ABSTRACT
The steady motion of rigid and fluid particles through quiescent unbounded (or infinite expanse of) fluids has been a subject of theoretical study for many years, dating back to the pioneering studies of Newton (1687), Hadamard and Rybczynski (Clift et al., 1978), and Stokes (1851) to mention a few. Owing to the finite size of vessels and tubes employed in such experimental studies, it is clearly not possible to realize the unbounded flow conditions. In practice therefore, the confining walls exert an extra retardation effect on a particle, whether settling freely in a quiescent fluid, or being suspended in an upward flowing stream of fluid; this effect has also been studied for centuries (Newton, 1687; Munroe, 1888; Ladenburg, 1907). The effect is caused by the upward flux of the fluid displaced by the particle; the smaller the gap between the particle and the boundary, more severe is the effect. A knowledge of this so-called wall effect for both rigid and fluid particles is necessary for a rational understanding and interpretation of experimental data in a number of situations of overwhelming pragmatic significance. For a rigid sphere, typical examples include falling ball viscometry, hydrodynamic chromatography, membrane transport, hydraulic and pneumatic transport of coarse particles in pipes, etc. Furthermore, in recent years, the problem of flow around solid particles in a tube has received further impetus from the use of electric fields to achieve enhanced rates of transport phenomena and of separations in multiphase systems. On the other hand, in the case of fluid particles, not only is their velocity influenced by the presence of boundaries, but their shapes are also greatly altered due to the extra dissipation at the rigid walls. Conversely, their free surface enables them to negotiate their way through the narrow throats in undulating tubes and in porous media, as encountered in the enhanced oil recovery processes. It is thus much more difficult to quantify the severity of wall effects for bubbles and drops than that for rigid particles. In view of the significant differences in the velocity field in the immediate vicinity of the particle, the rate of interphase heat and mass transfer is also influenced (generally enhanced) due to the confining walls in relation to the unconfined case. Evidently, the magnitude of the wall effect will depend upon the size and the shape of the confining walls, that is, whether the particle is moving axially or non-axially in circular or noncircular ducts (such as
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Drops, and
square, triangular, elliptic cross-sections, planar slit) or it is sedimenting toward or parallel to a plane wall, etc.
