.

Where, g0 is the c-c tight binding energy. aC–C, the nearest neighbour distance (.142nm).Tunnel currents I as a function of the bias voltage V applied to the sample

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were recorded with a home-built STM while scanning and feedback were switched off.

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4. FLUID FLOW THROUGH CARBON NANOTUBE

Recently there has been extensive study on the effect of fluid flow through nanotubes,which is a part of an ongoing effort worldwide to have a representative in the microscopic nano-world of all the sensing elements in our present macroscopic world. Indian Institute of Science has a major contribution in this regard. It was theorotically predicted that flow of liquid medium would lead to generation of flow-induced voltage. This was experimetally established by two Indian scientist at IISc. Only effect of liquid was theorotically investigated and established experimentally, but effect of gas flow over nanotubes were not investigated, until A.K Sood and Shankar Ghosh of IISc investigated it experimentally and provided theorotical explanation for it. The same effect as in case of liquid was observed, but for entirely different reason.These results have interesting application in biotechnology and can be used in sensing application. Micro devices can be powered by exploiting these properties.

4.1 Effect Of Liquid Flow Through Nanotube

P král and M shapiro published a paper in Physical review letters [ Vol.86 No.131 (2001)], that dealt with development of voltage / current when liquid flows through CNTs. Generally an electric current in a material is produced when flow of free charge carriers is induced in the material. According to Král and Shapiro, the generation of an electric current in a nanotube is essentially due to transfer of momentum from the flowing liquid molecules to acoustic phonons in nanotube so as to have a dragging effect on the free charge carriers in the nanotube. The outcome, according to these workers, is a linear dependence of the induced electric current on the flow velocity.

Another mechanism involved, as per these authors involves a direct scattering of the free carriers from the fluctuating Coulombic fields of the ions or polar molecules in the flowing liquid. They argued, however, that the latter mechanism creates a current that is five orders of magnitude smaller than the current that results from the phonon-induced electron drag.

These predictions were experimentally verified by A K Sood and Shankar Ghosh of IISc. In sharp contrast, Sood and coworkers have found that the behaviour is highly sub linear where the induced voltage fits a logarithmic velocity dependence over nearly six decades of velocity. Strong dependence of induced voltage on polarity and ionic nature of the liquid and relatively weak dependence on its viscosity was revealed from this experiment.

4.1.1 Verification on Theorotical Prediction:

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Experimental setup, observed results and hence the inference gathered from the observations, dependencies of voltage induced on various factors that has been observed are explained in following sections

4.1.2 Specification of materials and instuments used:

The SWNT bundles used for the experiment were prepared by electric arc method, followed by purification process. The dimensions and physical properties of samples are listed below:

Diameter of nanotube 1.5nmResistivity 0.02Ω-m

Sensor using this tube was prepared by densly packing nanotubes between two metal electordes. The dimensions of Sensor:

Along the flow 1mmThickness 0.2mmWidth 0.2mm

The specimen was placed inside glass tube of innner dia 0.03 and length 0.9m , kept vertically. Voltage mesurment were used by using KEITHLEY 2000 multimeter.

Hydrocloric and Glycerine to increase polarity and viscocity of fluid media respectively.

4.1.3 The Experiment:

The scematic representation of experiment is shown in figure 4.To avoid any turbulent flow that may have been caused by the expansion of the flow at the inlet of the flow chamber it was placed at the center of glass tube. The velocity u of the liquid flowing past the sample was measured from the bulk flow rate, which was varied by adjusting the height of the reservoir and the opening of the valve. The liquid enters the flow chamber against gravity such that the formation of air

pockets is avoided. The flow at the center of the cell is expected to be laminar because the Reynolds number (Re) (~300 for a velocity of 10-

2 m/s) was much less than the critical value of 2000 for the onset of turbulent flow in a pipe. The measurements shown here were taken after the transients had subsided.

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Fig 4 : Experimental setup where R is the reservoir, L is the valve controlling the liquid flow, S is the cylindrical glass flow chamber, and G is the Voltmeter.

