Non-Stokesian Particles

Derivation of a modified equation of motion for the particle that accounts approximately for the non-Stokesian motion of the particles is based on the general expression for the drag on a fixed spherical particle in a gas of uniform velocity, U (Brun et al., 1955)  

This expre.ssion defines the drag coefficient, which by dimensional analysis is a function 

In general, it is necessary to use the results of experiments and semiempirical correlations to relate the drag coefficient to the Reynolds number. The expression 

For steady flow of an aerosol around a collector such as a cylinder or sphere, a force balance can be written on a particle by considering it to be fixed in a uniform flow of elocity u — uy  

As in the case of Stokesian panicles, the contribution of panicle acceleration to the drag has been neglected. Clearly, (4.37) is on shaky ground from a theoretical point of view. Its application should be tested experimentally, but a rigorous validation has never been carried out. In nondimensional form. (4.37) can be written as follows  

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This analysis provides a lower anchor point for curves of impaction efficiency as a function of Stokes number. It applies also to non-Stokesian particles, discussed in the next section, because the point of vanishing efficiency corresponds to zero relative velocity between particle and gas. Hence Stokes law can be used to approximate the particle motion near the stagnation point. This is one of the few impaction problems for which an analytical solution is possible. 

The drag coefficient for non-Stokesian particles can be represented by the expression... 

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