Concentrated suspensions microstructure

As particle concentration increases, particle interactions and multiple scattering invalidate Eq. (33). The cross terms (y /) in the static and dynamic structure factors. Eq. (29), no longer cancel out, and thus they lead to more complex relationships [l 15-119] for (l>(diffusive motion of interacting particles also becomes more complex, depending on colloidal and hydrodynamic interactions among the particles and their spatial configurations. DLS measurements of particle motion can provide information about suspension microstructure and particle interactions. 

In this way, /3 is related to the particle volume fraction in terms of the maximum packing fraction such that the separation between the particle surfaces approaches zero in the limit effective microstructure of a flowing suspension is a simple cubic (, = 0.52), or body centered cubic = 0.68), or face centered cubic = 0.74). It is therefore assumed that Eq. (9.3.9) is also applicable to other effective suspension microstructures such as the random microstructure. Equation (9.3.8) is appropriate only for high solid volume fractions ( 2 0.25) since it was developed for concentrated suspensions for which the average separation distance between two similar size particles is close to or less than the particle size. 

Letwimolnun et al. [2007] used two models to explain the transient and steady-state shear behavior of PP nanocomposites. The first model was a simplified version of the stmcture network model proposed by Yziquel et al. [1999] describing the nonlinear behavior of concentrated suspensions composed of interactive particles. The flow properties were assumed to be controlled by the simultaneous breakdown and buildup of suspension microstructure. In this approach, the stress was described by a modified upper-convected Jeffery s model with a modulus and viscosity that are functions of the suspension structure. The Yziquel et al. model might be written ... 

However, ar rheometry presents an important drawback, i.e.. the sample microsmicture may be destroyed during the test run. This is especially true for weak gels or pastes, even at low shear rates or shear stresses. Much information about the fluid microstnicture is lost in this manner, in this case, creep and oscillatory rheometry are more convenient. The creep and viscoelastic parameters may be related to the strength of flocculation or aggregation, and a better knowledge of the microstructure is obtained. Useful information about the application of these methods for the study of suspensions of clay paniclc.s. creams, and concentrated suspensions of latex particles can be found in Refs. 12.49. and 50. respectively. 

The structure of the suspension and the compression rheological properties determine much of the consolidation behaviour. Colloidally stable, dilute suspensions of monodisperse spherical particles are well described by the relationships described above. The effect of the shape of the particles and the particle concentration can be accounted for by multiplying the expression given in equation (9.22) by suitable factors. For flocculated suspensions, the situation is much more complex. The attractive interparticle forces can produce a cohesive network of particles, which will resist consolidation depending on its strength. Because flocculation generally affects the suspension microstructure, the permeability will change. 

When multiple scattering is discarded from the measured signal, DLS can be used to study the dynamics of concentrated suspensions, in which the Brownian motion of individual particles (self-diffusion) differs from the diffusive mass transport (gradient or collective diffusion), which causes local density fluctuations, and where the diffusion on very short time-scales (r < c lD) deviates from those on large time scales (r c D lones and Pusey 1991 Banchio et al. 2000). These different diffusion coefficients depend on the microstructure of the suspension, i.e. on the particle concentration and on the interparticle forces. For an unknown suspension it is not possible to state a priori which of them is probed by a DLS experiment. For this reason, a further concentration limit must be obeyed when DLS is used for basic characterisation tasks such as particle sizing. As a rule of thumb, such concentration effects vanish below concentrations of 0.01-0.1 vol%, but certainty can only be gained by experiment. 

Detailed studies ofmicrostmctural transitions when colloidal crystals are sheared can be found in Chen (1992, 1994). Above a critical volume fraction, concentrated suspensions of charged particles thicken in a discontinuous manner. In suspensions of latex particles that have a deep van der Waals minimum, the thickening is irreversible, while in silica dispersions that have a shallow minima, the thickening is reversible. There have been a number of studies which try to relate the observed thickening to underlying microstructure (Maranzano, 2002 Bender, 1996 Chow, 1995b). 

Morris, J. F. 2009. A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta. 48, 909. 

