Particle shape flocculent

A final assumption made in the derivation of Stokes law was that the particles of interest were spheres. In many cases this is not true. Particles may have irregular shapes, depending on how they were formed and the amount of agglomeration which may have taken place. Liquid aerosols are always spherical, so that for liquid aerosols the assumption of sphericity holds. For isometric particles this assumption can also be used with little error. For long chains of particles or flocculated particles, large deviations from Stokes law are possible. 

With all the methods, complications or uncertainties of interpretation arise due to effects associated with particle shape and with flocculation, so that the results given by different methods do not necessarily agree and usually have relative rather than absolute significance. Fig. 4.1, curve R, shows the cumulative PSD, obtained using an X-ray sedigraph, for a... 

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. 

Particle Shape. Shape Factors. The method of formation plays a major role in shaping the resultant particles. Particles generated by comminution, attrition, or disintegration resemble the parent material. However, if the method of formation is condensation from vapor or precipitation from solution, the smallest unitary particle may be spherical or cubical. Often condensation is followed immediately by solidification and the formation of chainlike aggregates (e.g., iron oxide fumes, carbon black). In liquid suspensions, similar particle aggregation or flocculation is important in determining suspension behavior. 

This chapter is an in-depth review on rheology of suspensions. The area covered includes steady shear viscosity, apparent yield stress, viscoelastic behavior, and compression yield stress. The suspensions have been classified by groups hard sphere, soft sphere, monodis-perse, poly disperse, flocculated, and stable systems. The particle shape effects are also discussed. The steady shear rheological behaviors discussed include low- and high-shear limit viscosity, shear thinning, shear thickening, and discontinuity. The steady shear rheology of ternary systems (i.e., oil-water-solid) is also discussed. 

Friedlander (11) has examined the effects of flocculation by Brownian diffusion and removal by sedimentation on the shape of the particle size distribution function as expressed by Equation 9. The examination is conceptual the predictions are consistent with some observations of atmospheric aerosols. For small particles, where flocculation by Brownian diffusion is predominant, p is predicted to be 2.5. For larger particles, where removal by settling occurs, p is predicted to be 4.75. Hunt (JO) has extended this analysis to include flocculation by fluid shear (velocity gradients) and by differential settling. For these processes, p is predicted to be 4 for flocculation by fluid shear and 4.5 when flocculation by differential settling predominates. These theoretical predictions are consistent with the range of values for p observed in aquatic systems. 

From the practical point of view, the change of filtration pressure, filtration area, filter medium, filtrate viscosity and solids loading is limited . To increase the filterability of the cake, most practical way, therefore, is to decrease the average specific cake resistance a. This could be accomplished by changing the particle shape, increasing the particles size and narrowing the size distribution of the particles in the cake. The latter two factors can be manipulated by polymer flocculation. 

Irregularly shaped particles and flocculates cause the development of a structure with its own yield stress level. As the particles move closer, the yield stress increases until equilibrium is reached. The weight of the overburden is then supported hy the saturated fluid and the compacted sediment. 

Particle size, particle size distribution, and particle shape Influences rheological properties over entire range of shear rates d viscoelastic pr< rties of paste. The particle size, etc., affects tiie particle concentration per unit volume and die rate of flocculation. 

Solids settling and deposition to bottom sediments is a complex process by which particulate materials, including both individual and aggregate solids, settle from the water column and adhere to the sediment bed. According to Stokes law, particle settling is dictated by particle diameter and density, but important factors causing nonideal settling include particle shape and concentration, flow velocity and turbulence, and flocculation. Deposition onto and attachment to the sediment bed are usually described as probabilistic processes, affected by turbulence at the sediment-water interface and by the cohesiveness of the solid material. 

Generally, measurable (directly or indirectly) physical properties of the solids and the water in which these solids are suspended effectively determine the rate at which particles settle and whether or not hydraulic shear forces are sufficient to keep the particles suspended in the water column. The chemical properties of the solids and the water can also influence the deposition process through particle aggregation (flocculation) and the effect this has on the effective size, density, and shape of the suspended material. 

Already dispersed pigment particles may for various reasons reassemble and form loosely combined units with various shapes. The most important among these are flocculates (Fig. 4), assemblies of wetted crystallites and/or aggregates or smaller agglomerates. They usually form in a low viscosity medium which fills the interior cavities of the pigment flocculates. Flocculates are therefore mechanically more labile than agglomerates and can usually be broken up by weak shear such as stirring. 

Concentrated particle suspensions may also show a yield point which must be exceeded before flow will occur. This may result from interaction between irregularly shaped particles, or the presence of water bridges at the interface between particles which effectively bind them together. Physical and chemical attractive forces between suspended particles can also promote flocculation and development of particle network structures, which can be broken down by an applied shear stress [2]. 

The solid particles to be separated are mainly cellular mass with the specific gravity of about 1.05 to 1.1, which is not much greater than that of the broth. Shapes of the particles may be spheres, ellipsoids, rods, filaments, or flocculents. Typical sizes for various cells vary widely such as,... 

Colloid behavior in natural soil-water systems is controlled by dispersion-flocculation processes, which are multifaceted phenomena. They include surface electrical potential (El-Swaify, 1976 Stumm and Morgan, 1981), solution composition (Quirk and Schofield, 1955 Arora and Coleman, 1979 Oster et al., 1980), shape of particles, initial particle concentration in suspension (Oster et al., 1980), and type and relative proportion of clay minerals (Arora and Coleman, 1979). When suspended in water, soil colloids are classified according to their settling characteristics into settleable and nonsettleable solids. 

The effects of various electrolytes are usually compared in terms of the flocculation values, or minimal concentrations (expressed in millimoles per liter), required to bring about coagulation. Flocculation values for nonspecific electrolytes can be interpreted in terms of electrostatic repulsion and van der Waals attraction. The van der Waals attractive forces vary with size and shape of the particles, but roughly speaking the force is appreciable between colloidal particles at distances of the order of magnitude of their own radii. The significant feature is that flocculation occurs before the zeta potential reaches zero, that is, when it reaches a small critical value. 

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