Rising speed

In all of these reactions (and in almost all others), increasing the temperature has a very pronounced effect, always speeding up the reaction. Two questions come to mind. Why does a temperature rise speed up a reaction and Why does a temperature rise have such a large effect To answer these questions, we return to our collision theory. 

Measurements of the vertical velocity, far from the injection site, were made at a fixed position using a hot-film system (e.g. [108]), from which the bubble diameter and rise speed could be calculated. The accuracy of the measurements have been extensively tested at low void fractions using LDV and optical methods. The time-series of the velocity measurements were converted into spatial information using a Taylor hypothesis that a mean flow advects disturbances past the probe. Examples of the velocity time-series is shown in Fig. 7.5. A more thorough description of the experimental technique and diagnostic tools applied to the data is given in [358],... 

Wu JC, Deluca RT, Wegener PP (1974) Rise speed of spherical cap bubbles at intermediate Reynolds number. Chem Eng Sci 29 1307-1309... 

Compared to the sandy slope, it took much more time for the silt slope to form the sliding belt and the moisture content. Compared with the sandy slope, the rising speed of seepage line inside the silt slope was slower than the speed on the sandy slope. Then the seepage line also reached the top of the slope. 

Takemura, F. and Yabe, A. 1999 Rising speed and dissolution rate of a carbon dioxide bubble in slightly contaminated water, J. Fluid Mech., 378, pp. 319-334. 

When the appropriate voltage rise speed (A = V/t) is selected, the current goes over the maximum, and from the peak time tmax (marked hy an arrow in Figure 31) the charge carrier mobility can be calculated as... 

The coefficient of friction between two unlubricated solids is generally in the range of 0.5-1.0, and it has therefore been a matter of considerable interest that very low values, around 0.03, pertain to objects sliding on ice or snow. The first explanation, proposed by Reynolds in 1901, was that the local pressure caused melting, so that a thin film of water was present. Qualitatively, this explanation is supported by the observation that the coefficient of friction rises rapidly as the remperarure falls, especially below about -10°C, if the sliding speed is small. Moreover, there is little doubt that formation of a water film is actually involved [3,4]. 

As load is increased and relative speed is decreased, the film between the two surfaces becomes thinner, and increasing contact occurs between the surface regions. The coefficient of friction rises from the very low values possible for fluid friction to some value that usually is less than that for unlubricated surfaces. This type of lubrication, that is, where the nature of the surface region is... 

The mathematical form of the PEF is in almost every case a compromise between speed and accuracy. As computer power continually increases, ideally following Moore s Law, and the cost/performance ratio is getting better, one might think that there is no longer a need to sacrifice accuracy to save computational time. This is not really true, because in direct proportion to the CPU speed is the rise in the scientists interest in calculating larger and larger molecules (in fact, their interest always rises faster than the CPU speed). 

Equation (2.106) gives rise to an implicit scheme except for 0 = 0. The application of implicit schemes for transient problems yields a set of simultaneous equations for the field unknown at the new time level n + 1. As can be seen from Equation (2.111) some of the terms in the coefficient matrix should also be evaluated at the new time level. Therefore application of the described scheme requires the use of iterative algorithms. Various techniques for enhancing the speed of convergence in these algorithms can be found in the literature (Pittman, 1989). 

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