Collision rate total

It should be noted, however, that gaining a deeper insight into the problem of ionization phenomena is not the only reason for steady interest in the problem. Data on charged particle impact ionization is used both for industrial applications and for fundamental scientific research. For applications it is the collisions rates and total cross sections which are usually the most relevant. But in studies focused on the understanding of collision mechanisms of ionization processes, most of the information is lost in the total cross sections due to the integration over the momenta of the ejected electrons in the exit channel. Therefore it is the singly and doubly differential cross sections which are of... 

Where most dispersed systems will not have a uniform size distribution it must be expected that this size distribution will also have an effect on the total collision rate. A method of calculating this influence has been indicated by Gillespie (Gla). 

The total number of collisions with the dead comers is proportional to the total number of drops in the surface layer opposite the dead comers and—when the theory of local isotropic turbulence holds here also—proportional to the turbulent fluctuation frequency u/d. Near the wall, however, the theory of local isotropic turbulence certainly will not hold and —more or less—stationary large scale eddies will occur. Therefore, centrifugal effects will strongly increase the collision rate when the dispersed phase... 

The experiments discussed above were all carried out with total pressures below 10-4 Torr. However, Hori and Schmidt (187) have also reported non-stationary state experiments for total pressures of approximately 1 Torr in which the temperature of a Pt wire immersed in a CO—02 mixture was suddenly increased to a new value within a second. The rate of C02 production relaxed to a steady-state value characteristic of the higher temperature with three different characteristic relaxation times that are temperature dependent and vary between 3 and 100 seconds between 600 and 1500 K. The extremely long relaxation time compared with the inverse gas phase collision rate rule out an explanation based on changes within the chemisorption layer since this would require unreasonably small sticking coefficients or reaction probabilities of less than 10-6. The authors attribute the relaxation times to characteristic changes of surface multilayers composed of Pt, CO, and O. The effects are due to phases that are only formed at high pressures and, therefore, cannot be compared to the other experiments described here. 

Kellert et al.M both measured the total depopulation rates of the initially populated Xe ni states and analyzed the final bound states resulting from these collisions. The total depopulation rates of the Xe ni states were measured by... 

Encounters with impact parameter b collision rate those with b> rA + rB do not. The total number of collisions per unit time per unit volume between A and B can be found from kinetic theory, and this collision rate is often called the collision frequency, Zab- This quantity is proportional to the numbers of molecules of A and B per unit volume, nA and nB ... 

The driving force for the transport is provided by a concentration gradient as the reactant moves further towards the center of the pellet its concentration is decreased by reaction. The resistance to the transport mainly originates from collisions of the molecules, either with each other or with the pore walls. The latter dominate when the mean free path of the molecules is larger than the pore diameter. Usually both type of collisions are totally random, which amounts to saying that the transport mechanism is of the diffusion type. Hence the rate of transport, expressed as a molar flux in mol mp2 s-1, in the case of equimolar counterdiffusion can be written as ... 

Bottke et al (2005a,b) found that the current asteroid size distribution arose early in its history, when the total mass and collision rate were much higher than today. Once the Asteroid Belt was dynamically depleted and reached roughly its current mass (via the processes described above), there was little further evolution of the size distribution, and hence it has been referred to as a fossil size distribution. Collisions still occur, albeit at a reduced rate, and large collisions lead to the formation of asteroid families, which are groups of asteroids that are clustered in orbital-element (a, e, i) space. Numerous asteroid families can be seen in Fig. 10.6. 

In this equation, is the total interaction energy between the two colliding particles defined in the previous section. The stability ratio, W, for the system gives the ratio of rapid coagulation, Jp, to slow coagulation, J[= J W], DQi) is the position-dependent diflusion equation. This diffusion coefficient ratio is a factor that decreases the collision rate because of the difficulty in draining the liquid between the two solid surfaces. This diffiision coefficient ratio is given by [60,61]... 

This quantity is named the bimolecular collision rate. The /x denotes the reduced mass and m = mi - - m2 represents the total mass associated with the center of mass of a two particle system. 

At fixed volume fraction oip, reducing increases the collision rate because the total number concentration of particles N increases significantly. 

A quantity related to / XK is AXk, the average fractional electron energy consumed in effecting the specified Reaction Rl per electron collision of all kinds. The average energy is F and when fx — 1 the total electron collision rate coefficient is 2 xk hence,... 

Molecules in a hquid are not fixed in a rigid lattice. Although they lack the total freedom of gaseous molecules, these molecules are in constant motion. Because liquids are denser than gases, the collision rate among molecules is much higher in the liquid... 

Fig. 7-2. Model size distributions of the marine background aerosol (a) particle number density, (b) surface area, (c) volume. The contribution of sea salt to the volume distribution is indicated by the shaded area, and arrows indicate the appropriate scale. By integration one obtains a total number density N =290 particles/cm3, a total surface area A = 5.8 x 10 7 cm2/cm3, and a total volume V= 1.1 x 10 " cm3/cm3. For an average density of 103 kg/m3, the mass concentration is 11 pig/m3 (5 pig/m3 of sea salt). The dashed curve gives the distribution of the surface area that is effective in collisions with gas molecules. For larger particles the collision rate is lowered by the rate of diffusion.

The collision rate we have derived is the rate, expressed as the number of 2 particles per second, at which the 2 particles collide with a single 1 (primary) particle. When there are Nu) 1 particles, the total collision rate between 1 and 2 particles per volume of fluid is equal to the collision rate derived above multiplied by Niq. Thus the steady-state coagulation rate (cm-3 s 1) between 1 and 2 particles is... 

We can integrate the collision rate over all aerosol particle sizes. Letting Ap = total aerosol surface area per unit volume of gas, the collision rate per unit volume is... 

The rate constant k in Equation 8.9 is roughly the collision rate constant, which controls the formation of product ions. As shown in Eigure 8.10, the density of product ions, for a sample at a constant concentration, is dependent on both residence time of the sample in the source and its concentration. The depletion of reaction ions is naturally rooted in kinetics of Equation 8.9 and parallels inversely the formation of product ions. The relationship is virtually stoichiometric. Eor a fixed time of residence of sample molecules in the reaction region, the number of product ions and their peak intensity in the mobility spectrum will be quantitatively proportional to the concentration of sample molecules. Also, increases in residence time for [M] in the source region will lead to an increase in the number of product ions as long as the source is not saturated with sample vapor. Once the reservoir of reactant ion charge is totally consumed, no additional increase in product ion intensity will be seen even with additional increase in the concentration of sample molecules. In practice, this limits the upper end of the linear range associated with ion sources at ambient pressure. 

The quantity z can be evaluated from Equation 3.78. It represraits the collision frequency of any one colloid particle. In the given system, the total number of collisions per second is (1/2 zc ), the factor 1/2 being included to avoid double counting. If every collision gives rise to flocculation, then the initial depletion rate in a monodispersed suspension is twice the collision rate, since each colhsion removes two particles ... 

If there are Nj j-particles per unit volume, then the total collision rate is ... 

The collision rate constants, and k, are given by Langevin theory [2, 3] nicely. It is detailed later in this section. It has already been pointed out (see Sect. 1.1) that this type of reaction is totally analogous to neutral radical combination reactions. 

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