Particle Rotation and Fluid Shear

It is convenient to distinguish between particle or fluid rotation about axes normal and parallel to the direction of relative motion. These two types of motion may be termed respectively top spin and screw motion (Til). Top spin is of more general importance since this corresponds to particle rotation caused by fluid shear or by collision with rigid surfaces. Workers concerned with suspension rheology and allied topics have concentrated on motion at low Re, while very high Reynolds numbers have concerned aerodynamicists. The gap between these two ranges is wide and uncharted, and we make no attempt to close it here. 

The angular velocity of the sphere, H, is taken as positive for rotation in the same sense as that of the fluid. The resulting lift on the particle is taken as positive in the direction Q x Ur.  

Much of the work on particle rotation at low Rqq follows from the early work of Jeffery (J2) who considered a rigid, neutrally buoyant spheroid subject to the uniform shear field defined by Eq. (10-30). Jeffery showed that the particle center moves with the velocity which the continuous fluid would have at that point in the absence of the particle, while the axis of the spheroid undergoes rotation in one of a family of periodic orbits with angular velocities 

For a sphere where a = b, the particle rotates with an angular velocity of G/2 and a period of rotation of 4ti /G. 

Mason and co-workers (B8, F3, Gll, M5, T15) have shown that Eqs. (10-32) to (10-35) can also be applied to disks and cylinders provided that one uses an apparent value of , calculated from Eq. (10-36) and the observed Bretherton (B15) considered more general shapes and proved that most bodies of revolution, except for some extreme shapes, show periodic rotation with no lateral migration (i.e., no lift) provided that inertia terms are neglected. In reality all these particles migrate in the direction of positive lift (see Chapter 9). For a useful extended review on particle motion in shear fields, see Goldsmith and Mason (G12). 

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