Rigid axisymmetric particles

Limiting Values of the Intrinsic Viscosity for Dilute Dispersions of Rigid Axisymmetric Particles... 

In comparison to suspensions of rigid spheres, the overwhelming additional effect with axisymmetric particles is orientation. Obviously the orientation of a nonspherical particle with respect to the flow will greatly affect the velocity field around it and thus the particle stress, Tp in eq. 10.2.8. For example, if the particle is a rod with its long axis aligned in the flow direction, the alteration of the... 

The system considered in this chapter is a rigid or fluid spherical particle of radius a moving relative to a fluid of infinite extent with a steady velocity U. The Reynolds number is sufficiently low that there is no wake at the rear of the particle. Since the flow is axisymmetric, it is convenient to work in terms of the Stokes stream function ij/ (see Chapter 1). The starting point for the discussion is the creeping flow approximation, which leads to Eq. (1-36). It was noted in Chapter 1 that Eq. (1-36) implies that the flow field is reversible, so that the flow field around a particle with fore-and-aft symmetry is also symmetric. Extensions to the creeping flow solutions which lack fore-and-aft symmetry are considered in Sections II, E and F. 

As for steady motion, analytic solutions for unsteady motion of rigid and fluid particles are available only in creeping flow. The solution was developed by Basset (B3) the outline given here follows the treatment of Landau and Lifshitz (L4). The governing equation is the unsteady form of Eq. (1-36), i.e., for axisymmetric flow,... 

Even for the simplest problems in aerosol science, such as the approach of a particle to equilibrium in the Brownian-particle approximation, detailed analysis has required treating the particles as rigid spheres or some other axisymmetric shape. Internal states of the particle have been largely ignored. Indeed, for ultrafine particles such states cannot even be inferred from knowledge of the bulk material. 

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