Particles Deposition on the Obstacles

The role of hydrodynamic interaction in Brownian diffusion was discussed in Section 8.2. Consider now its effect on turbulent coagulation. Formally, it can be taken into account in the same manner as in Brownian motion, by introducing a correction multiplier into the factor of turbulent diffusion (10.57). Another, more correct way (see Section 11.3) is to use the Langevin equation that helped us determine the factor of Brownian diffusion in Section 8.2. As was demonstrated in [60], the factor of turbulent diffusion is inversely proportional to the second power of the hydrodynamic resistance factor  

A further discussion of these issues and the review of the pertinent works in this field is offered in [61-63] (see also part V). 

Consider now some technical apphcations of the models of particle interaction (with no hydrodynamic interaction forces) that have been presented earlier. 

In the following discussion we neglect the inertia of particles. We also ignore surface (molecular and electrostatic) interactions. The proper account of surface forces will be made in the following section, and of inertia - in Section 10.5. Problems on deposition of small particles on obstacles are presented in works [36, 52, 58, 61], 

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Knowing the characteristics of the flow and the obstacle, we can calculate the parameter Ci and can determine r Q. On the basis of the capture coefficient and the number of particles in the stream, we can calculate the number of particles deposited on the obstacle by using Eq. (IX.32). It is also possible to solve the reverse problem i.e., from the number of adherent particles and the value of r o, we can calculate the dust content of the stream. 

In flow around lateral surfaces, the detaching force increases as a result of the increasing flow velocity. On the backside of the obstacle, the adhesion is greater because of vortices, particularly in the case of small particles. The mechanism of particle deposition on the front and rear sides of the object in the... 

When the wind blows past an obstacle, the streamlines of air flow diverge to pass round it. Particles carried in the wind tend to carry straight on and may impact on the obstacle. The efficiency of impaction C, is defined as the ratio of the number of impacts to the number of particles which would have passed through the space occupied by the obstacle if it had not been there. If vg is the velocity of deposition relative to the profile area of the obstacle, then C = vglux where ux is the free stream air velocity. C, is thus analogous to Cd, the drag coefficient of the obstacle. 

Adhesion of Dust to Cylindrical and Spherical Surfaces. The number of particles of a given size deposited on an obstacle can be calculated from the equation... 

Impaction is caused by the inertial mass of the traveling aerosol particles that forces them to move in a straight-line direction even when the flow of the inhaled air transporting them is bent around a curvature. Hence the particles tend to deposit on obstacles placed in the path of their travel. The inertial mass depends on particle size, density, and velocity. The stopping distance S of a particle having mass mP and initial velocity v0iP is defined according to... 

When aerosols are in a flow configuration, diffusion by Brownian motion can take place, causing deposition to surfaces, independent of inertial forces. The rate of deposition depends on the flow rate, the particle diffusivity, the gradient in particle concentration, and the geometry of the collecting obstacle. The diffusion processes are the key to the effectiveness of gas filters, as we shall see later. 

When particles experience a mean curvilinear motion and also have Brownian agitation, they are deposited on obstacles by both mechanisms. For very small particles of radii less than 0.1 /xm, Brownian motion dominates particle collection on surfaces. For larger particles, inertial forces dominate. An example of the difference in collection efficiency for spherical collectors of different size is shown in Fig. 3 for different particle diameters and aerosol flow velocity. 

Consider deposition of particles on an obstacle due to Brownian diffusion in a slow flow whose velocity far from the obstacle is U [36]. As an obstacle, we take a solid sphere of radius a. 

Consider now the effect of inertial deposition, which plays a noticeable role in deposition on obstacles of rather large particles whose density differs strongly from that of the ambient liquid. 

The behavior and stability of suspensions and colloidal systems, including non-charged and charged suspensions, along with the coagulation and sedimentation of particles and their deposition on obstacles, are considered in Section IV. Chap-... 

The greater the absolute and relative values of dynamic hardness of the material, the fewer the number of particles that will be deposited on this material, and the higher the value of the second critical velocity (see Fig. IX. 1). The data we have obtained can also be used in calculating the depth of particle embedment in the material of an obstacle. On the basis of the value of the relative dynamic hardness o, which is equal to the ratio m/ w (the subscript m is... 

