Spherical particles of silica and other materials are tightly packed at very high pressures (>10,000 psi) into narrow columns (< 5 mm i.d.) for separating mixtures. The smaller the width of the separated bands, the higher the quality of the packed bed in terms of micro-structure. In reality, it is always a random closed packing of hard spheres.
Please see the attached file, where authors purpose different flow patterns which can develop in a packed bed. They do not show any calculations nor give a reference to flow profiles in a packed bed (which is quite wide in diameter).
The question is related to figure 3 (c) and it says that exceptionally narrow separated bands can be seen as a result of this flow profile. Is anyone aware of oscillating flow profiles in packed beds or is it just authors' imagination?
Thank you.
From a practical engineering point of view one of the major design diffi-
culties in dealing with multiphase flow is that the mass, momentum, and
energy transfer rates and processes can be quite sensitive to the geometric
distribution or topology of the components within the flow. For example, the
geometry may strongly effect the interfacial area available for mass, momentum
or energy exchange between the phases. Moreover, the flow within each
phase or component will clearly depend on that geometric distribution. Thus
one recognize that there is a complicated two-way coupling between the flow
in each of the phases or components and the geometry of the flow (as well as
the rates of change of that geometry). The complexity of this two-way coupling
presents a major challenge in the study of multiphase flows and there
is much that remains to be done before even a superficial understanding is
achieved. An appropriate starting point is a phenomenological description of the
geometric distributions or flow patterns that are observed in common multiphase
flows. In tight packing there should no gap, and it can be removed off by using vaccum filling of silica after making slurry of beads either in PBS or a suitable solvent. Do not pack the column in a single go, slowly slowly pack the column and keep it in vertical position easily find a tight packing due to gravitation force and vacuum pump suction pressure.
it may be the chance when the tube is fully compacted at the required pressure. in the meantime the flow continuously passes through the tube it starts digging the compacted one through the flow vs pressure.
if the pressure applying is not constant the problem may occur.
What do you mean by oscillating profile? Do you mean oscillating in time or just the shape on Fig 3c?
This kind of profile with extra high velocity near the wall is caused by higher porosity and thus lower resistance to flow in wall region.
This packing density variation is typical for higher d/D of packed column and for beds of spheres with nearly identical diameters.
This topic was discussed few months ago. search for packing beds density changes
It is worth remembering that for such a narrow tube the rules which normally apply to larger packed beds may be modified by the domination of surface effects. In addition, the possible presence of trapped gas bubbles which can compress may give variable effects. Within the bed there may be regions with particular flow characteristics, possibly giving some microfluidic character, which can include oscillation.
I don't think there is any theoretical reason to think that the profile would be parabolic, yet alone double parabolic. Flow between particles is governed by stokes equation (assuming no inertial effects), but the bulk averaged flow for packed beds is governed by darcy's law, which basically says that the velocity vectors of the flow field are coincident with the pressure gradient. Since there is no radial pressure drop and the axial pressure drop is not radially varying, this suggests something that looks like an axial plug flow.
Having said that, porosity (I.e. Permeability) variations over the bed will drive secondary perturbation flows to the basic plug flow profile. In this case, the strongest porosity perturbation is close to the wall, so I guess there would be a faster plug flow down the wall. Things may be different close to the entry and exit of the tube as the flow will not be fully developed at these points.
Hello Adam, you are right that in packed beds pure open tube like parabolic flow profile should not be assumed but in general, the chromatographic literature says that the velocity in the center of the bed is higher than around periphery. I think you pointed out an important point that the permeability of the bed is not radially uniform, which in turn makes the flow non-uniform. The aim of (theoretical aspects) of high performance chromatography is to keep the band of solute (in other words velocity profile) as flat as possible, in that case one may get exceptionally high efficiency of separation. On the other hand, it is quite impossible to have a flat flow profile in a packed bed. This will imply that the bed is uniformly packed from the wall to the center. What do you think about the Figure 3 c in the attachment? Do you think it was author's imagination but his idea for high efficiency is really appealing i.e. how to practically produce a bed of particles which is radially uniform in permeability.
Prof. Zylla, by oscillating flow profile in Figure 3 c, I meant oscillating in shape, what Dr. Adam has termed as double parabolic flow. Note that the wall region where the permeability is really extends only to 20-30 particle diameters. Imagine using a wide bore column (4.6 mm) and very small particle size (2 micron), as in Figure 3c. we will have several thousand particles along the diameter of the column. Under what conditions this wall effect will extend into the center of the packed bed? Is there any practical possibility of having no radial variation in bed density of spherical particles?
Hello Farooq, the proportion of "oscillation" of profile on Fig 3c is exagarated. And can be two reasons for this shape. One may explain the parabolic shape in the centre: changed viscosity due to temperature change caused by friction. Closer to wall heat dissipation is better and temperature is lower thus higher viscosity.
The second reason is changed porosity attained at packing (forced) time. I believe that during pressing of the bad by some kind of piston some particles are crushed and are not really spherical. Some material removed from contact (sphere-sphere) points stays near and additionally blocks free space.
Sorry I am not manufacturer of such beds and have not microscopic photos of sliced bed.
Romuald corectly enlarges the point I was making. If you assume the bed is normally distributed random perfect spheres, it may be hard to explain. However, there is actually no evidence, just an implicit assumption of perfection in particles and distribution.
Hi Farooq Yes, I think that this is most likely a figment of the authors imagination.
on the other hand the thermal profile theory Romuald suggests might have potential to generate a flow with a somewhat parabolic form. Is there any literature on the thermal effect? Have people successfully measured these kinds of floral ow profiles? I know that Lynn gladdens group at Cambridge have done some MRI flow imaging and modelling on flow through packed beds, although I don't have copies to hand and can't remember what they observed.
Perhaps not quite scientific assumption, but if the particles are filled not when dry, but when there is significant flow through the column, the packing density will depend on the velocity. Also going from hard sphere model to real deformable particles might flatten the plug flow.
Another modification might be achieved with heating/cooling the column, creating expansion/contraction profile and depending on the elastic properties to change the form and packing densities. So column manufacturing vs column working conditions might be hidden trick.
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