Approximate ratios of the velocity constants for the hydrolysis in basic media of di- and monoesters of homologous dibasic acids are given in the second column of Table The logarithm of this ratio, [Pg.74]

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. [Pg.89]

Figure 3. Brittle material AE responses as count velocity N and logarithm spectrum log (S) characteristics of the process |

The sedimentation coefficient may be determined by measuring the velocity of the particle at a fixed centrifuge speed (o>, in radians per second) and, from a series of observations, plotting the logarithm of the distance moved (x) against the time taken in seconds (t). The relationship is expressed by the equation [Pg.163]

This gives us a mean particle diameter, that has the same free-falling velocity as the set of particles of different sizes. Taking a logarithm of Eq. (14.65), we get [Pg.1332]

It is interesting to note that this logarithmic velocity profile is followed over most of the cross section of the pipe, not just where f tw. [Pg.92]

In these equations, e and m are respectively the electron charge and mass, v is the electron velocity at energy E, e is the base of natural logarithm, and 6max is the maximum transferable energy. [Pg.27]

No and Kazimi (1982) derived the wall heat transfer coefficient for the forced-convective two-phase flow of sodium by using the momentum-heat transfer analogy and a logarithmic velocity distribution in the liquid film. The final form of their correlation is expressed in terms of the Nusselt number based on the bulk liquid temperature, Nuft [Pg.298]

Fig. 21—Comparisons of friction forces from simulations of commensurate and incommensurate SAMs in relative sliding (a) friction exhibits a linear dependence on applied normal load, (b) friction increases logarithmically with the sliding velocity. |

One of the apparent results of introducing couple stress is the size-dependent effect. If the problem scale approaches molecular dimension, this effect is obvious and can be characterized by the characteristic length 1. The size effect is a distinctive property while the film thickness of EHL is down to the nanometre scale, where the exponent index of the film thickness to the velocity does not remain constant, i.e., the film thickness, if plotted as a function of velocity in logarithmic scale, will not follow the straight line proposed by Ham-rock and Dowson. This bridges the gap between the lubrication theory and the experimental results. [Pg.71]

If we take the natural logarithm of both sides of Eq. (15) and differentiate with respect to one of the component velocities, say vx, we have [Pg.638]

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