Influence of Flow Velocity on Adhesion of Particles to Plates. The adhesion of particles to plates will depend on the velocity of the dust-laden stream (see Fig. IX.7). As the air-flow velocity is increased from 5 to 25 m/sec, we also see an increase in the relative amount of fine particles attached to the surface (lines a and b), apparently because of the specific features of the flow around the obstacle. The influence of air-flow velocity is taken into account only indirectly in Eq. (IX.42), through the number n. Only at the initial moment, when there are no adherent particles on the surface, will the number of deposited particles be proportional to the number of particles striking the surface. Thereafter, there is an increased probability that the incident particles will strike particles previously stuck to the surface, so that the probability of particle rebound is increased. 

The effect of an electric field on the processes of deposition and adhesion of particles can be arbitrarily classified as either weak or strong. The effect of an electric field is considered to be weak if it is not able to change the trajectory of particle flight. If the field has a strong effect, the movement of the particles near an obstacle and the particle adhesion will be determined mainly by the presence of the electric field. If a field with a strong effect is present, the particle adhesion will depend on the relationship between the parameters G and H. The lack of any adhesion under the influence of an electric field is shown in Fig. IX.9 as cases c, e, and f adhesion to part of the surface is shown as cases b and d and adhesion across the entire surface of the obstacle is shown as case a. 

Dust carried by a stream may adhere to the inside surfaces of air ducts or to obstacles placed in the stream. In order to prevent the deposition and adhesion of particles on the bottom of an air duct, the vertical pulsating velocity of the stream must exceed the settling rate of the dust particles. If the flow velocity is limited to about 30 m/sec, this is possible only for small particles with diameters less than 10 /xm larger particles may adhere to the bottom of the air duct. 

The deposition of particles on individual fibers and wires differs from the filling of a filter with dust particles. First, deposition depends not only on adhesion, but also on the conditions of flow around the obstacle and on the elastic properties of the surface (see Section 39) second, in the actual filtration process, the particles fill up the pore space of the filter and block this space. 

The coefficient of deposition (K ep) depends both on the conditions governing the flow around obstacles and on the elastic properties of the surface. For the same flow conditions the value of Kdep is directly proportional to the ratio Fad/Feias- Since the value of this ratio increases with diminishing particle size, K j p will increase as r falls. This was in fact observed by Tekenov [83] in experiments on the adhesion of loess particles to a glass surface (Fig. VI.19). For low velocities (up to 4 m/sec) particles of all sizes adhere to a plane glass surface. On increasing the airflow velocity the adhesion of the large particles diminishes (curves 1 and 2). Particles less than 1 m in diameter adhere even for relatively large flow velocities (up to 15 m/sec). 

In the present case, Kdep is the ratio of the number of adhering particles to the total number of particles which have passed through the middle section of the obstacle. The amount of adhering dust and the value of the deposition coefficient depend on tiie conditions governing the flow of the dust-laden air stream around the obstacles, the possible rebounding of particles from the surface, and also the adhesive forces capable of holding these particles. 

The number of particles adhering to an obstacle is determined by the coefficient of deposition, the value of which depends both on the size distribution of the dust and the dimensions of the... 

For a flow velocity exceeding a certain value (first critical velocity) the particles will rebound. The value of the first critical velocity depends on the elastic properties of the particle and obstacle surfaces and is inversely proportional to the particle size [see formula (V.ll)l. The coefficient of deposition increases when the possibility of particle rebound is eliminated. This may be achieved by making the surface tacky or increasing the adhesive force, particularly by virtue of the triboeffect and the cooling of the molten zone of contact. 

The deposition of particles on single filaments and wires is to be distinguished from the filling of a filter with dust particles. Whereas, in the first case, deposition depends on the flow conditions around the obstacle and the elastic properties of the surface as well as adhesion (see 34), in the second (the filtration process) the whole volume of the pores in the filter is filled with particles and clogging takes place. 

I 70 Stability of Suspensions, Coagulation of Particles, and Deposition of Particles on Obstacles Introduce the volume concentration of particles... 

The conditions governing the deposition of dust particles on obstacles lying in an air flow were studied e q)erimentally in [312-3161. 

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