Deposition Brownian

The aerosol model In VICTORIA accounts for the following basic mechanisms (1) condensation or evaporation from aerosol particle surfaces (2) deposition onto structural surfaces (3) agglomeration of aerosol particles (4) and transport of aerosols from one cell to another by advection. The deposition mechanisms modeled are gravitational settling, laminar or turbulent deposition. Brownian motion, thermophoresis, diffusiophoresis, and inertial deposition in curved channels (bends). Agglomeration mechanisms include Brownian motion, relative gravitational motion. Interactions In a shear field, and inertia in a turbulent field. 

Other lesser mechanisms that result in aerosol removal by filters are (1) gravitational settling due to the difference in mass of the aerosol and the carrying gas, (2) thermal precipitation due to the temperature gradient between a hot gas stream and the cooler filter medium which causes the particles to be bombarded more vigorously by the gas molecules on the side away from the filter element, and (3) Brownian deposition as the particles are bombarded with gas molecules that may cause enough movement to permit the aerosol to come in contact with the filter element. Browruan motion may also cause some of the particles to miss the filter element because they are moved away from it as they pass by. For practical purposes, only the three mechanisms shown in Fig. 29-1 are normally considered for removal of aerosols from a gas stream. 

Mean airflow velocities approach zero as the inspired airstream enters the lung parenchyma, so particle momentum also approaches zero. Most of the particles reaching the parenchyma, however, are extremely fine (< 0.5 pm MMAD), and particle buoyancy counteracts gravitational forces. Temperature gradients do not exist between the airstream and airway wall because the inspired airstream has been warmed to body temperature and fully saturated before reaching the parenchyma. Consequently, diffusion driven by Brownian motion is the only deposition mechanism remaining for airborne particles. Diffusivity, can be described under these conditions by... 

Particulate diffusion does not play a significant role in the deposition of pharmaceutical aerosols. However, it is worth noting the mechanism by which diffusion of particles occurs in the lungs. The principle of Brownian motion is responsible for particle deposition under the influence of impaction with gas molecules in the airways. The amplitude of particle displacement is given by the following equation ... 

In the general case, when arbitrary interaction profiles prevail, the particle deposition rate must be obtained by solving the complete transport equations. The first numerical solution of the complete convective diffusional transport equations, including London-van der Waals attraction, gravity, Brownian diffusion and the complete hydrodynamical interactions, was obtained for a spherical collector [89]. Soon after, numerical solutions were obtained for a panoplea of other collector geometries... 

The main disadvantage of the perfect sink model is that it can only be applied for irreversible deposition of particles the reversible adsorption of colloidal particles is outside the scope of this approach. Dahneke [95] has studied the resuspension of particles that are attached to surfaces. The escape of particles is a consequence of their random thermal (Brownian) motion. To this avail he used the one-dimensional Fokker-Planck equation... 

Valdes models the electro-deposition of Brownian particles on a RDE, by solving the steady-state convective diffusion equation ... 

The previous models were developed for Brownian particles, i.e. particles that are smaller than about 1 pm. Since most times particles that are industrially codeposited are larger than this, Fransaer developed a model for the codeposition of non-Brownian particles [38, 50], This model is based on a trajectory analysis of particles, including convective mass transport, geometrical interception, and migration under specific forces, coupled to a surface immobilization reaction. The codeposition process was separated in two sub-processes the reduction of metal ions and the concurrent deposition of particles. The rate of metal deposition was obtained from the diffusion... 

Polymerization in microemulsions allows the synthesis of ultrafine latex particles in the size range of 5 to 50 nm with a narrow size distribution [33], The deposition of an ordered monolayer of such spheres is known to be increasingly difficult as the diameter of such particles decreases [34], Vigorous Brownian motion and capillary effects create a state of disorder in the system that is difficult... 

Elimelech, M., and Ch. R. O Melia (1990), "Effect of Particle Size on Collision Efficiency in the Deposition of Brownian Particles with Electrostatic Energy Barriers", Langmuir 616,1153-63. 

Diffusion here refers to the movement of ions and/or neutral species through the deposition bath or solution as a consequence of concentration gradients. It is primarily the result of random (Brownian) molecular motion, and it serves to produce more uniform distribution of the various component species in the bath. Depletion of ions next to the cathode will result in movement of the species from the (nearly unchanged) bulk of the bath toward the cathode. 