Characteristic microstructural properties of TiOj membranes produced in this way are given in Table 2.5. Mean pore diameters of 4-5 nm were obtained after heat treatment at T < 500°C. The pore size distribution was narrow in this case and the particle size in the membrane layer was about 5 nm. Anderson et al. (1988) discuss sol/gel chemistry and the formation of nonsupported titania membranes using the colloidal suspension synthesis of the type mentioned above. The particle size in the colloidal dispersion increased with the H/Ti ratio from 80 nm (H /Ti = 0.4, minimum gelling volume) to 140 nm (H /Ti " — 1.0). The membranes, thus prepared, had microstructural characteristics similar to those reported in Table 2.5 and are composed mainly of 20 nm anatase particles. Considerable problems were encountered in membrane synthesis with the polymeric gel route. Anderson et al. (1988) report that clear polymeric sols without precipitates could be produced using initial water concentrations up to 16 mole per mole Ti. Transparent gels could be obtained only when the molar ratio of H2O to Ti is < 4. Gels with up to 12 wt.% T1O2 could be produced provided a low pH is used (H /Ti + < 0.025). 

In non-ideal mixtures, or systems where scattering of ultrasound is significant, the above equations are no longer applicable. In these systems the ultrasonic properties depend on the microstructure of the system, and the interactions between the various components, as well as the concentration. Mathematical descriptions of ultrasonic propagation in emulsions and suspensions have been derived which take into account the scattering of ultrasound by particles [20-21]. These theories relate the velocity and attenuation to the size (r), shape (x) and concentration (0) of the particles, as well as the ultrasonic frequency (co) and thermophysical properties of the component phases (TP). 

NMR imaging techniques were applied to the measurements of velocity field in opaque systems such as tomato juice and paper pulp suspensions [58-60]. In both cases, the particle concentrations are sufficiently high that widely applied techniques such as hot film and laser Doppler anemometry could not be used. The velocity profile for a 6 % tomato juice slurry clearly showed a power-law behavior [58, 59]. Row NMR images for a 0.5 % wood pulp suspension provided direct visual of three basic types of shear flow plug flow, mixed flow and turbulent flow as mean flow rate was increased. Detailed analysis of flow NMR image is able to reveal the complex interaction between the microstructure of suspensions and the flow [60]. 

The main problem in extending the microstructural theories to high Peclet number and volume fraction is related to the formulation of the many-body interactions. Recently, based on the Smoluchowski equation, Nazockdast and Morris (2012) developed a theory for concentrated hard-sphere suspensions under shear. The theory resulted in an integro-differential equation for the pair distribution function. It was used to capture the main features of the hard sphere structure and to predict the rheology of the suspension, over a wide range of volume fraction (<0.55) for 0 < Pe < 100 (Nazockdast and Morris 2012). 

Hirata Y., Onoue K. and Tanaka Y., 2003. Effects of pH and concentration of aqueous alumina suspensions on pressure filtration rate and green microstructure of consolidated powder cake, J. Ceram. Soc. Jpn., Ill, 93-99. 

Difficulties arises in smooth-walled viscometers because placing a structured liquid next to the wall changes the local microstructure [1]. For a simple suspension of smooth spherical particles, the spatial concentration of particles deep in the bulk of the sample, well away from the wall, is random. However, right at the wall, the particle concentration is zero. How do these two points join The answer is that the concentration rises rapidly as one moves away from the wall shows a decaying oscillatory behaviour, then it smoothes to the bulk concentration, see figure 1. This whole process from zero to average concentration takes about five particles diameters. The result is that the material near the wall is essentially different from the bulk, however worse than this is the effective lubricating layer near the wall where the particle concentration is first zero, and is small even up to half a particle diameter. The phenomenon of lower concentration next to the wall is called wall depletion, but is popularly known as sUp, see chapter 15 section 10 for more details. 

Most concentrated structured liquids shown strong viscoelastic effects at small deformations, and their measurement is very useful as a physical probe of the microstructure. However at large deformations such as steady-state flow, the manifestation of viscoelastic effects—even from those systems that show a large linear effects—can be quite different. Polymer melts show strong non-linear viscoelastic effects (see chap. 14), as do concentrated polymer solutions of linear coils, but other liquids ranging from a highly branched polymer such as Carbopol, through to flocculated suspensions, show no overt elastic effects such as normal forces, extrudate swell or an increase in extensional viscosity with extension rate [1]. 

How do these effects occur When any suspension of particles is placed next to a smooth wall, the original microstructure is locally disturbed. For a simple suspension at rest where the particles are randomly dispersed in space, the concentration of particles undergoes a damped oscillatory variation as one moves away from the wall, see figpre 16, where the concentration is at the maximum packing fraction, so that the effect is enhanced. The new distribution has two effects, first that the variation in concentration does not die out until about five particle radii away from the wall, and secondly that the average particle concentration is zero at the wall and less than average for a small distance away from the wall. 

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