4.1.4 Observations and Inferences:

When the sample was immersed in water at rest, a voltage (~1 mV) developed along the sample as an electrochemical potential difference at the interface of the SWNT bundle with the metal electrodes. This offset voltage was subtracted from the voltage measured at finite velocities of the liquid to obtain the flow-induced voltage. The voltage developed only along the flow direction; no voltage was generated in the direction perpendicular to the flow (i.e., along the width).Figure 5 shows the observed dependence of the flow induced voltage on flow velocity of water. Even at a very low speed of 5x10-6 m/s, a voltage of 0.65 mV was generated. The solid line in Fig5 is a fit to empirical relation:

V= a log(ub+1)

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Where a and b are parameters, a= 0.6mV and b= 6.5 x 106 s/m. Figur

e 6 compares the voltage developed along nanotubes as a function of the flow velocity for a series of fluid mixtures. A notable effect is the strong dependence of the flow-induced voltage on the ionic strength of the flowing liquid. It can be seen that for u = 10-4 m/s, the voltage for 1.2 M HCl is about five times that for water.A comparison of expected results as per Král and shapirov and experimental results are compared in following paragraph,

They considered metallic nanotubes that were densely packed in two layers separated by a layer of water of thickness d (~10 nm). In their mechanism, the force exerted by the liquid with a flow velocity u on the surface of the nanotubes is:

F = (hu/d) X interface periphery X interface length. This force results in the steady-state quasi-momentum (p) transfer to the

phonon bath was calculated using p ~ Ft where h is the shear viscosity of the

liquid, t known as phonon umklapp time. Using this value of p, the resulting current was calculated, the results showed that current depends on viscosity of fluid and flow velocity Vs flow induced voltage would be linear in nature. Using glycerol mixed with water at ratios 88:12 and 75:25 having h= 113 and h= 234 mPa s respectively revealed the weak dependence of induced voltage on h. The induced voltage decreased with increase in shear viscosity yet the effect was negligible.

The experiment also revealed the dependence of flow induced voltage on polarity of liquid which is clear from figure 6, there is a steep increase in flow induced voltage with increase in polarity of liquid. 0.6 M and 0.12 M HCL and methanol were used for this purpose. Thus, for u =6 x10-4 m/s, Vwater = 2.1 mV, whereas Vmethanol = 0.2 mV. Thus, data set reveals three features: the sublinear (almost logarithmic) voltage response to flow velocity, its strong dependence on the ionic and polar nature of the flowing liquid, and its relatively weak dependence on the liquid viscosity—the latter, in fact, acting to reduce the flow-induced voltage.

The predominant mechanism here that results in the flow induced voltage is fluctuating columbic fields.

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As ions and polar molecules have fluctuating Coulomb fields, Sood and coworkers have assigned the observed behaviour to scattering of free carriers by these fluctuating fields. The exact model is termed as ‘the pulsating asymmetrical ratchet model’. The terms describe the phenomenon itself, whereby ions flowing past a certain point in the nanotube produce Coulomb pulses while the asymmetry is provided by the velocity gradient at the liquid–solid interface.

An important point must be made regarding the direction (polarity) of the voltage and current in relation to the fluid flow direction. In the experiments, it was observed that the electric current and the fluid were flowing in the same direction. In a linear response theory based on the viscous drag (the phonon wind), the particle current has the same direction as the fluid flow velocity, and, therefore, the sign of the electric voltage and current is determined by the sign of the charge carriers (electron or hole). Thus, for the hole like carriers, the induced voltage and current have the same direction as the flow velocity. This, however, is not the case for a pulsating ratchet model in general. For a given direction of the asymmetry, the direction of the voltage is independent of the sign of the charge on the carriers. It will, of course, depend on the sense of the bias (asymmetry) of the ratchet potential. In a polar fluid of a given ionic strength, such as concentrations of H+ and OH– ions (along with their hydration shells), it is expected to have ratchet potentials of either sign (bias). The net effect is then determined by the dominant ratchet. What is important here, however, is that there is no a priori (symmetry) reason to expect the oppositely biased ratchets to give an exact cancellation.