Deposition efficiencies for particles in the respiratory tract are generally presented as a function of their aerodynamic diameter (e.g. [8,12]). Large particles (> 10 pm) are removed from the airstream with nearly 100% efficiency by inertial impaction, mainly in the oropharynx. But as sedimentation becomes more dominant, the deposition efficiency decreases to a minimum of approximately 20% for particles with an aerodynamic diameter of 0.5 pm. When particles are smaller than 0.1 pm, the deposition efficiency increases again as a result of dif-fusional displacement. It is believed that 100% deposition due to Brownian motion might be possible for particles in the nanometer range. 

Other factors also come into play in laboratory systems. For example, McMurry and Rader (1985) have shown that particle deposition at the walls of Teflon smog chambers is controlled by Brownian and turbulent diffusion for particles with Dp 0.05 yxm and by gravitational settling for particles with Dp > 1.0 yxm. However, in the 0.05- to 1.0-yxm range, the deposition is controlled by electrostatic effects Teflon tends to... 

In contrast, the three- or two-dimensional morphologies of colloidal aggregates via Brownian particle trajectories show a fractal-like structure. One of the most prominent features of the surface deposits formed by the diffusion-limited aggregation mechanism is the formation of isolated treelike clusters (9). In our experiments, the surface morphology of the silica-coated polyethylene composite prepared by... 

The deposition of particles on macroscopic surface is the primary goal in CVD processes, bnt rednces the efficiency of vapor phase particle synthesis. Particles can deposit by Brownian motion, bnt in high-temperature reactors, thermophoretic deposition often dominates. Thermophoresis is the migration of small aerosol particles as a resnlt of a temperatnre gradient. It causes particles carried in a hot gas to deposit on a cool surface. Eor small particles, Kn 1, a dimensionless group can be created to describe thermophoresis, Th ... 

Let us apply the interpolation procedure to a case involving an electric field. It is well known that the efficiency of the granular bed filters can be significantly increased by applying an external electrostatic field across the filter. In this case, fine (<0.5-/rm) particles deposit on the surface of the bed because of Brownian motion as well as because of the electrostatically generated dust particle drift [51], The rate of deposition can be calculated easily for a laminar flow over a sphere in the absence of the electrostatic field [5]. The other limiting case, in which the motion of the particles is exclusively due to the electric field, could also be treated [52], When, however, the two effects act simultaneously, only numerical solutions to the problem could be obtained [51],... 

Attachment of decay products to nuclei greatly affects the process of deposition, because the Brownian diffusivity of nuclei is typically about four orders of magnitude less than the molecular diffusivity of unattached decay products. The lifetime of decay products in air before deposition on surfaces is shorter if the air is clean than if it is dirty. 

Air movement indoors is much slower than outdoors, but it is usually enough to ensure that concentrations are fairly uniform in a room. Convection from heating appliances gives air speeds typically in the range 0.05-0.5 m s-1 (Daws, 1967). However, to undergo deposition, vapour molecules or particles must be transported across the boundary layer, typically a few millimetres thick, of almost stagnant air over surfaces. This may be achieved by sedimentation, molecular or Brownian diffusion, or under the action of electrostatic or thermophoretic forces. 

Figure 1.10 shows the velocities of deposition to a smooth surface of attached and unattached decay products, with a range of possible values of D. The scales are m s-1 for the attached and mm s 1 for the unattached decay products, illustrating the effect of attachment on diffusivity. For a nucleus of unit density with diameter, dp, equal to 0.17/um, the sedimentation velocity is 2 jum s 1, and deposition by Brownian diffusion and by sedimentation to upwards-facing surfaces are of comparable efficiency. For smaller particles, Brownian diffusion is always more effective. 

Deposition other than in rain is termed dry deposition, and this includes sedimentation of particles, molecular and Brownian diffusion to surfaces, impaction on roughness elements and deposition under electrical or thermophoretic forces. The velocity of deposition is defined... 

