Aerosol Reynolds number

Reynolds number is a fundamental parameter used to describe the fluid properties associated with an aerosol. Equations describing the resistance offered by a particle depend on whether the flow is laminar or turbulent, and the Reynolds number provides knowledge of the type of flow present. 

Example 4.2 An aerosol comprised of 1.0-p.m-diameter spheres flows through a 16-in-diameter duct with a velocity of 3500 ft/min. Determine the Reynolds number of the air flowing in the duct and of the particles in the air. 

Equations of motion presented here were developed for cases of uniform medium velocity and are oversimplified for many other cases regarding aerosols. In addition, evaluation of the equations for the trajectories of aerosol particles is sometimes impossible because of the difficulty in accurately describing the field of flow. Although for laminar flow Eq. 6.6 can be separated into x and y components, with increasing Reynolds number the nonlinearity of the resisting force prevents separation of the vector equation. Fortunately, most aerosol problems can be treated in the low-Reynolds-number regime. 

Even though the Reynolds number is small, there are many practical situations in which Pe = Re Sc is large because the Schmidt number, Sc. for aerosols is very large. For Pe I, two important simplifications can be made in the equation of convective diffusion. First, diffusion in the tangential direction can be neglected in comparison with convective transport ... 

Because /lisa relatively slowly varying function of Reynolds number, the efficiency varies approximately as which means that fine fibers are more efficient aerosol collectors than coarse ones. Because Pe = // ), tj/f ond for the continuum and... 

SOLUTION To analyze the problem, consider particle deposition on a single cylinder placed normal to an aerosol flow. The Reynolds number for the flow, based on the cylinder diameter, is 2320, which is sufficiently large to use the potential flow approximation for the stagnation region. We know that the critical Stokes number for the cylinder is... 

A duct 4 ft in diameter with a 90 bend has been designed to carry particles In the range I < dp < 20 which adhere when they strike the wall. Before construction, it is proposed to carry out bench scale experiments to determine the particle deposition rate in the bend. The model is to be built to 1/10 scale, and the same aerosol will be used as in the full-scale system, Show that it is not pos.siblc to ntainlain both Stokes and Reynolds number similarity in the full-scale and model systems. If Stokes similarity is to be preserved, calculate the Reynolds number ratio for the model to full-scale systems. Why is it more important to preserve Stokes than Reynolds similarity in such experiments ... 

An aerosol with particles in the micron size range flows around a smooth solid sphere a few millimeters in diameter. At sufficiently high Reynolds numbers, a laminar boundary layer develop.s over the sphere from the stagnation point up to an angle of about 110 at which. separation takes place. The removal of particles by direct interception can be calculated from the velocity distribution over the forward. surface of the sphere, up to 90 from the forward stagnation point (Fig. 4.P4). 

In experiments designed to test the scaling laws, size distributions and number concentrations of dibutyl phthalate (DBP) aerosol were measured for different jet velocities, vapor concentrations, nozzle diameters, and sampling positions in a bench-scale condensing Jet. Two different nozzle diameters were used, 0.235 and 0.375 cm, and jet Reynolds numbers were greater than 3000. 

The stream splitting concept was tested experimentally by measuring the particle concentration in jets with two different nozzle diameters and the same Reynolds number. The results are shown in Fig. 10.12. For a given axial position and vapor concentration, the aerosol concentration measured on the Jet centerline was proportional to the nozzle diameter. For example, at 20 nozzle diameters, for Re = 4700, the concentration in the Jet with d = 0.375 cm was 5400/cm, and the one with d = 0.235 cm was 2I00/cm . The ratio of the two mea.sured particle concentrations was close to the theoretically predicted value (0.375/0.235) = 2.6. The stream splitting correlation held for the entire range of vapor concentrations tested in the experimenLs. 

In Chapters 3 and 4 we analyze mass and heat transfer in plane channels, tubes, and fluid films. We consider the mass and heat exchange between particles, drops, or bubbles and uniform or shear flows at various Peclet and Reynolds numbers. The results presented are of great importance in obtaining scientifically justified methods for a number of technological processes such as dissolution, drying, adsorption, aerosol and colloid sedimentation, heterogeneous catalytic reactions, absorption, extraction, and rectification. 

The Reynolds number for a particle Rep of supercritical size, deposited on the surface of a sufficiently large bubble (for which a potential distribution of the liquid velocity field is valid), is much larger than imity. In this case, the hydrodynamic resistance is expressed by a resistance coefficient. In aerosol mechanics a technique is used (Fuks, 1961) in which the non-linearity from the resistance term is displaced by the inertia term. As a result, a factor appears in the Stokes number which, taking into account Eq. (11.20), can be reduced to (l + Rep /b). This allows us to find the upper and the lower limits of the effect by introducing K instead of K " into Eq. (10.47) and the factor X in the third term. 

Separate from particle/droplet size and the Knudsen number, there is another reason that aerosol sedimentation does not always follow Stokes law. As the flow regime goes from laminar flow (viscous dominated Reynolds number, Af u < 1) to turbulent flow (inertia dominated Reynolds number, Nr > 1000), things change (see Section 6.1 and Equation 6.6 for more on the Reynolds number). 

Figure 2.24 Illustration of flow regimes in aerosol sedimentation, as the flow regime goes from laminar flow (viscous dominated Reynolds number, Nf, < 1) to turbulent flow (inertia...

Diffusion is the primary transport mechanism of a nanoaerosol. The thermal velocities of nanoaerosol particles follow certain distribution due to the random motion of the surrounding gas molecules. The actual velocity distribution is not well determined, but most researchers assume it to follow the Maxwell-Boltzmaim distribution [1]. The diffusion coefficient of aerosol particles in the air with low Reynolds number is determined by the Stokes-Einstein equation... 

FIGURE 13.1. In the movement of aerosol particles, the type of flow in the gas phase will significantly affect the fate of the particles. For Reynolds number, Re, <1, laminar flow will prevail (a). However, since gases are usually of very low viscosity compared to liquids, it is more common to encounter the situation where Re > 1000. In that case, turbulent flow is common and particle dynamics is much more difficult to model. 

McLaughlin [141] used the one-way coupling approach to simulate the motion of aerosol particles in a turbulent channel flow. The particle Reynolds number was smaller than unity for most of the particles although some particles occasionally attained Reynolds numbers larger than unity as a result of interaction with unusually strong eddies. 

L. de Juan and J. Fernandez de la Mora, Size analysis of nanoparticles and ions Running a Vienna DMA of near optimal length at Reynolds numbers up to 5000, J. Aerosol Sci. 29, 617-626, 1998. 

Collins LR, Keswani A Reynolds number scaling of particle clustering in turbulent aerosols. New J Phys 6 119, 2004. http //dx.doi.Org/10.1088/1367-2630/6/l/119. 

Figure 8.9. The movement of aerosol particles in the gas phase and its relation to the Reynolds number. Re (a) Re < 1 (laminar flow) (b) Re > 1000 (turbulent flow).

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