Transition of turbulent pipe flow

The velocity profile in turbulent pipe flow is usually divided into two regions, a wall or inner region and a core or outer region. For the inner region, the viscosity and wall shear stress are the important parameters governing the velocity distribution whereas for the outer region, the wall reduces the velocity below the maximum velocity independent of viscosity. In the present work, a velocity model is proposed for turbulent flow in the wall region of a pipe covering the entire transition from smooth to rough flows. Coupling this model for the wall region with the power law velocity model for the core region, an equation for the friction factor is obtained. The model constants are evaluated by using Nikuradse's experiments in the fully smooth and rough turbulent flows. The model shows good agreement with the friction factor and the velocity profiles obtained by Nikuradse for the transition region of turbulent flow.

Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes

This paper represents the effect of nonlocal scale parameter on the wave propagation in multi-walled carbon nanotubes (MWCNTs). Each wall of the MWCNT is modeled as first order shear deformation beams and the van der Waals interactions between the walls are modeled as distributed springs. The studies shows that the scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or group speed tends to zero). The frequency at which this phenomenon occurs is called the ``Escape frequency''. The analysis shows that, for a given N-walled carbon nanotube (CNT). the nonlocal scaling parameter has a significant effect on the shear wave modes of the N - 1 walls. The escape frequencies of the flexural and shear wave modes of the N-walls are inversely proportionl to the nonlocal scaling parameter. It is also shown that the cut-off frequencies are independent of the nonlocal scale parameter. (C) 2009 Elsevier B.V. All rights reserved.

Separation of Metallic and Semiconducting Single-Walled Carbon Nanotubes Through Fluorous Chemistry

Separation of metallic from semiconducting single-walled carbon nanotubes has been a major challenge for some time and some previous efforts have resulted in partial success. We have accomplished the separation effectively by employing fluorous chemistry wherein the diazonium salt of 4-heptadecafluorooc tylaniline selectively reacts with the metallic nanotubes present in the mixture of nanotubes. The resulting fluoroderivative was extracted in perfluorohexane leaving the semiconducting nanotubes in the aqueous layer. The products have been characterized by both Raman and electronic absorption spectroscopy. The method avoids the cumbersome centrifugation step required by some other procedures.

A germanium/single-walled carbon nanotube composite paper as a free-standing anode for lithium-ion batteries

Paper-like free-standing germanium (Ge) and single-walled carbon nanotube (SWCNT) composite anodes were synthesized by the vacuum filtration of Ge/SWCNT composites, which were prepared by a facile aqueous-based method. The samples were characterized by X-ray diffraction, field emission scanning electron microscopy, and transmission electron microscopy. Electrochemical measurements demonstrate that the Ge/SWCNT composite paper anode with the weight percentage of 32% Ge delivered a specific discharge capacity of 417 mA h g-1 after 40 cycles at a current density of 25 mA g-1, 117% higher than the pure SWCNT paper anode. The SWCNTs not only function as a flexible mechanical support for strain release, but also provide excellent electrically conducting channels, while the nanosized Ge particles contribute to improving the discharge capacity of the paper anode.

Binding of nucleobases with single-walled carbon nanotubes: Theory and experiment

We report the binding energy of various nucleobases (guanine (G), adenine (A), thymine (T) and cytosine (C)) with (5,5) single-walled carbon nanotube (SWNT) calculated using first-principle Hartre–Fock method (HF) together with classical force field. The binding energy without including the solvation effects of water decreases in the order G>A>T>C. The inclusion of solvation energy changes the order of binding preference to be G>T>A>C. Using isothermal titration (micro) calorimetry experiments, we also show the relative binding affinity to be T>A>C, in agreement with our calculations.

Field performance of in-service cast iron gas reticulation pipe buried in reactive clay

Field instrumentation of an in-service cast iron gas pipe buried in a residential area is detailed in this paper. The aim of the study was to monitor the long-term pipe behavior to understand the mechanisms of pipe bending in relation to ground movement as a result of seasonal fluctuation of soil moisture content. Field data showed that variation of soil temperature, suction, and moisture content are closely related to the prevailing climate. Change of soil temperature is generally related to the ambient air temperature, with a variation of approximately −3°C −3°C per meter depth from the ground surface in summer (decrease with depth) and winter (increase with depth). Seasonal cyclic variation in moisture content was observed with maxima in February and March, and a minimum around September. The pipe top was under tensile strain during summer and subsequently subjected to compressive strain as soil swelling occurred as a result of increase in moisture content. The study suggests that downward pipe bending occurs in summer because of soil shrinkage, while upward pipe bending occurs in winter when the soil swells.

