The flow of non-Newtonian liquids through beds of particles is treated in an
analogous way to that adopted in Chapter 3 for the flow through ducts of
regular cross-section. No complete analytical solution is, however, possible
and a degree of empiricism complemented by the use of experimental results
is often necessary. Firstly, however, the basic nature and structure of porous
media (or beds of particles) will be briefly discussed.
5.6.1 Porous media
The simplest way of regarding a porous medium is as a solid structure with
passages through which fluids can flow. Most naturally occurring minerals
(sand, limestones) are consolidated having been subjected to compressive
forces for long times. Packed beds of glass beads, catalyst particles, Raschig
rings, berl saddles, etc. as used in process equipment are unconsolidated.
Unconsolidated media generally have a higher permeability and offer less
resistance to flow. Packing may be ordered or random according to whether
or not there is a discernable degree of order of the particles, though completely
random packing hardly ever occurs as ‘order’ tends to become apparent as the
domain of examination is progressively reduced in size. Cakes and breads are
good examples of random media!
Porous media may be characterized at two distinct levels: microscopic and
macroscopic. At the microscopic level, the structure is expressed in terms of a
statistical description of the pore size distribution, degree of inter-connection
and orientation of the pores, fraction of dead pores, etc. In the macroscopic
approach, bulk parameters are employed which have been averaged over scales
much larger than the size of pores. These two approaches are complementary
and are used extensively depending upon the objective. Clearly, the microscopic
description is necessary for understanding surface phenomena such as adsorption
of macromolecules from polymer solutions and the blockage of pores,
etc., whereas the macroscopic approach is often quite adequate for process
design where fluid flow, heat and mass transfer are of greatest interest, and the
molecular dimensions are much smaller than the pore size. Detailed accounts
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