Deposition from Laminar Flow

The deposition of ultrafine particles has been measured in replicate hollow casts of the human tracheobronchial tree. The deposition pattern and efficiency are critical determinants of the radiation dose from the short lived decay products of Rn-222. The experimental deposition efficiency for the six airway generations just beyond the trachea was about twice the value calculated if uniform deposition from laminar flow is assumed. The measured deposition was greater at bifurcations than along the airway lengths for 0.2 and 0.15 ym diameter particles ... 

Fig. 3.6 Top Density profile of an irreversibly adsorbed species deposited from laminar flow in circular tubes. The reduced distance is z = tf/°z = Jt Dz/Q Analytical solution for hydrody-namically developed flow is given by Eqs. 2.47 (near inlet) and 2.44 - corresponding parts of the curve are divided by the thick mark the engineering approach is Eq. 2.59 with Sh from Eq. 2.54. In the case of hydrodynamicafly developing flow, i// taken from Eq. 2.61 was substituted into Eq. 2.59.

Pich, J., Theory of Gravitational Deposition of Particles from Laminar Flow in Channels, Aerosol Sci. 3 351-361 (1972). 

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. 

Many non-Newtonian slurries are relatively viscous so that laminar flow occurs frequently. The slurries often contain a significant concentration of particles coarse enough to form deposits. It is known that the transition from turbulent flow to laminar flow for a non-Newtonian slurry often results in a deposit being formed. On the other hand many slurries do not form deposits in laminar flow, especially when the pressure gradient is high. These observations are qualitatively consistent with those known to occur with Newtonian slurries. 

Essentially, except for once-through boilers, steam generation primarily involves two-phase nucleate boiling and convective boiling mechanisms (see Section 1.1). Any deposition at the heat transfer surfaces may disturb the thermal gradient resulting from the initial conduction of heat from the metal surface to the adjacent layer of slower and more laminar flow, inner-wall water and on to the higher velocity and more turbulent flow bulk water. 

In the case of laminar flow, the velocity of the gas at the deposition surface (the inner wall of the tube) is zero. The boundary is that region in which the flow velocity changes from zero at the wall to essentially that of the bulk gas away from the wall. This boundary layer starts at the inlet of the tube and increases in thickness until the flow becomes stabilized as shown in Fig. 2.4b. The reactant gases flowing above the boundary layer have to diffuse through this layer to reach the deposition surface as is shown in Fig. 2.3. 

Fig. 3. Diagrams of electrochemical cells used in flow systems for thin film deposition by EC-ALE. A) First small thin layer flow cell (modeled after electrochemical liquid chromatography detectors). A gasket defined the area where the deposition was performed, and solutions were pumped in and out though the top plate. Reproduced by permission from ref. [ 110]. B) H-cell design where the samples were suspended in the solutions, and solutions were filled and drained from below. Reproduced by permission from ref. [111]. C) Larger thin layer flow cell. This is very similar to that shown in 3A, except that the deposition area is larger and laminar flow is easier to develop because of the solution inlet and outlet designs. In addition, the opposite wall of the cell is a piece of ITO, used as the auxiliary electrode. It is transparent so the deposit can be monitored visually, and it provides an excellent current distribution. The reference electrode is incorporated right in the cell, as well. Adapted from ref. [113],...

In comparison with the large amount of literature that is available on the deposition of particles from laminar fluid flows, literature on turbulent deposition is virtually non-existant [114]. It was mentioned that the trajectory and convective diffusion equations also apply when the fluid inertial effects are considered, including the case of turbulent flow conditions, provided one is able to express the fluid velocities explicitly as a function of position and time. 

An important factor that influences the lead distribution, especially in the channeled monolith bodies, is the character of flow. There is strong evidence that an induced change of the flow from laminar to turbulent augments the deposition of lead. An example is given in Fig. 7 by the deposition pattern of lead in a dual catalyst. Within each of the catalysts, the deposit pattern is in agreement with those shown in Figs. 4 and 5. However, the lead deposit on the inlet of the oxidation catalyst exceeds con-... 

The flow velocity in a pipe or stirred vessel that corresponds to a transition from laminar to turbulent flow conditions, or vice versa. See also Critical Deposition Velocity. 

The efficiency predicted by Eq. 8.15 is only a rough estimate the equation estimates a shape in the efficiency-versus-particle-size curve that is different from what is actually observed. There are a number of factors not considered in this elementary derivation. First, laminar flow is assumed, but turbulent flow is often observed in practice. The effect of turbulence will be to move particles away from the cyclone walls or resuspend deposited ones. Hence, turbulence will decrease cyclone efficiency. Second, the width of the cyclone inlet is not as important a parameter as overall cyclone diameter, since it is the width of an element of gas within the cyclone that determines particle deposi-... 

The above evidence establishes that fracturing and seismic behavior can extend well into the zone of mid to lower crustal metamorphism at rock pressures of —0.5-1 GPa. Veins preserve a valuable record of this brittle deformation they are fractures in which mineral mass has been deposited. The most common vein-forming minerals are quartz, calcite, and the feldspars, but a huge variety of other minerals are also observed. Fractures tend to focus flow, because they are zones of elevated permeability. Fracture flow is commonly approximated using the well-known expression from fluid mechanics for laminar flow between two parallel plates (e.g., White, 1979). For a set of parallel fractures, the flux is approximated by (e.g., Norton and Knapp, 1977) ... 

Figure 3.6 displays graphs of the pertinent formulae for the laminar flow regime from Sect. 2.2. They describe the profile of the deposit density q>v(z ) and that of penetration Fp(zv) - the fraction of the adsorbable particles still staying in gas at the exit of the channel. Notice that the reduced distance also equals the ratio of the doubled gas hold-up time fg in a tube of the length z to the average time needed by the particles to diffuse across the channel diameter dc ... 

In this section and the next, we discuss particle deposition by diffusion from laminar and turbulent flows through a. smooth-walled pii>e. The particle diameter is assumed to be much smaller than the lube diameter (or viscous sublayer thickness for turbulent flow), so the mterception parameter that was important in the previous discussions does not play a role. 

Note that the surface roughnesses associated with smooth stone, galvanized steel, and painted surfaces are hydraulically smooth, that is they should have no substantial effects on boundary profiles and hence deposition velocity. Between 0.33 and 3mm, transition from laminar to turbulent flow may occur, depending on the Reynolds number. 

The Oroskar-Turian s correlation and previous ones were developed to determine the critical deposit velocity of Newtonian carrier fluids with various particle sizes and concentrations. Shah and Lord (7) generalized equation 2 to extend its capability to correlate the critical deposit velocity for non-Newtonian carrier fluids (power law). The parameter X was eliminated from equation 2 because of its insignificant contribution to the correlation results and because it would be undefined for the laminar flow regime of non-Newtonian fluids. The generalized form of equation 2, which can be applied to either critical deposit (VD) or resuspension velocity (Vs), is as follows ... 

Castillo, J.L. and Rosner, D.E., 1988, Non-equilibrium theory of surface deposition from particle laden dilute condensable vapour containing steam, allowing for particle thermophoresis and vapour scavenging within the laminar boundary layer. Int. J. Multiphase Flow 14, 1, 99. 

The deposition of nanoparticles is an important aspect of a nanostmctures creation on a substrate [1,2]. A better understanding of complex interaction in gas dynamic processes, heat transfer and Brownian diffusion is important for proper control of the deposition. In this paper we investigate steady-state deposition of nanoparticles from a laminar flow of a hot gas between two cold flat substrates. We will use a two-dimensional description of all processes in the model. 

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