Floes particle shape

In the course of further work on characterizing the MCC sols it was found that the CCC of a variety of salts varied both with the solids content and temperature. Investigation of these parameters forms the basis of the study. It will be shown that as a result of particle shape, concentration and surface characteristics, coagulation leads to a gel-like structure. On further addition of salt the coagulated gel-like structure aggregates into floes that are irreversible. In this paper, we outline the experimental parameters which lead to these phenomena and present some possible explanations. 

Barker and Grimson (1991) modeled the flow of deformable particles after a free-draining floe whose shape, orientation, and internal structure ranged between the extremes of an extended chain and a folded globule. They interpreted the unhindered motions of free-flowing, deformable droplets to result from an unbalanced force imposed by the flow field, resulting in rotations around the particles center of mass this rotation is superimposed on the steady translational motion. 

It has been claimed that particle shape, roughness and the nature of the material has little effect on the analysis [30] but there is considerable evidence that the size measured is the envelope of the particle. Comparison with other techniques gives good agreement for homogeneous spherical particles for non-spherical particles results may differ [31,32]. For porous particles the measured volume may be several times the skeletal volume, and the apparent volume for floes is greater than the volume of the particles that make up the floes [20]. 

Theories for the steady-shear viscosity are complex. They involve assumptions about the dependences on shear rate of floe size, shape, and floc-floc interactions. The simplest might consider is the limit of very high shear rates and not-too-high particle... 

Flow of any concentrated suspension will become impossible when the solid particles can form a continuous three-dimensional network of contacts throughout the sample. This so-called maximum packing fraction 4> depends mainly on the particle size distribution and the particle shape. Broader particle size distributions result in lower values of 4>m, because the smaller particles can fill the gaps between the bigger ones, and a deviation from spherical shape results in lower values of 4>m due to steric hindrance of packing. Also flocculation will result in a decrease in the value of 4>in, because the individual floes are only loosely packed. 

I Goodarznia, DN Sutherland. Floe simulation Effects of particle size and shape. Chem Eng Sci 30 407-412, 1975. 

As stated above, Afd is related to the contact pair potential Afg(0). In a floe, each particle is in close contact with z other particles. If A/a is small, the z lens-shaped overlap volumes (see Figure A) surrounding each particle do not overlap with each other, and Afd equals zAf (0)/2 where Afg(0) is given by Equation 8. For higher values of A/a, the lenses overlap partly, and Afd < zAfs(0)/2. Above a certain value of A/a (which depends on the packing of the particles in the floe), there is no polymer left within the interstices of the floe and all the solvent in the floe is within a distance A from the surface of at least one particle. Then the volume of solvent which is transferred towards the solution when a particle is added to the floe is readily calculated. 

While the system conforms to coagulation in a secondary minimum, the redispersion region is best accounted for in terms of gel formation originating from the rod-like shape of the particles and hydrated surface. During the final coagulation process additional attractive forces such as dipolar and hydrogen bonding form floes which are irreversible and denser than those formed at a lower salt concentration. 

Examination of the precipitate showed that it consisted of floes of irregularly shaped particles 1-5 g, in size. Accordingly, at low organic lead concentrations of, e.g., 10 ppm, the use of Centriflo membrane filters was required for efficient separation of the precipitate from solution. The filters, holding 7-ml aliquots of the aqueous phase were centrifuged for 3 min at 1500 rpm. 

Shape effect of PFPE molecules or magnetic particles in suspension, including agglomeration phenomena at low concentration, interaction among these particles, and effects of floes can be examined via solution viscosity (r ) measurement. For a very dilute polymer solution [108], there is no interaction among polymer molecules, and the solution viscosity results from the contribution of the solvent plus the contribution of the individual polymer molecules. The intrinsic viscosity, therefore, is a measure of the hydrodynamic volume of a polymer molecule as well as the particle aspect ratio. Figure 1.24 shows the determination of the intrinsic viscosity for Zdol4000 in three different solvents. 

CLSM) has been used to generate three-dimensional information on particle size, shape and porosity [141]. The CLSM has been used to measure particle size distribution in situ and ex situ using computer based image analysis system [142]. A model was developed to assess processing conditions to produce a floe with desirable characteristics in an enhanced actinide removal. Ferreira et.al. [143] present some additional methods of measuring wood pulp fibers and compares these with data from CLSM... 