4.2 Applications

Flow sensor that is based on SWNT directly produces an electrical signal in response to a fluid flow. This sensor can be scaled down to length dimensions of the order of micrometers—i.e., the length of the individual nanotubes—making it usable in very small liquid volumes. The sensor also has high sensitivity at low velocities and a fast response time (better than 1 ms). The nanotubes also could be used to make a voltage and current source in a flowing liquid environment, which may have interesting biomedical applications.

In bio medical applications it is speculated that carbon nanotubes can be used to power coronary heart pace makers using flowing blood as source of power this would make the use of batteries in coronary heart pace makers obsolete. The results using blood have shown encouraging results.

Another application would be as a chemical sensor which can be used to check the polarity, acidity and detecting any impurities (that are polar in nature) present in the liquid media.

If CNTs become cheaper and economically viable then it can be used in bulk to produce electricity in small scale using flowing water as source of active media.

4.3 Effect of Gas Flow over Carbon Nanotubes

The effects of Gas flow over CNTs were not studied both theoretically and experimentally, until A K Sood and his Co workers investigated on it. Papers pertaining to these works were published in Physical Review letters on 20 Aug

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2004. Research works on these findings and possible applications are being investigated by Sood and coworkers.

The same effect of flow induced current/voltage observed with liquid media was observed when gas medium was used. Although the effect is same, yet the reason for it is completely different from that of liquid flow. Further this effect is not confined to nanotubes, same effect is observed in wide range of solids including semiconductors, metals for wide range of velocities.

The underlying principle is an interesting interplay of Bernoulli’s Principle and Seebeck effect. Pressure differences along the streamlines give rise to temperature difference along the tube which, in turn produce the measured voltage. Unlike in case of liquid the flow induced voltage in gas, depends not only on flow velocity but also on the orientation of specimen. The experimental setup, observation, findings, inferences and theory behind this phenomenon is explained in the following sections.

4.3.1 Specifications of Specimen and Instrument:

To establish the ubiquity of this phenomenon variety of solids were used, they include nanotubes, semiconductors and metal which are described below:

n-type Ge(Sb-doped) of s(conductivity)=100/Wcm, p-type Si s =100/Wcm, n-

type Si s =100/Wcm, SWNTs, MWNTs graphite, poly-crystalline cooper and platinum were used. The sizes of the semiconducting samples and copper are about 3 mm along the flow and 1mm perpendicular to the flow. The electrical contacts for the semiconducting materials (Si, Ge) were made with copper leads of 1.3X10-4 m dia using silver emulsion [shown by shaded region in schematic representation of experimental setup fig.7] The exposed (active) portion of the sample, that is not covered by silver emulsion is about 2mm [marked as d in Fig 7b] along the flow and 1mm perpendicular to the flow. The samples of SWNTs, MWNTs and graphite, prepared by densely packing the powder between two metal electrodes, were about 1mm along the flow, 2mm wide and 0.2mm thick. Proper electromagnetic interference shielded cables were used to measure the signals using a KEITHLEY 2000 multimeter.

Active medium i.e. gases used were oxygen, argon, nitrogen and air. These were contained in a gas chamber kept at a pressure of 150 bars. The flow velocity was measured indirectly using a Rota meter.

4.3.2 Experimental setup, Observations and Inferences:

Figure 7, (next page) shows a schematic layout of experiment of the experimental setup to achieve a calibrated gas flow velocity on the sample. The gas from a compressed gas cylinder (maximum pressure of 150 bars) is let out at a given pressure in a tube of diameter 7 X 10-3 m. The flow rate Q is measured using a Rotameter as shown in Fig. 7(a). The average velocity u at the end of the tube with cross-sectional area (Φ) is deduced from Q as u= Q ∕Φ. The sample is kept at an angle α=π∕4 with respect to the horizontal axis to achieve the optimal signal. At an angle α= 0 ْ would produce no effect since the pressure gradient is zero, and α=π∕2 too would give no signal due to symmetry. The results are similar when the

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sample is kept inside the tube (at a distance of 2 X 10-2 m from the exit point) or 1 X 10-2 m outside the tube.