Experiments on transfer of submicrometre radioactive particles to smooth surfaces (Wells Chamberlain, 1967 Chamberlain et al., 1984) have shown that the dependency of vg on D213 holds over many orders of magnitude of D. This means that the transport by Brownian diffusion becomes progressively less effective as the particle size increases. For example a particle of 0.1 pm diameter has a diffusivity of 6.8 x 10 10 m2 s 1, a factor 1.2 x 104 smaller than that of I2 vapour. Since D does not depend on the particle density, it is appropriate to discuss transport by Brownian motion in terms of the particle diameter. The aerodynamic diameter, dA, is equal to dppp2 where pp is the particle density in c.g.s. units (g cm-3) not SI units (kg m-3), and is the appropriate parameter for particles with dp> 1 pm, for which impaction and sedimentation are the mechanisms of deposition. 

The different mechanisms of deposition determine the shape of the curves in Fig. 6.9. For particles of diameter less than 0.2 /tm, Brownian diffusion is the dominant mechanism and vg varies according to Dm, as expected from equation (6.4). The minimum is at dp between 0.1 and 1 /un, where particles are too large to have appreciable Brownian motion but too small to impact. 

In the pulmonary region, air velocities are too low to impact particles small enough to reach that region, and the mechanisms of deposition are sedimentation and Brownian diffusion. The efficiency of both processes depends on the length of the respiratory cycle, which determines the stay time in the lung. If the cycle is 15 breaths/min, the stay time is of the order of a second. Table 7.1 shows the distance fallen in one second and the root mean square distance travelled by Brownian diffusion in one second by unit density particles (Fuchs, 1964). Sedimentation velocity is proportional to particle density, but Brownian motion is independent of density. Table 7.1 shows that sedimentation of unit density particles is more effective in causing deposition than Brownian diffusion when dp exceeds 1 pm, whereas the reverse is true if dp is less than 0.5 pm. For this reason, it is appropriate to use the aerodynamic diameter dA equal to pj dp when this exceeds 1 pm, but the actual diameter for submicrometre particles. 

The lines in Fig. 7.4 are the results of theoretical calculations, using models of the respiratory tract (Yu Diu, 1982). The points are measurements with radioactive aerosols. Numerous other determinations of fractional deposition in the whole tract have been made, using non-radioactive methods to count the number of particles in the inhaled and exhaled air (Heyder et al., 1986 Schiller et al., 1988). Fractional deposition is least for particles of about 0.2 to 0.5 m diameter. Table 7.1 shows that the combined effect of sedimentation and Brownian motion is then at a minimum. 

A comparison of the results with other data on the deposition of submicrometre aerosols, all related to a tidal volume of 11, is shown in Fig. 1.14. Although the density of the lead particles was greater than that of the other particles, the fractional deposition was similar, except possibly for the 0.5 pm size, because deposition was by Brownian motion. The percentage deposition increases for particles of diameter less than 0.1 /urn, and this means increased uptake of lead, relative to a given PbA, for persons exposed to non-aggregated aerosol, as found alongside major roads. 

Airborne particles may be delivered to surfaces by wet and dry deposition. Several transport mechanisms, such as turbulent diffusion, precipitation, sedimentation, Brownian diffusion, interception, and inertial migration, influence the dry deposition process of airborne particles. Large particles (dNIOAm) are transported mainly by sedimentation hence, large particulate PAHs tend to be deposited nearer the sources of emission Small particles (dblAm), which behave like gases, are often transported and deposited far from where they originated (Baek et al., 1991 Wu et al., 2005). 

Filtration is a physical separation whereby particles are removed from the fluid and retained by the filters. Three basic collection mechanisms involving fibers are inertial impaction, interception, and diffusion. In collection by inertial impaction, the particles with large inertia deviate from the gas streamlines around the fiber collector and collide with the fiber collector. In collection by interception, the particles with small inertia nearly follow the streamline around the fiber collector and are partially or completely immersed in the boundary layer region. Subsequently, the particle velocity decreases and the particles graze the barrier and stop on the surface of the collector. Collection by diffusion is very important for fine particles. In this collection mechanism, particles with a zig-zag Brownian motion in the immediate vicinity of the collector are collected on the surface of the collector. The efficiency of collection by diffusion increases with decreasing size of particles and suspension flow rate. There are also several other collection mechanisms such as gravitational sedimentation, induced electrostatic precipitation, and van der Waals deposition their contributions in filtration may also be important in some processes. 

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