Particle interparticle forces affecting

The stability and the structure of dispersions (structure here means the spatial organization of the colloidal particles) are topics of considerable research activity currently there is a lot that we do not know despite the long-standing focus on these topics in colloid science. The first step in approaching problems in this area is to study the origin and the nature of the interparticle forces and how they affect coagulation in dilute dispersions. This is what we focus on in this chapter. 

The motion of particles is affected by the short-range interparticle forces such as the van der Waals force, electrostatic force, and collision force. It is also affected by the long-range field forces such as the gravitational force, electric force, and magnetic force. This section discusses the basic relationships which quantify these interparticle and field forces. 

Consider the collision of particles due to wake attraction, as shown in Fig. E3.1. It is assumed that (a) the motion of the leading particle is not affected by the approach of the trailing particle (b) particles are equal-sized, rigid, and spherical and (c) initially, the particles move nearly at their terminal velocities with a very small velocity difference and are separated by a characteristic distance Zo- An empirical relation can be used to describe the effects of the interparticle distance Z and particle Reynolds number Rep on the drag force of the trailing particle as... 

The dimerization is easily understood considering the optical potential created by the trapping laser. Figure 18.2b shows the calculated optical potential experienced by a silver nanoparticle that is fi ee to move in a Gaussian laser focus at a wavelength of 830 nm. The particle is also affected by the optical interparticle force from an immobilized silver particle located at different separations from the laser focus. It is clear that a deep potential minimum is induced when the trapped particle approaches the immobilized one, giving rise to spontaneous optical dimerization and a SERS hot spot in the optical trap. Note that the two particles are expected to ahgn parallel to the laser polarization in this case, as has been demonstrated experimentally recently [88]. 

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. 

In concentrated suspensions, the motion of particles is cmcially affected by hydrodynamic interaction between neighbouring particles, which strongly depends on the interparticle distances, i.e. on the suspension structure (cf. Overbeck et al. 1999 Watzlawek and Nagele 1997, 1999). This structure is clearly influenced by the inteiparticle forces, in particular by the forces that occur when the EDL of two particles overlap (e.g. Russel 1978 Quemada and Berli 2002). When a suspension contains only a single particulate component, such a double layer overlap leads to repulsions and, thus, decreases the particle mobility and increases the suspension viscosity (Fig. 3.5). This effect is called secondary electroviscous effect. Its... 

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... 

Additional interparticle forces exist in colloidal systems. They can be derived from a potential because they depend only on interparticle distance. Hence they act as springs and as such can cause pronounced elastic effects. However, the spring force depends on interparticle distance, and the springs even rupture when the particles move too far apart. This results in a highly nonlinear material response. During flow, the potential forces will affect the interparticle distances and consequently the frictional forces and the viscosity. We review each of these forces briefly in Sections 10.4.1-10.4.4. More thorough discussion can be found in Russel et al. (1989). 

The different phases arise from the competition between the interparticle forces, which try to produce a regular arrangement of the particles, and the internal energy, which tries to destroy such an arrangement. Applied pressures affect the role played by the interparticle forces so that the phase in which a particular substance exists depends on both the temperature and pressure. 

The capillary force as usually measured in experiments and as relevant in theoretical calculations calling for an effective interparticle force is actually a so-called mean force, that is, the result after all the degrees of freedom other than the particle position and orientation have been integrated out. Consider, for example, the simplest case of two identical, spherical particles a distance d apart. Let E pid) denote the parametric d-dependence of the free energy stemming from the terms affected by interfacial deformation (see, e.g., Equation 2.11). Then, E id) is a potential of mean force and the capillary force is defined as the derivative = -E fd). In this respect, two observations are in order concerning particularly the case n(r) 0 ... 

The interrelated effects of adsorption on flocculation are summarized in Table 5. Surface reactions affect suspension stability through changes in the strength of interparticle repulsive forces and, if adsorptive macromolecules are involved, through changes in particle association mechanisms. Flocculation is thus viewed as the result of a reduction in... 

Die fill characteristics depend upon material flow properties that are primarily affected by particle size and shape. Additionally, high interparticle friction can have a detrimental effect on die fill characteristics due to powder bridging and non-uniform flow characteristics. A non-uniform particle size distribution may also lead to material segregation resulting in uniformity problems. Tablet presses employ volumetric filling of the material into the die cavity. Most high-speed tablet presses are equipped with force feeders, which use rotating paddles to promote uniform die fill characteristics. For certain materials, attention must be... 

Particle size. For anisometric particles, their size has an effect. Small particles show rotational diffusion, and this is more rapid for a smaller particle. This affects the average orientation of the particles, hence the increase in viscosity due to anisometry. Smaller particles would thus give a higher viscosity. Also Factor 2 can come into play the smaller the particles at a given value of q>, the smaller the interparticle distance and the larger the effect of repulsive interaction can be. On the other hand, attractive forces tend to have a smaller effect on smaller particles. 

The surfactant is any substance which affects the surface or interfacial tension of the medium in which it is dissolved. Surfactants can increase or decrease the surface tension by spreading on the surface or interface. Surfactants are used for the synthesis of nanoparticles to reduce the interparticle interaction due to increased repulsive forces to control the particle size and their distribution in most chemical methods. 

In this paper we review principles relevant to colloids in supercritical fluids colloids in liquids are discussed elsewhere [24]. Thermodynamically unstable emulsions and latexes in CO2 require some form of stabilization to maintain particle dispersion and prevent flocculation. Flocculation may be caused by interparticle van der Waals dispersion forces (Hamaker forces). In many of the applications mentioned above, flocculation of the dispersed phase is prevented via steric stabilization with surfactants, in many cases polymeric surfactants. When stabilized particles collide, polymers attached to the surface impart a repulsive force, due to the entropy lost when the polymer tails overlap. The solvent in the interface between the particles also affects the sign and range of the interaction force, and the effect of solvent is particularly important for highly compressible supercritical solvents. Since the dielectric constant of supercritical CO2 and alkanes is low, electrostatic stabilization is not feasible [24] and is not discussed here. For lyophobic emulsion and latex particles (-1 xm), the repulsive... 

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