Instantaneous limit

Williams (1964) derived the relation T = kBTrQV3De2, where T is the recombination time for a geminate e-ion pair at an initial separation of rg, is the dielectric constant of the medium, and the other symbols have their usual meanings. This r-cubed rule is based on the use of the Nernst-Einstein relation in a coulom-bic field with the assumption of instantaneous limiting velocity. Mozumder (1968) criticized the rule, as it connects initial distance and recombination time uniquely without allowance for diffusional broadening and without allowing for an escape probability. Nevertheless, the r-cubed rule was used extensively in earlier studies of geminate ion recombination kinetics. 

By using the expanding sphere electrode model for the DME, Koutecky obtained the following expression for the instantaneous limiting current [35-37] ... 

Therefore, very high instantaneous limiting current densities can be obtained with MREF electrolysis as compared to DC electrolysis. The pulse on-time, t , may be reduced by increasing the frequency or decreasing the duty cycle. 

By virtue of modern electronic techniques, especially microcomputer chips, it is possible to provide additional characteristics to inverse relays in particular. At the high multiples of current one or more instantaneous limits can be provided. These can be adjusted by the user to create a type... 

The instantaneous limit corresponds to the O — 0 limit, high nucleation rate A on small number density of active sites No, while the progressive situation results when the value of A is low and/or No is elevated, that is, when a —> oo. The current density is obtained as the planar diffusive flux to an electrode of fractional area 0[Pg.1015]

My own conclusion is to accept the predictions of Sections 17.1 and 17.2 as qualitative guides that are not quantitatively exact. In other words, I use them more to make initial approximations and to organize experimental results than I use them to make a-priori predictions. This is especially true because the kinetics in many cases may not fall cleanly into the limit of a fast reaction or an instantaneous one. Here, the half life of the reaction is believed to be about 10 seconds, so that this reaction is effectively instantaneous. In contrast, the reaction of carbon dioxide is less easy to characterize. Even with sodium hydroxide, this reaction can fall in the transition between the fast and the instantaneous limits. Some of the difficulties with a carbon dioxide system are explored in the example that follows. 

Droplet trajectories for limiting cases can be calculated by combining the equations of motion with the droplet evaporation rate equation to assess the likelihood that drops exit or hit the wall before evaporating. It is best to consider upper bound droplet sizes in addition to the mean size in these calculations. If desired, an instantaneous value for the evaporation rate constant may also be used based on an instantaneous Reynolds number calculated not from the terminal velocity but at a resultant velocity. In this case, equation 37 is substituted for equation 32 ... 

A solution of sulfur trioxide [7446-11-9] dissolved in chlorosulfonic acid [7990-94-5] CISO H, has been used as a smoke (U.S. designation FS) but it is not a U.S. standard agent (see Chlorosulfuric acid Sulfuric acid and sulfur trioxide). When FS is atomized in air, the sulfur trioxide evaporates from the small droplets and reacts with atmospheric moisture to form sulfuric acid vapor. This vapor condenses into minute droplets that form a dense white cloud. FS produces its effect almost instantaneously upon mechanical atomization into the atmosphere, except at very low temperatures. At such temperatures, the small amount of moisture normally present in the atmosphere, requires that FS be thermally generated with the addition of steam to be effective. FS can be used as a fill for artillery and mortar shells and bombs and can be effectively dispersed from low performance aircraft spray tanks. FS is both corrosive and toxic in the presence of moisture, which imposes limitations on its storage, handling, and use. 

Water Hammer When hquid flowing in a pipe is suddenly decelerated to zero velocity by a fast-closing valve, a pressure wave propagates upstream to the pipe inlet, where it is reflected a pounding of the hne commonly known as water hammer is often produced. For an instantaneous flow stoppage of a truly incompressible fluid in an inelastic pipe, the pressure rise would be infinite. Finite compressibility of the flmd and elasticity of the pipe limit the pressure rise to a finite value. The Joukowstd formula gives the maximum pressure... 

A CT is provided in series with the spark gap to sense its operation during a line fault. As soon as there is arcing, it provides an instantaneous command to a short-circuit relay. The relay, in turn, closes the bypass breaker, within 3 to 5 cycles, leaving only the natural line impedance in the faulty eircuit. Now = 0, which limits the fault current to the natural level of the system, as if the capacitors were not connected. The shorting device is restored to its original status as soon as the fault condition is cleared. The device must be capable of interrupting the line fault... 

The seeond method of overeurrent proteetion is pulse-to-pulse overcurrent protection. This method guarantees a maximum safe power switeh eurrent. A eurrent sensing element (resistor or eurrent transformer) is plaeed in series with the power switeh(es). It views the instantaneous eurrent flowing through the power switeh and will instantly eutoff the power switeh if a preset instantaneous eurrent limit is exeeeded. This eireuit must be very fast and will proteet the power switeh from all forms of instantaneous overeurrents ineluding eore saturation. It is not a form of eurrent-mode eontrol sinee this proteetion limit is fixed and not infiueneed by external parameters. 

TLV-c, THRESHOLD LIMIT VALUE - CEILING (usa) A limit fof the atmosplieiic concentration of a chemical which may not be exceeded at any time, even instantaneously in workroom air. 

Conduct work in designated controlled areas (e.g. in UK these are areas in which instantaneous dose rates >7.5 pSv/hour occur, or where employees may exceed 6 mSv annual dose limit, or where air concentration or surface contamination exceeds specified levels). 

Creep the dimensional change of a plastic under load with time followed by the instantaneous elastic or rapid deformation at room temperature permanent deformation caused by prolonged application of stress below the elastic limit. 

AFTOX is a Gaussian dispersion model that is used by the Air Force to calculate tu accidental releases. Limited to non-dense gases, it calculates the evaporation rate from liquid spills. It treats instantaneous or continuous releases from any elevatic ... 

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