Inner friction

FIGURE 9.20 Model of the functionally graded structure of the MoDTC/ZDDP tribofilm. A low-friction inner-skin layer formed hy MoSj nanostrips has low yield strength and acts as a lamellar solid lubricant in lowering the friction coefficient of the MoDTC/ZDDP tribofilm. High concentrations of Ca, O, P, and S oil additive elements in the middle layer decreased and disappeared from the base layer, while the Fe concentration increased from an ultralow level in the surface layer to the same level as the steel disk at the tribofihn-disk interface. 

Nanotubular materials are important building blocks of nanotechnology, in particular, the synthesis and applications of CNTs [82, 106, 107], One application area has been the use of carbon nanotubes for molecular separations, owing to some of their unique properties. One such important property, extremely fast mass transport of molecules within carbon nanotubes associated with their low friction inner nanotube surfaces, has been demonstrated via computational and experimental studies [108,109], Furthermore, the behavior of adsorbate molecules in nano-confinement is fundamentally different than in the bulk phase, which could lead to the design of new sorbents [110],... 

The net viscous force acting on this volume element is given by the difference between the frictional forces acting on the outer and inner surfaces of the shell ... 

Correlations for Convective Heat Transfer. In the design or sizing of a heat exchanger, the heat-transfer coefficients on the inner and outer walls of the tube and the friction coefficient in the tube must be calculated. Summaries of the various correlations for convective heat-transfer coefficients for internal and external flows are given in Tables 3 and 4, respectively, in terms of the Nusselt number. In addition, the friction coefficient is given for the deterrnination of the pumping requirement. 

Fanning friction factor /i for inner wall and / 2 for outer wall of annulus /l for ideal tube bank sldn friction drag coefficient Dimensionless Dimensionless... 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

PTFE is used for lining chutes and coating other metal objects where low coefficients of friction or non-adhesive characteristics are required. Because of its excellent flexing resistance, inner linings made from dispersion polymer are used in flexible steam hose. A variety of mouldings are used in aircraft and missiles and also in other applications where use at elevated temperatures is required. 

Example 2.6 The bobbin shown in Fig. 2.16 has been manufactured by sliding the acetal ring on to the steel inner and then placing the end-plate in position. At 20°C there are no stresses in the acetal and the distance between the metal end-plates is equal to the length of the acetal ring. If the whole assembly is heated to 1(X)°C, calculate the axial stress in the acetal. It may be assumed that there is no friction between the acetal and the steel. The coefficients of thermal expansion for the acetal and the steel are 80 x 10 °C and 11 X 10 °C respectively. The modulus of the acetal at 100°C is 1.5 GN/m. ... 

L is the duct length D is the inner diameter / is the flow friction factor... 

The friction factor / is plotted in Figure 32.30 against the Reynolds number, based on the pipe inner diameter D... 

Rolling-element bearings The ability to monitor rolling-element or anti-friction bearing defects requires the inclusion of multiples of their rotating frequency. For example, with ball-pass inner-race bearings, the bandwidth should include the second harmonic (2x). 

Because this is a friction-driven motion, the cage turns much slower than the inner race of the bearing. Generally, the rate of rotation is slightly less than one-half of the shaft speed. FTF is calculated by the following equation ... 

Air at 330 K, flowing at 10 m/s, enters a pipe of inner diameter 25 mm, maintained at 415 K. The drop of static pressure along the pipe is 80 N/m2 per metre length. Using the Reynolds analogy between heat transfer and fluid friction, estimate the air temperature 0.6 m along the pipe. 

Celata et al. (2006) studied experimentally the drag in glass/fused silica microtubes with inner diameter ranging from 31 to 259 jam for water flow with Re > 300. The drag measurements show that the friction factor for all diameters agrees well with predictions of conventional theory A = 64/Re (for the smallest diameter 31 pm, the deviations of experimental points from the line A = 64/Re do not exceed... 

Kakiuchi [41] has examined the transport mechanism in some detail. He considers the interface as a region of thickness k in which friction is considerably larger than in the bulk. The transferring ion has different electrochemical potentials = 1, 2) in the two bulk phases as usual, they can be decomposed into their chemical and their electrostatic parts /x,- = /x,- -t-zeo, where z is the charge number of the ion. When the system is in equilibrium, and the concentration of the ion is the same in the two solutions, then the difference in the inner potential is given by ... 

Measurements by FIA occur under conditions where laminar flow predominates over turbulent flow (Fig. 3, a and b) and hence a parabolic profile of the concentration of analyte solution inside the carrier stream is developed. The layers of the analyte that are adjacent to the inner surface of the transportation tube flow slowly owing to the friction forces developed between these two different... 

Tangney et al.92 studied the friction between an inner and an outer carbon nanotube. Realistic potentials were used for the interactions within each nanotube and LJ potentials were employed to model the dispersive interactions between nanotubes. The intra-tube interaction potentials were varied and for some purposes even increased by a factor of 10 beyond realistic para-meterizations, thus artificially favoring the onset of instabilities and friction. Two geometries were studied, one in which inner and outer tubes were commensurate and one in which they were incommensurate. 

In the simulations, the inner nanotube was initially displaced relative to the outer tube by a distance x. To reduce surface area, the inner nanotube was pulled into the outer tube and a potential energy minimum was found to exist when the inner tube is completely embedded. However, because of the accumulation of kinetic energy, the inner tube will move past this minimum and extend beyond the other end of the outer tube. In the absence of frictional forces, one would anticipate that this process would be repeated indefinitely, with the relative displacements of the two nanotubes oscillating between +x and —x. In the presence of frictional forces, the maximum displacement will decrease with time. This can be seen from the data shown in Figure 24, where the relative displacement of the nanotubes and frictional forces are shown as functions of time. 

Lhymn and Schultz, 1983). This observation is analogous to the fracture process in the outer process zone which is termed the dissipation zone as distinct from the inner process zone ahead of crack tip (Lauke and Schultrich, 1986b Lauke and Pompe, 1988). In the dissipation zone, intensive energy dissipation by fiber-matrix interfacial debonding and post-debonding friction is concentrated mainly at the fiber... 

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