Drag effect, boundary layer

When we consider many particles settling, the density of the fluid phase effectively becomes the bulk density of the slurry, i.e., the ratio of the total mass of fluid plus solids divided by the total volume. The viscosity of the slurry is considerably higher than that of the fluid alone because of the interference of boundary layers around interacting solid particles and the increase of form drag caused by particles. The viscosity of a slurry is often a function of the rate of shear of its previous history as it affects clustering of particles, and of the shape and roughness of the particles. Each of these factors contributes to a thicker boundary layer. 

The flow conditions in the boundary layer are of considerable interest to chemical engineers because these influence, not only the drag effect of the fluid on the surface, but also the heat or mass transfer rates where a temperature or a concentration gradient exists. 

If the particle Re is well above the creeping flow range, mean drag may be increased or decreased by freestream turbulence. The most significant effect is on the critical Reynolds number. As noted in Chapter 5, the sharp drop in Cd at high Re results from transition to turbulence in the boundary layer and consequent rearward shift in the final separation point. Turbulence reduces Re, presumably by precipitating this transition." ... 

At Re = 20, Cn increased sharply to pass through a maximum of approximately 0.22 at Re = 40, declining to be very small for Re > 150. Large normal drag is probably related to wake development, and similar effects may be expected whenever the flow pattern changes markedly with Re. In the critical range, lateral acceleration would tend to produce asymmetric boundary layer transition, so that significant lift can be anticipated. 

Johnson B, Barchi RH (1968) Effect of drag reducing additives on boundary-layer turbulence J Hydronautics 2 108... 

Saltation of solids occurs in the turbulent boundary layer where the wall effects on the particle motion must be accounted for. Such effects include the lift due to the imposed mean shear (Saffman lift, see 3.2.3) and particle rotation (Magnus effect, see 3.2.4), as well as an increase in drag force (Faxen effect). In pneumatic conveying, the motion of a particle in the boundary layer is primarily affected by the shear-induced lift. In addition, the added mass effect and Basset force can be neglected for most cases where the particle... 

Particles of interest to wafer cleaning are small with respect to typical hydrodynamic boundary layers which can be as thick as a few tenths of a millimeter so the drag force actually exerted on the particle is that of a much slower moving fluid than the nozzle velocity of the jet. While more effective for small particles than brush scrubbing, the pressure required for submicrometer particle removal is too high for patterned wafer application. 

The phenomena that affect drag force also affect heat transfer, and this effect appears in the Nusselt number. By nondimensionalizing the boundary layer equations, it was shown in Chapter 6 that the local and average Nusselt numbers have the functional form... 

The boundary layer theory has been widely accepted and used to describe the transport phenomena in CVD processes. High-performance CVD systems require designers to focus on the geometrical parameters of the reaction chamber, the orientation and arrangement of the preforms in the chamber, as well as some other important components, such as pipes, distributor, exit and so forth. Due to drag effects around the boundary layer of preforms, it is very important to design the preforms and the reaction chamber and aim to avoid the boundary layer separation such that they experience a minimum drag force. The details of these effects are discussed in Chapter 6. 

While the virtual mass force accounts for the form drag on the particle due to relative acceleration between the particle and the surrounding fluid, the history term accounts for the corresponding viscous effects. Moreover, the history force originates from the unsteady diffusion of the vorticity around the particle so there is a delay in the boundary layer development as the relative velocity changes with time [96, 97, 22]. This means that when the relative velocity between the particle and the fluid varies, the vorticity present at the particle surface changes and the surrounding flow needs a flnite time to readapt to the new conditions. 

The analysis neglects boundary layer effects and is probably best applied when the particle diameter is larger than, or of the order of, the boundary layer thickness. The change in the drag law as the particle approaches the surface is also not taken into account. Hence the criterion provides only a rough estimate of the range in which the impaction efficiency becomes small. 

For practical values of H and Prf, Eq. 14.33 was found to be near unity, indicating that acceleration and convection effects are negligible. Chen [34] included the effect of vapor drag on the condensate motion by using an approximate expression for the interfacial shear stress. He was able to neglect the vapor boundary layer in the process and obtained the results shown in Fig. 14.8. The influence of interfacial shear stress is negligible at Prandtl numbers of ordinary liquids (nonliquid metals, Pr< > 1). Chen [34] was able to represent his numerical results by the approximate (within 1 percent) expression ... 

---