In water treatment besides particle size and shape, an important characteristic of particles in suspension, be it colloidal clay particles, floes or algae, is their clogging properties in relation to rapid and slow sand filtration and membrane filtration. 

The coalescent principle becomes the significant principle for small-oil-droplet removal. When the droplets coalesce, they do not form floes as the solid particles can, but coalesce into larger droplets. Interfacial or surface tension of the liquid tends to make the droplets from spherical shapes, which follows the assumption of Stokes s law mentioned previously. With coalescent principle, the Stokes s law can be applied. The coalescent technique widely used in oil droplet removal is the plate separator. 

The efficiency of the separation process, described as overall solids retention, was derived from particle-counting analyses through summation and integration. An attempt was also made to evaluate and interpret the observed removal behavior by analyzing data on specific microscopic suspension parameters such as floe shape. However, these latter data have not yet been incorporated into mathematical models. They have been used qualitatively to explain incongruencies observed in the performance of sedimentation and flotation tanks. 

FIGURE 8.23 Particles are formed from coacervates of crystallites that condense over tactoids and crystalloids to particulate floes. Upon aging the floes condense to dense agglomerates, but maintain the shape of the original crystallites. (From Heller, W., in Polymer Colloids II, R.M. Fitch, Ed., Plenum Press, New York, 1980. With permission of Elsevier Science.)... 

However, remembering the mechanisms of growth agglomeration (Section 7.1), if particles can be forced to impact with each other, it is possible that they adhere to one another. Therefore, when water, that is contaminated with suspended fine solids, is stirred, floes may form naturally. If this happens, the size and shape of these aggregates depend on the circumferential speed of the stirrer and the processing time. Fig. 10.42 shows that floes are larger if the shear forces are low and the processing time is... 

The individual particles of which we have spoken seem, in many cases, amenable to a relatively simple geometric description. In solution, however, particles may floe or aggregate due to random particle-particle and particle-floc collisions, and generally complex shapes arise that belie the much simpler shape of the original particle. Figure 1.3.5 from Weitz Oliveria (1984) shows in two-dimensional projection an irreversible aggregate of uniform-size, spherical gold particles with diameter 15 nm. 

On standing, concentrated suspensions reach various states (structures) that are determined by (1) Magnitude and balance of the various interaction forces, electrostatic repulsion, steric repulsion and van der Waals attraction. (2) Particle size and shape distribution. (3) Density difference between disperse phase and medium, which determines the sedimentation characteristics. (4) Conditions and prehistory of the suspension, e.g. agitation, which determines the structure of the floes formed (chain aggregates, compact clusters, etc.). (5) Presence of additives, e.g. high molecular weight polymers that may cause bridging or depletion flocculation. 

The above-described interparticle interactions lead to formation of suspension structures at rest. The type of suspension structure formed depends on whether the interparticle forces are attractive or repulsive in nature. With strong repulsive interactions, solid crystaUme structures can be formed. The attractive interaction appears to be more common with paste materials. The flow behavior of the suspension is strongly affected by the nature of the suspension structure. The extreme cases are the formation of chainhke structures or formation of spherically shaped clusters of particles. The two shapes are the extreme simplifications of the real structures and are often used as structural models. The type of suspension structure developed depends on interparticle interactions, the shape and size of solid particles, solid surface characteristics, particle concentration, mixing conditions, shear history, etc. The basic flow units, called floes, are formed by random packing of primary particles. At low shear or at rest, the floes group into clusters of floes called aggregates, as shown in... 

Because of these constraints many particle size methods are not applicable to floes. For example the uncertainty and variability of floe density within the outer envelope volume, the possible irregularity of shape and their fragile nature means, that all types of sedimentation method are inapplicable. 

The secondary minimum that results due to the often weakly bounded floes (loose aggregates) deserves more discussion. For very small particles (radius less than about 10 nm) the secondary minimum is not deep enough to get flocculation. If the particles are larger, flocculation in the secondary minimum may cause observable effects. Secondary minimum flocculation is considered to play an important role in the stability of certain emulsions and foams as well as several colloidal systems containing odd-shaped particles like iron oxide and tobacco mosaic vims. 

Figure 6.12(a) is for systems where the range (L) of the attractive forces is much smaller than the particle radius (a) it shows a gas+solid coexistence region, which is an equivalent description to the dispersed + floe phase region shown in Figure 6.10. The left-hand boundary in Figure 6.12(a) is similar in shape to that in Figure 6.10, at low 0.5.

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