Velocity, particle theoretical considerations

Stokes established, from theoretical considerations, that for small particles which settle at very low velocities, the settling velocity is independent of the density of the fluid except in so far as this affects the buoyancy. Show that the settling velocity must then be inversely proportional to the viscosity of the fluid. 

The transmitting frequency / of the UVP-DUO systems is 4 MHz in all tests. The ultrasound wavelength X is 370 pm and the sound velocity in water c is 1,480 m/s. 100 mm ion exchange (Diaion) particles are added to the flow as flow tracers their ability to follow the liquid flow has been assessed using Basset s analysis (Melling, 1997). Owing to theoretical considerations, the size of the flow tracers must be larger than one quarter of the emitted ultrasonic burst (Met-Flow, 2002). 

Detonation Front and Shock Front. Detonation Zone and Shock Zone. The shape of the detonation wave and density-distance particle velocity-distance relations behind the wave front are of considerable practical theoretical importance. The deton wave emerging from the end of an unconfined cylindrical chge of a condensed expl is in general spherical in shape. The curvature of this front has a marked effect on both rate pressure of deton. It has been found that there is a minimum radius of convex curvature for each expl, below which deton will not propagate. The min radius of curvature is primarily that at which the divergence is so great that the energy released from the chem reaction of the very small vol of expl involved is insufficient to compensate for the rapid increase in area in the deton front. 

Detonation Wave Shape and Density. Properties This is the title of Chapter 5 in Cook s book (Ref 52 pp 91-122). On p 91, under the title "Theoretical Wave Profiles," Cook stated that the shape of the deton wave and the density- distance p(X) as well as the particle velocity-distance W(x) relations behind the wave front are of considerable importance. Langweiler (Ref 3a, quoted in Ref 52, p 91) assumed for the plane-wave case a simplified constant p(x) and W(x) contour followed by a sharp (presumable discontinuous ) rarefaction. He gave as the velocity of the rarefaction front the value (D + W)/2, where D = deton velocity and W = particle vel. He also stated that in an expl of infinite lateral extent, the compressional region or detonation head of wave should grow in thickness accdg to the equation ... 

In pressure-driven operation, considerable band broadening was observed at high linear velocity, although the separation impedance was much lower than that of a particle-packed column owing to the much lower flow resistance. The separation impedance (E = AP to / r N2 = (AP / N) (to / N) (l/r )) expresses the total column performance in terms of the reciprocal number of theoretical plates per unit time and pressure drop. Because the contributions of the B- and C-terms are expected to be similar for a pressure-driven mode and an electro-driven mode, the difference in performance can be attributed to the greater contribution of the A-terms in Eqn. 5.2 in the pressure-driven mode. The contribution of the A-term is known to be less in CEC than in HPLC [6],... 

It may be seen that the structure of a coating will depend upon the velocity, temperature and size of the particles at the moment of impact. Analysis of the process is, however, made difficult because there will be a statistical distribution of each of these parameters and it is only possible to make some general theoretical predictions Such analysis are, however, of considerable importance for the interpretation of experimental studies of coating structure. 

Besides these practical considerations, describing the motion of particles or individuals by a persistent random walk has several advantages from a theoretical viewpoint (i) The persistent random walk is a generalization of Brownian motion it contains the latter as a limiting case, see above, (ii) The persistent random walk overcomes the pathological feature of Brownian motion or the diffusion equation discussed above it fulfills the physical requirement of bounded velocity, (iii) The persistent random walk provides a unified treatment that covers the whole range of transport, from the diffusive limit to the ballistic limit. 

The two principal factors that have concerned those who attempt to describe theoretically the flux of small particles to horizontal surfaces are their inertia and their low diffusivity. These limitations suggest that particles are incapable of responding to the high-frequency turbulent motions that transport material in the immediate vicinity of a surface. Moreover, transport of particles across any limiting laminar sublayer by molecular diffusion will be exceedingly low, should such a layer exist. As a direct result of considerations such as these it has been predicted that the effective deposition velocity of small particles Jo smooth surfaces would be small, perhaps as low as 10 cm s (10). 

Gillespie [240] performed similar experiments on wires with aerosols of paraffin, stearic acid, and lycopodium powder. For low-flow velocities, the actual and theoretical quantities of collected dust were in good agreement. As the flow velocity was increased, however, the actual quantity of precipitated dust became considerably less than the theoretical quantity. For wires treated with viscous silicone fluids, the number of particles collected was close to the theoretical, whereas on untreated wires the number collected was approximately half of the theoretical number. Under certain conditions, some of the particles became charged, which favored collection of the particles and better adhesion [239]. 

To conclude this section, it should be noted that virtually all the previous considerations for electron impact also hold for the impact by a very fast heavy particle (proton, a-particle), For instance, the expression for the electronic ionization cross section can also be used in the calculation of the cross section for ionization by protons and %-particles, if the particle velocity equals that of the ionizing electron and therefore is substantially higher than the motion velocity of electrons in the ionized atoms and molecules. For this reason, the mass spectra obtained for collisions of fast heavy particles with molecules closely resemple those for electron impact. The theoretical expressions are in fair agreement with... 

---