Fig 7 : (a) Schematic of the experimental setup. The flow rate at the exit point is deduced from the measured flow rate at the side port using the rotameter. (b) Sample: shaded portions mark the electrodes. The positive terminal of the voltmeter is connected to the right ® of the sample of active length d kept at and angle α=π∕4 with respect to the horizontal axis.

Figure 8 below shows the voltage across the n-Ge sample as a function of time when the gas flow (u= 7 ms) over the sample is switched on and off. The gas used here is argon. Data for the steady flow voltage V for a variety of samples and flow velocities are shown in Figs. 9 and 10. It can be clearly seen that for nitrogen gas over p-Si, n-Si, n-Ge, p-Ge, SWNT, MWNT and graphite, the voltage V

generated varies as u2 over a wide range of u ( as does the current, not shown). Figure 9 shows the fit to V= Du2 with fit parameter D given in Table2. This is even clearer in Fig 9 which shows the same data plotted versus M2, where M is the

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Mach number given by M=u / c, c being the sound velocity (=333 m/s for nitrogen and 323 m/s for argon at 300K). The solid lines fit to curve V=AM2, where A is a fitting parameter also given in Table 2. Experiments using polycrystalline copper sheet for which the slope A is very small. It can be seen that the sign of P-type Si and SWNT is opposite to that for n-type Si, n-type Ge, graphite and copper. SWNT samples are usually

unintentionally p-doped, which can explain the sign of the flow-induced voltage which was found to be the same for SWNT and p-Si. The inset in fig10 shows the slope A versus the known Seebeck coefficient S of the samples of the same d, as given in Table 2. The coefficient depends linearly on S, as shown by fitted line in the inset, with slope=60K.Figure 10 shows the generated voltage V over a large range of values of M2 for the flow of argon (solid squares) and nitrogen gases (open circles) over n-Ge. A change in slope is clearly seen around M2≤.05 (Called regime 1) is higher for argon than for nitrogen.

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The ratio of slopes [A (argon) / A (nitrogen) = 1.2]. That there are actually two M2 regimes is clear from our theoretical analysis of the mechanism behind the generation of electrical signal induced by the flow of gases over the solids, and is discussed below. For the adiabatic steady inviscid flow of a gas, Bernoulli’s equation gives the pressure difference along a streamline in terms of Mach number M as:

CP (CV) being the specific heat at a constant pressure (volume). The values of

g for argon and nitrogen are 1.667 and 1.404, respectively. In eq1 P0 is the maximum pressure at a point on the streamline where velocity is zero . Such a

point is the leading edge on the surface of the sample past which the gas is moving and is called the stagnation point. For the sample geometry shown in Fig. 7 (b), the pressure difference between the two ends of the active sample exposed to the gas flow (i.e., without the electrodes) is hence:

The subscripts L(R) denote the left (right) of the active sample when the gas flows from left to right. From the ideal gas law, the fractional temperature difference DT/T is related to the pressure difference DP/P and the density difference Dr/r as

DT/T=DP/P-Dr/r. When M<<1, the change in density of the gas is negligible, i.e., the fluid is essentially incompressible and hence DT/T=DP/P. Therefore, the temperature difference along a streamline between two points separated by distance d for M<<1 (called regime I) is:

Where, DT= TL - TR > 0. The gas flowing past the sample kept at an angle a with respect to the horizontal axis corresponds to an accelerating flow and hence MR>ML.The tangential component of the velocity u of the outer flow depends on the streamline distance x measured along the flat boundary as:

For this geometry a= pi/4 and hence u(x) .The temperature difference along the streamline in the gas

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flow will induce a temperature difference in the solid along the flow direction. The temperature difference, in turn, will result in a voltage difference V, defined as VL – VR, due to the Seebeck effect. Thus:

