Surface drag force, example

Landau and Levich solved Eq. (6.66) without the gravity term pg. The solution is then a competition between viscous drag and surface tension forces (see for example Ref. [62] or [59]). They obtained... 

The steady drag is the component of the hydrod3mamic force acting on the particle surface in the continuous phase flow direction. One might, for example, imagine a uniform velocity in the z-direction as sketched in Fig 5.1, and describe the external flow using the Cartesian coordinate system, then the steady drag force is defined by [14, 30] ... 

The aerodynamic diameter dj, is the diameter of spheres of unit density po, which reach the same velocity as nonspherical particles of density p in the air stream Cd Re) is calculated for calibration particles of diameter dp, and Cd(i e, cp) is calculated for particles with diameter dv and sphericity 9. Sphericity is defined as the ratio of the surface area of a sphere with equivalent volume to the actual surface area of the particle determined, for example, by means of specific surface area measurements (24). The aerodynamic shape factor X is defined as the ratio of the drag force on a particle to the drag force on the particle volume-equivalent sphere at the same velocity. For the Stokesian flow regime and spherical particles (9 = 1, X drag... 

Example 5-5 Consider the pneumatic flow of gas and solids in a horizontal bend. For analysis on the solid flow, consider that the fluid drag force is negligible in comparison to the sliding force of the particle on the bend surface (Haag, 1967). See Fig. 5-5. 

This review will develop a picture of likely deviations and the locality of accumulations of the fractions of the bulk material that were initially more uniformly dispersed through the mass. It will be clear that particles that are dissimilar in some physical manner may respond differently to forces originating from varied sources. For example - surface shape and texture differences that influence viscous drag in a fluid media have effects unrelated to differential restraint arising from variation in the surface friction values. Similarly, particle size and density dominate or correlate with other mechanistic processes. The potential for segregation to occur in various handling operations, because of particular flow regimes, is indicated in Table 3. 

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