New Strategies for the Enrichment of Metallic Single-Walled Carbon Nanotubes

Enrichment of metallic single-walled carbon nanotubes (SWNTs) has been accomplished by several means, including new extraction and synthetic procedures and by interaction with metal nanoparticles as well as electron donor molecules. In the presence of Fe(CO)(5) the arc discharge method yields nearly pure metallic nanotubes. Fluorous chemistry involving the preferential diazotization of metallic SWNTs offers a good procedure of obtaining the pure metallic species. Interaction of gold or platinum nanoparticles as well as of electron-donor molecules such as aniline and tetrathiafulvalene (TTF) transform semiconducting SWNTs into metallic ones. Raman and electroni spectroscopies provide ideal means to monitor enrichment of metallic SWNTs.

Excitation energy transfer from a fluorophore to single-walled carbon nanotubes

We study the process of electronic excitation energy transfer from a fluorophore to the electronic energy levels of a single-walled carbon nanotube. The matrix element for the energy transfer involves the Coulombic interaction between the transition densities on the donor and the acceptor. In the Foumlrster approach, this is approximated as the interaction between the corresponding transition dipoles. For energy transfer from a dye to a nanotube, one can use the dipole approximation for the dye, but not for the nanotube. We have therefore calculated the rate using an approach that avoids the dipole approximation for the nanotube. We find that for the metallic nanotubes, the rate has an exponential dependence if the energy that is to be transferred, h is less than a threshold and a d(-5) dependence otherwise. The threshold is the minimum energy required for a transition other than the k(i,perpendicular to)=0 and l=0 transition. Our numerical evaluation of the rate of energy transfer from the dye pyrene to a (5,5) carbon nanotube, which is metallic leads to a distance of similar to 165 A degrees up to which energy transfer is appreciable. For the case of transfer to semiconducting carbon nanotubes, apart from the process of transfer to the electronic energy levels within the one electron picture, we also consider the possibility of energy transfer to the lowest possible excitonic state. Transfer to semiconducting carbon nanotubes is possible only if>=epsilon(g)-epsilon(b). The long range behavior of the rate of transfer has been found to have a d(-5) dependence if h >=epsilon(g). But, when the emission energy of the fluorophore is in the range epsilon(g)>h >=epsilon(g)-epsilon(b), the rate has an exponential dependence on the distance. For the case of transfer from pyrene to the semiconducting (6,4) carbon nanotube, energy transfer is found to be appreciable up to a distance of similar to 175 A degrees.

Terahertz wave characteristics of a single-walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model

This paper presents the effect of nonlocal scaling parameter on the terahertz wave propagation in fluid filled single walled carbon nanotubes (SWCNTs). The SWCNT is modeled as a Timoshenko beam,including rotary inertia and transverse shear deformation by considering the nonlocal scale effects. A uniform fluid velocity of 1000 m/s is assumed. The analysis shows that, for a fluid filled SWCNT, the wavenumbers of flexural and shear waves will increase and the corresponding wave speeds will decrease as compared to an empty SWCNT. The nonlocal scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or wave speed tends to zero). The frequency at which this phenomenon occurs is called the ``escape frequency''. The effect of fluid density on the terahertz wave propagation in SWCNT is also studied and the analysis shows that as the fluid becomes denser, the wave speeds will decrease. The escape frequency decreases with increase in nonlocal scaling parameter, for both wave modes. We also show that the effect of fluid density and velocity are negligible on the escape frequencies of flexural and shear wave modes. (C) 2010 Elsevier B.V. All rights reserved.

Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

Steady laminar flow with suction or injection and heat transfer through porous pipe

Following the method due to Bhatnagar (P. L.) [Jour. Ind. Inst. Sic., 1968, 1, 50, 1], we have discussed in this paper the problem of suction and injection and that of heat transfer for a viscous, incompressible fluid through a porous pipe of uniform circular cross-section, the wall of the pipe being maintained at constant temperature. The method utilises some important properties of differential equations and some transformations that enable the solution of the two-point boundary value and eigenvalue problems without using trial and error method. In fact, each integration provides us with a solution for a suction parameter and a Reynolds number without imposing the conditions of smallness on them. Investigations on non-Newtonian fluids and on other bounding geometries will be published elsewhere.