Particle situation

In planar waves the amplitude A(r) = Aq is a constant. All particles situated within a plane normal to the wave vector move at the same time. Longitudinal waves are planar waves where the displacements are parallel to the wave vector (v and c are colinear). Longitudinal waves can propagate in every material media. These are compression or dilatation waves. In transverse waves, v and c are orthogonal. Transverse waves do not propagate in fluids. 

Figure 19.12 Geometrical parameters defining size and shape of a lenticular 0 particle situated on a grain boundary in phase a.

For the sintering of small (metal) particles situated on a support surface, several simple mechanisms have been proposed ... 

Probability of photooxidation is different in different points of polymer. First, particles, situated in the points, where quantum yield is higher undergo a reaction. That is why quantum yield gradually decreases during the reaction. 

These zones are approximated as being cylindrical, with the particle situated at the symmetry axis. If a random spatial distribution of microparticles is assumed, the respective diffusion domains (cylinders) are of different sizes, with a probability distribution function as follows [41] ... 

The overall composition of the layers can be characterized by the C/Ni atomic ratio, which was found to be about unity for all of the Ar ion etched samples, except the ones grown at 600 °C, having this ratio of 2.4 and 1.8 for C-Ni and CNX-Ni films, respectively. In comparison with fig. 4, this can be interpreted, that the 10 min etching was sufficient to remove the majority of the Ni particles situated on the film surface. 

FIGURE 12.8 Various modes of bridging two colloidal particles. Situation (c) can only occur for emulsion drops (or possibly gas bubbles) and (d) generally for solid particles. Not to scale the number of polymer molecules involved in situations (a) and (b) would be very much larger than depicted. 

In describing thermodynamic and equilibrium statistical-mechanical behaviors of a classical fluid, we often make use of a radial distribution function g r). The latter for a fluid of N particles in volume V expresses a local number density of particles situated at distance r from a fixed particle divided by an average number density p = NjV), when the order of IjN is negligible in comparison with 1. Various thermodynamic quantities are related to g(r). For a single-component monatomic system of particles interacting with a pairwise additive potential 0(r), the relationship connecting the pressure P to g(r) is the virial theorem, ... 

Applying these equations to the bubble particle situation and. siih.srituting for the bubble rise velocity u gives new equations for t j and y a... 

By solving Eq. (IV.30), an expression has been obtained [137] for calculation of the limiting value of the charge remaining on a particle situated on a grounded surface ... 

Disjoining Pressure and Particle Adhesion. Let us imagine a particle situated on a flat surface in a liquid medium (Fig. Vl.S.a). According to Deryagin [24], the total disjoining effect will be... 

The conditions of flow around particles situated in the stream itself are not the same as the conditions of flow around particles attached to the walls. The air velocity in the main part of the stream is distributed more or less uniformly. In flow around adherent particles lying in the boundary layer, the flow velocity varies from zero up to a certain value. This variation has a substantial effect on the effective air-flow velocity, which determines the drag. Moreover, the particle drag coefficient Cx that appears in Eq. (X.3) depends on the Reynolds number, which in turn is a function of flow velocity, i.e., =/i(Re) and Re =f2(v). 

The conditions for detachment of particles situated in a turbulent boundary layer depends on the relationship between the particle diameter and the thicknesses of the laminar sublayer, the buffer layer, and the turbulent core. If the particle diameter is less than or equal to the thickness of the laminar sublayer,... 

Detachment of Particles Situated in a Laminar Boundary Layer. The action of an air stream on adherent particles under the conditions of a laminar boundary layer (see Fig. X.l. a) or a laminar boundary sublayer (see Fig. X.l. b) have certain features in common but others that differ. The common feature is that there is a linear velocity distribution across the thickness of the laminar layer or sublayer (line c). The difference is that the laminar boundary layer is in direct contact with an air flow having a velocity of Uoo. In the case of a turbulent boundary layer, there is no direct contact between the laminar sublayer and the free stream, which are separated by a buffer layer 3 and a turbulent core 4 (see Fig. X.l.b). These features do affect the drag. 

For flow around a particle situated in a stream, the dynamic pressure is given by... 

Detachment of Adherent Particles Situated in a Laminar Sublayer with Turbulent Flow Over the Surface. Let us examine the conditions for the detachment of adherent particles under conditions of turbulent flow across a dust-covered surface. We will first dwell on the simplest special case in which the particles are located in the laminar sublayer (see Fig. X. 1. b, Position III). The velocity increases within the boundary layer as we go from the laminar sublayer 2 to the buffer layer 3 (curve c). Such an increase in velocity, in accordance with Eq. (X.3), leads to an increase in drag and in the number of detached particles. Hence the thickness of the laminar sublayer is an important quantity, through which we can evaluate the conditions for detachment of adherent particles. 

Detachment of Particles Situated in a Turbulent Boundary Layer. Let us examine the most difficult case, in which the diameter of the adherent particles is commensurate with the thickness of the turbulent boundary layer and is considerably greater than the thickness of the laminar sublayer (see Fig. X.l.b, Position V). In order to determine the drag, we must first determine the drag coefficient of the particle Cx- Under conditions of a turbulent boundary layer, the Reynolds number may vary over a range 1 < Re < 100, and the drag coefficient is approximated here by the following expression [273] ... 

EDS analyses proved that degradation of the cementite lamellae in the steel took place under the influence of sulfur. The results of the analyses shown in Table 4.3 indicate that large amounts of sulfur were present in the degraded particles situated beneath the IS of the tube, down to a depth of 3.5 mna. The greatest concentration of sulfur was found 0.2 mm beneath the surface and the concentration gradually decreased towards the middle-wall. The degraded particles were also emiched in trace elements manganese, chromium and sihcon. 

The curl of a vector field, representing the velocity of a fluid, is related to the phenomenon of rotation of the fluid. Consider V a vector field that represents the velocity field of a fluid particle, and let a point located at (x, y, z). The particles situated in the vicinity of this point tend to rotate around the axis formed by the... 

This loss in signal gives valuable information about the percentage of metal particles situated at the inner surface of the tube. 

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