Brownian motion deposition

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 ... 

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... 

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... 

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. 

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],... 

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. 

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. 

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. 

The rate of deposition of particles onto a surface, in the presence of London, double-layer, and gravitational forces, is calculated in terms of the energy of interaction between cell and surface by assuming that Brownian motion over a potential energy barrier is the rate-determining step of the... 

Rates of deposition of cells in a gravitational field are calculated in the current paper by considering Brownian motion over a potential barrier formed by London and double-layer forces acting between the cells and the surface on which they deposit. 

In short, the rate of deposition of cells onto a surface has been evaluated in terms of the potential energy of interaction for cases in which Brownian motion of the cells over a potential barrier is the rate-determining step of the process. The rate is exponentially sensitive to the height of the barrier. However, accurate calculation of deposition rates in biological systems awaits an appropriate expression for the interaction forces that considers the complexities observed for such systems. 

However, Ruckenstein Prieve (1975a) pointed out that cells are able to overcome the potential barrier between the secondary and the primary minima by a stochastic process similar to Brownian motion. The time delay in the experiments of Weiss Harlos (1972) was explained by suggesting that this escape over the potential barrier is the time consuming step in the overall process of deposition, because only a small fraction of the cells are able, at a given time, to be carried over the barrier. 

The diffusion force, giving the local action of the Brownian motion on the deposition of the microparticle. A modified Peclet... 

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