Diffusional deposition

The basic operations in dust collection by any device are (1) separation of the gas-borne particles from the gas stream by deposition on a collecting surface (2) retention of the deposit on the surface and (3) removal of the deposit from the surface for recovery or disposal. The separation step requires (1) application of a force that produces a differential motion of a particle relative to the gas and (2) a gas retention time sufficient for the particle to migrate to the coUecting surface. The principal mechanisms of aerosol deposition that are apphed in dust collectors are (1) gravitational deposition, (2) flow-line interception, (3) inertial deposition, (4) diffusional deposition, and (5) electrostatic deposition. Thermal deposition is only a minor factor in practical dust-collectiou equipment because the thermophoretic force is small. Table 17-2 lists these six mechanisms and presents the characteristic... 

The principal mechanisms of disposition in dust collectors are (1) gravitational deposition, (2) flow-line interception, (3) inertial deposition, (4) diffusional deposition, and (5) electrostatic deposition. During the initial operating period, particle deposition takes place mainly by inertial and flow-line interception, diffusion, and gravity. Once the dust layer has been fully established, sieving is probably the dominant deposition mechanism. 

Values for the average vapor-transfer coefficient from the gas phase to the airway epithelium can also be estimated from heat-transfer data in straight, curved, or bifurcating cylindrical tubes by using the analogy between heat transfer and mass transfer. Such an approach has been used by Yeh to predict the diffusional deposition of small particles in the conducting airways. 

Inertial impaction has many inaccuracies and limitations and there are also some relevant differences between deposition in vitro (impactor) and in vivo (respiratory tract) which cause poor correlation between impactor data and lung deposition data. The most important difference is that deposition in vitro is by inertial impaction only, whereas deposition in vivo is by sedimentation and diffusional deposition as well. Except for the possible passage of the final stage (by the finest particles), particle collection in vitro is almost 100% efficient. In con-... 

It is possible to make a rough estimate of the diffusional deposition in a tube of radius R by assuming a residence time of t = Liu, where u is the velocity in a tube of length L ... 

Furthermore, the result is interesting because it indicates that for diffusional deposition with a fixed flow rate, deposition is the same whether one uses a large tube with a low velocity or a small tube with a high velocity. 

In many experiments described and referenced in Chapter 1 an important role was played by diffusional deposition of nonvolatile molecular species (and of particulate matter) on the surface of gas ducts. First of all, in chromatographic columns, the nonvolatile molecules deposit within a short distance from the inlet and contribute to decontamination of the elements under study from interfering radioactive nuclides. Meanwhile, especially in chemical experiments with the aid of aggressive gases, unwanted aerosols occasionally form. The latter diffuse much more slowly, and when they catch and then carry a fraction of the nonvolatile molecular species, they make the depositional decontamination less efficient. 

For the rectangular channels the diffusional deposition problem was solved only for an infinitely wide duct. Real channels have a finite ratio of the height to the width, bh/bw. If it is 1, the formula allows one to use the flow rate rather than the flow velocity. The general form of the solution for such channels with... 

Because Sc is inversely proportional to D, the values of Schmidt number for aerosols are much larger than unity. In practice one meets the problem of diffusional deposition of polydisperse aerosols. A solution to this problem for rectangular and circular tubes was proposed in Refs. [10,20]. 

The mathematics of diffusional deposition is the same for particles ranging from atoms to aerosol particulates. Because of smaller diffusion coefficients, tiny aerosols deposit more slowly than do the molecular entities. 

When looking for a reasonable approximation of p(t] ), one can consult the equations of Sect. 2.2. They describe diffusional deposition in channels under various flow regimes, when the tracer is evenly distributed over the inlet area. The solutions for both hydrodynamically and diffusionally developing flow directly apply to the problem of the first jump down the column. It is the common experimental situation... 

The limit is somewhat shorter than the longest component of the diffusional deposition profile from laminar flow given by Eq. 2.45, for which the numerical coefficient in the denominator is 3.65 cf. the discussion in Sect. 2.2.2. From the formula 4.50 it follows that the limiting // depends on the temperature as t] 1 /but does not depend on pressure or on the column diameter. 

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