Where, S is the Seebeck coefficient of the solids, positive for p-type and negative for n-type materials. The factor k depends on the specific interactions between the gas and the solid surface as well as on the boundary conditions of the temperature difference between the gas and the solid. In nonrarefied gases, the boundary conditions at the surface of a solid is that the temperatures of the gas and solid are equal, in which case k=1. But this boundary condition applies only if the mean free path of the gas molecules is vanishingly small. The factor k takes into account all the differences from this ideal boundary condition. The present phenomenon of voltage generation by flow of gases is not applicable to the flow of liquids where the viscous drag dominates.Beyond a certain value of M (~0.2), called regime II the density changes of the gas should be taken into account, which gives:

And hence:

On comparing the predictions of this model with the experiments:

1. From equation 4 that it can be deduced that induced voltage V is directly proportional to M2 and the experimental results show that the curve fits to V=A M2 .

2. From eq 5 the slope A should depend linearly on S in regime 1 where :

The inset in figure 10 agrees with the result obtained theoretically.

3. Another property can be deduced from the equations above that for substance that has S=0 will have no induced voltage. Results with platinum as specimen have showed no induced voltage (for Pt S~0).

4. From equation 5 in regime 1 ratio of voltage generated for argon and nitrogen with same velocities for same samples were 1.2 which is the ratio of g (argon) / g (nitrogen), hence consistent with theoretical predictions.

Hence, the theoretical predictions deduced are consistent with the experiment.

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4.4 Applications

The experiments clearly suggest that a sensor to measure the flow velocity of the gases can be made based on the generated electrical signal. It is an active sensor which gives direct electrical response to the gas flow. This should be compared with the widely used gas flow sensor based on thermal anemometry, wherein the fluid velocity is sensed by measuring changes in heat transfer from a small, electrically heated sensor (wire or thin film) exposed to the fluid. Thermal anemometry works on heat balance equations and hence any small changes in the temperature, pressure, or composition of the gas can cause erroneous readings. Such effects are minimum or can be easily taken into account in the sensors based on the direct generation of flow-induced voltage or current in the sensor material.The magnitude of generated voltage can be easily scaled up by using series and parallel and connections of sensing elements. This suggests that flow energy can be directly converted into electrical signal without any moving part, thus having a potential for application in generating electricity.

Ajay Sood and his coworkers have shown that this property can be exploited for construction of nanotube based vibrational sensor in liquids and as accelerometer. The SWNT based accelerometer has so far measured the frequency range 0.5 Hz to 1 kHz and the minimum detectable acceleration by the accelerometer is 10-3 g.

5. CONCLUSION

The Past as Indication of the Future: The exponential increase in patent filings and publications on carbon nanotubes indicates growing industrial interest that parallels academic interest. Nanotubes electronic devices might be the most promising field. Impressive advances have been made in demonstrating nanotube electronic device concepts, but a decade or more of additional progress is likely required to reliably assess if and when these breakthroughs will reach commercial application, So will the nanotube sensing applications as flow sensors / electrical signal generators. As for now control on their electronic properties which is not so impressive where large scale production is considered, poses a major hurdle in this regard. Possible chemical sensing applications of nonmetallic nanotubes are interesting, because nanotube electronic transport and thermo power (voltages between junctions caused by inter-junction temperature differences) are very sensitive to substances that affect the amount of injected charge. The main advantages are the minute size of the nanotube sensing element and the correspondingly small amount of material required for a response. The mechanical robustness of the nanotubes dramatically increase probe life and minimize sample damage during repeated hard crashes into. These uses may not have the business impact of other applications, but they increase the value of measurement systems for

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characterization and manipulation on the nanometer scale. With the addition of this new phenomenon i.e. flow induced voltage nanotube seems to head for ubiquity in nanoworld as sensor, actuator probes, energy storage and generating devices.Independent of the outcome of the ongoing races to exploit nanotubes in applications, carbon nanotubes have provided possibilities in nanotechnology that were not conceived in the past. Nanotechnologies of the future in many areas will build on the advances that have been made for carbon nanotubes.