Particle concentrated suspension

The remainder of this contribution is organized as follows. In section C2.6.2, some well studied colloidal model systems are introduced. Methods for characterizing colloidal suspensions are presented in section C2.6.3. An essential starting point for understanding the behaviour of colloids is a description of the interactions between particles. Various factors contributing to these are discussed in section C2.6.4. Following on from this, theories of colloid stability and of the kinetics of aggregation are presented in section C2.6.5. Finally, section C2.6.6 is devoted to the phase behaviour of concentrated suspensions. 

Altliough tire behaviour of colloidal suspensions does in general depend on temperature, a more important control parameter in practice tends to be tire particle concentration, often expressed as tire volume fraction ((). In fact, for hard- sphere suspensions tire phase behaviour is detennined by ( ) only. For spherical particles... 

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

Orthokinetic flocculation is induced by the motion of the Hquid obtained, for example, by paddle stirring or any other means that produces shear within the suspension. Orthokinetic flocculation leads to exponential growth which is a function of shear rate and particle concentration. Large-scale one-pass clarifiers used in water installations employ orthokinetic flocculators before introducing the suspension into the settling tank (see Water,... 

The behavior of colloidal suspensions is controlled by iaterparticle forces, the range of which rarely extends more than a particle diameter (see Colloids). Consequentiy suspensions tend to behave like viscous Hquids except at very high particle concentrations when the particles are forced iato close proximity. Because many coating solutions consist of complex mixtures of polymer and coUoidal material, a thorough characterization of the bulk rheology requires a number of different measurements. 

Highly concentrated suspensions of fine sohd particles frequently... 

Hindered Settling When particle concentration increases, particle settling velocities decrease oecause of hydrodynamic interaction between particles and the upward motion of displaced liquid. The suspension viscosity increases. Hindered setthng is normally encountered in sedimentation and transport of concentrated slurries. Below 0.1 percent volumetric particle concentration, there is less than a 1 percent reduction in settling velocity. Several expressions have been given to estimate the effect of particle volume fraction on settling velocity. Maude and Whitmore Br. J. Appl. Fhys., 9, 477—482 [1958]) give, for uniformly sized spheres,... 

Settling does not give a complete separation one product is a con-centratea suspension and the other is a hquid which may contain fine particles of suspended sohds. However, settling is often the best way to process veiy large volumes of a dilute suspension and remove most of the hquid. The concentrated suspension can then be filtered with smaller equipment than would be needed to filter the original dilute suspension, and the cloudy liquid can be clarified if necessaiy. Settlers can also be used for classifying particles by size or density, which is usually not possible with filtration. 

Several devices are available commercially to measure mobihty. One of these (Zeta-Meter Inc., New York) allows direct microscopic measurement of individual particles. Another allows measurement in more concentrated suspensions (Numinco Instrument Corp., Monroeville, Pa.). The state of the charge can also be measured by a streaming-current detecdor (Waters Associates, Inc., Framingham, Mass.). For macromolecules, more elaborate devices such as the Tisehus moving-boundaiy apparatus are used. 

The most favorable filtration operation with cake formation is process whereby no clogging of the filter medium occurs. Such a process is observed at sufficiently high concentrations of solid particles in suspension. From a practical standpoint this concentration may conditionally be assumed to be in excess of 1% by volume. Filtration is frequently accompanied by hindered or free gravitational settling of solid particles. The relative directions of action between gravity force and filtrate... 

Hence, the application of these formulas only applies to very dilute systems. At high particle concentrations, mutual interference in the motion of particles exists, and the rate of settling is considerably less than that computed by the given expressions. In the latter case, the particle is settling through a suspension of particles in a fluid, rather than through a simple fluid medium. 

The construction of calibration curves is recommended in nephelometric and turbidimetric determinations, since the relationship between the optical properties of the suspension and the concentration of the disperse phase is, at best, semi-empirical. If the cloudiness or turbidity is to be reproducible, the utmost care must be taken in its preparation. The precipitate must be very fine, so as not to settle rapidly. The intensity of the scattered light depends upon the number and the size of the particles in suspension, and provided that the average size of particles is fairly reproducible, analytical applications are possible. 

For the transport of a dilute suspension of solids, uR will approximate to the free-falling velocity uq of the particles in the liquid. For concentrated suspensions, a correction must be applied to take account of the effect of neighbouring particles. This subject is considered in detail in Volume 2 (Chapter 5) from which it will be seen that the simplest form of... 

Prager [302] examined diffusion in concentrated suspensions using the variational approach. (A discussion of the basic principles in variational theory is given in Ref. 6.) Prager s result is applicable to a very general class of isotropic porous media. Prager s solution for a limiting case of a dilute suspension of particles was... 

Reactors containing electrodes of this kind are used when reactants are present in the solution in an extremely low concentration, and their rate of diffusion to a quiescent electrode (even a porous one) would be too low. An acceleration of the reaction at three-dimensional electrodes is attained owing to shorter dilfusional transport distances to the closest particles in suspension and also owing to strong turbulence in the system. 

S. A. Altobelli, E. Fukushima, L. A. Mondy, T. S. Stephens 1991, (Experimental observations of particle migration in concentrated suspensions — Couette flow),/. Rheol. 35, 773. 

The process of thickening involves the concentration of a slurry, suspension, or sludge, usually by gravity settling. Because concentrated suspensions and/ or fine particle dispersions are often involved, the result is usually not a complete separation of the solids from the liquid but is instead a separation into a more concentrated (underflow) stream and a diluted (overflow) stream. Thickeners and clarifiers are essentially identical. The only difference is that the clarifier is designed to produce a clean liquid overflow with a specified purity, whereas the thickener is designed to produce a concentrated underflow product with a specified concentration (Christian, 1994 Tiller and Tarng, 1995 McCabe et al., 1993). 

For greater concentrations of fine particles the suspension is more likely to be non-Newtonian, in which case the viscous properties can probably be adequately described by the power law or Bingham plastic models. The pressure drop-flow relationship for pipe flow under these conditions can be determined by the methods presented in Chapters 6 and 7. 

Viscosities of concentrated suspensions of carbon black in a white mineral oil (Fisher "paraffin" oil of 125/135 Saybolt viscosity) were measured with a Brookfield viscometer as a function of OLOA-1200 content. Figure 13 shows the viscosities of dispersions with 30 w%, 35 w% and 70 w% carbon black. In all cases the viscosity fell rapidly as the 0L0A-1200 content increased from 0 to 1%, then fell more gradually and levelled off as the 0L0A-1200 content approached 2%. In many respects the reduction in viscosity with increasing OLOA-1200 content parallels the conductivity measurements both phenomena are sensing the buildup of the steric barrier, and this steric barrier weakens, softens, and lubricates the interparticle contacts. As evidenced in foregoing sections, the particles are still flocculated but can be easily stirred and separated mechanically. The onset of electrostatic repulsion at OLOA-1200 contents in excess of 2.5% did not affect viscosities. 

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