Particle cross section

Table 1 illustrates the difference in values obtained using three impact sensy techniques, F.l, (see Vol 6, F39-R to F40-R), P.I.G. and P.S.G. The expls used contain known percentages of -100 to +200 mesh carborundum of 1.2 x lO mm2 avg particle cross section Refs 1) Cook (1948), 178-83 2) F.P. 

For a fixed number of colloidal-size spherical particles, 90° scattering intensity appears to be essentially proportional to the particle radius squared (Siebert, 2000) this was attributed to the particle cross-sectional area. 

The total cross section for collision with a fast particle is never greater than twice the geometrical cross-sectional area of the nucleus and therefore, fast particle cross-sections are rarely much larger than 10- 4 cm (radii of the heaviest nuclei are about 10- cjjij Hence a cross-section of 10-24 considered as... 

Figures 4A and 4B are the ultra-thin cross-sections of OsOi+-stained two-stage (styrene//styrene-butadiene) and (styrene-butadiene/ /styrene) latex particles at the stage ratio of 50/50 (LS-10 and LS-11), respectively. Latex samples were mixed with a polymerizable monomer mix of butyl and methyl methacrylates, cured, and microtomed for examination. Figure 4A shows particle cross-sections much smaller than the actual particle size of LS-10. It appears that since the embedding monomer solution was a solvent for polystyrene, the continuous polystyrene phase was dissolved and small S/B copolymer microdomains were left behind. This is further evidence that the second-stage S-B copolymers phase-separated as microdomains within the first-stage polystyrene phase, as shown in Figures 1A and 1A. Figure 4B shows somewhat swollen and deformed particle cross-sections, suggesting that the first-stage cross-linked S-B copolymers were a continuous phase. Indeed, the former (LS-10) behaved like a hard latex, but the latter (LS-11) behaved like a soft latex.

When the size distribution of particles embedded in a continuous solid phase is required, the general approach is to deduce the distribution from the size of particle cross-section in a plane cut through the particle bed. The problem has occupied the attention of workers in diverse fields of science, who have tended to work in isolation and this has led to much duplication of effort. The historical development of this technique has been reviewed by Eckhoff and Enstad [51] and the relevant theory of Scheil by Dullien et. al. [52]. A theoretical analysis [53] has been criticized on several grounds [54]. 

The results of the study are summarized in Table 7.5, along with a brief account of the features of each pj-parameter model. Each model was fitted by least squares to 283 observations of the functions InA iu, where Niuz is the measured axial flux of species i in the wth event, in g-moles per second per cm of particle cross section. This corresponds to using the same variance for each response function lnA j 2. Lacking replicates, we compare the models according to Eq. (7.5-16) with a variance estimate = 0.128/(283 — 6), the residual mean-square deviation of the observations... 

Additionally, a neutron transmission (NT) experiment on H20 / D20 mixtures was recently presented, reporting results in agreement with conventional theory and claiming to present a proof of the absence of the QE effect under consideration [Blostein 2003 (a)]. However, also this experiment does not provide the appropriate, and well defined, sub-femtosecond scattering time [Karlsson 2004], Moreover, it was discussed by Karlsson and Mayers that the neutron coherence length in this NT experiment is much shorter than that in NCS (being about 2.5 A, cf. [Karlsson 2003 (b)]). Thus there are no reasons whatsoever to expect deviations from the conventional, individual particle cross sections [Karlsson 2004],... 

Figure 5.3 Increase in particle cross-section as temperature rises...

Table I lists several properties for target atoms and the detection limits using the NDP facility at the NBS 20 MW reactor. Isotopes with charged particle cross sections of about a barn or greater are given. The detection limits listed in Table I were calculated assuming 0.1 counts per second detected and an acceptance solid angle of 0.1 percent.

This defines the scattering cross section which has the dimension of area but is not in general equal to the particle cross-sectional area. Indeed it is customary to define the scattering efficiency... 

If there are dN particles in the size range dj, to dp + d dp) per unit volume of air, this corresponds to a total particle cross-sectional area of Kd /4)dNdz over the light path length, dz, per unit area normal to the beam. The attenuation of light over this length is given by the relation... 

Fig. 3.3 seems to show particles and their distribution. In reality, what is visible are cross sections through particles at a specific level. If another random section through the same agglomerate is made, a totally different image is obtained. Moreover, particles that seem to float in space are in contact with other particles at some level. For example, the shaded cross section may be the result of cutting the particle shown in elevation on the side of Fig. 3.3, at the indicated line. Obviously this particle will have a completely different outline at another level. The same observation is true for the void spaces (porosity) that are visible between the particle cross sections. 

Because of ionic inertia of the Helmholtz electrical double layer at the surface of the particles, the electrical resistivity becomes infinite as a result, the term (fi /fip) can be neglected. Furthermore, if the particle cross-sectional area Ap is very small compared with the orifice area A0, equation 46 reduces to... 

Let A0 and A represent the orifice cross-sectional area and the particle cross-sectional area projected on the orifice face. Assuming spherical particles, several investigations have been conducted to integrate equation 47 giving... 

Since for small Debye length the situation is completely complementary to the electroosmotic case, we may apply the result of Eq. (7.4.5), identifying Ap as the force per unit particle cross-sectional area exerted by the fluid on the particle. Assuming Stokes flow, we use STTixaU for the force on a single particle if there are n particles per unit volume, then the total force per unit volume is taken to be nF. With the potential drop measured over the suspension height H, it readily follows that... 

The calculated influence of pore diffusion on the coke bum-off (Fig. 4) is also reflected by the measured carbon distribution over the particle cross section for catalyst samples, which were regenerated at different temperatures up to a defined bum-off degree of about 55%. Fig. 5 shows that a pronounced gradient of the carbon load over the particle cross section for a bum-off temperature of 530°C is developed. For a temperature of430°C no gradient is determined. The rate of the oxygen conversion is then so slow, that the diffusion in the pores has no influence and the coke is uniformly burned within the particle according to the (intrinsic) rate of the chemical reaction. Both results are consistent with the kinetic measurements und calculations (see Fig. 4). 

In that a double integration is involved and that a theoretical instead of experimental single particle cross-section is employed, this agreement between theory and experiment should not be construed as a sensitive check on the momentum distribution of nucleons. Their calculation should be considered as indicating the feasibility of interpreting photomeson production from complex nuclei in terms of purely kinematical factors. The possibility of obtaining information on nucleon momentum distributions from more elaborate photomeson production experiments is under investigation by Rankin etal,. ... 

Our model implies independent scattering (the assumption that we share with the great majority of photobioreactor researchers). Indeed, typical biomass concentrations within the process are low enough to reasonably assume that each microbial ceU interacts with radiation independently. We can therefore define particle cross sections a that characterize the radiative properties of microbial cells independently of their concentration Q and keM.p = where... 

The area fraction of the particle cross-section on the unit composite surface, /b. 

For a more exact evaluation of adhesive force, calculations must be based not on the particle cross-sectional area, but rather on the number of contacts between the particles and the surface. Then the specific force of adhesion of a layer of particles F[ can be expressed by the equation [29] ... 

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