Interparticle Force Theory

With the Interparticle Force Theory, interparticle forces (van der Waals, etc.) are what cause the bed to be elastic. Bed elasticity is characterized by an Elasticity Modulus, M.. The criterion which determines when the fluidized bed starts to bubble is determined by the relative magnitudes of the two sides of Eq. (7). 

B. W. Ninham, Hierarchies of forces The last 150 years, Advan. Colloid. Interface Sci. 16 3 (1982). Another must-reading article, this one dealing with the limitations of interparticle force theories that assume the liquid phase to be a continuum dielectric. 

The theory presented in this section is based on the grand canonical ensemble formulation, which is perfectly well-suited for the description of confined systems. Undoubtedly, in the case of attractive-repulsive interparticle forces unexpected structural and thermodynamic behavior in partly... 

Hydrody namical ly, fluidized beds are considered to be stable when they are not bubbling and unstable when they are bubbling. Several researchers (Knowlton, 1977 Hoffman and Yates, 1986 Guedes de Carvalho et al., 1978) have reported that fluidized beds become smoother at elevated pressures (i.e., have smaller bubbles) and, therefore, are more stable at high pressures. There are generally two approaches as to what causes instability in fluidized beds. Rietema and co-workers (Rietema et al. 1993) forwarded the theory that the stability of the bed depends on the level of interparticle forces in the bed. However, Foscolo and Gibilaro (1984) have proposed that hydrodynamics determines whether a fluidized bed is stable. 

Thus, within the context of the Newtonian force atom and the caloric theory of heat, solids, liqitids, and gases were all viewed as organized arrays of particles produced by a static equilibrium between the attractive interparticle forces, on the one hand, and the repulsive intercaloric forces, on the other. The sole difference was that the position of eqitilibriitm became greater as one passed from the solid to the liqitid to the gas, due to the increasing size of the caloric envelopes siuToittrding the component atoms (Figures 5 and 6). 

We examine some major conditions under which Einstein s theory breaks down. For our purpose, (he two important reasons are (a) the effect of the concentration of the dispersion and (b) the effects of interparticle forces, particularly the electrostatic repulsive forces or polymer additives. This leads us next to the non-Newtonian behavior of dispersions. 

Clearly, W is a function of any property of the dispersion that affects the strength of the interparticle forces and the energy barrier that slows down (or prevents) coagulation. A classical goal of colloid science has been to develop the equations necessary to predict the extent of stability of dispersions so that the results could be used in combination with the theories of interaction forces developed in previous chapters to promote or prevent the stability of dispersions. 

The DLVO-theory is named after Derjaguin, Landau, Verwey and Overbeek and predicts the stability of colloidal suspensions by calculating the sum of two interparticle forces, namely the Van der Waals force (usually attraction) and the electrostatic force (usually repulsion) [19],... 

Clearly, much work remains to be done in this subarea. Evolutionary operators need to be refined in order to deal efficiently with clusters and their ligand layers separately, as well as simultaneously. Suitable levels of theory for the interparticle forces have to be found and tested. And, of course, the size gap between application calculations and experiments needs to be closed. 

The kinetic theory of matter explains the properties of solids, liquids, and gases, and explains changes of state in terms of interparticle forces and energy. It also quantitatively relates the pressure, volume, and temperature of gases. By studying how gases behave under different conditions, you will soon begin to understand how all matter behaves. 

The soft (electrostatic) and van der Waals interparticle forces are described in the well-established theory of the stability of lyophobic dispersions (colloidal... 

Theories of interparticle forces play a fundamental part in many theoretical aspects of colloidal behaviour. It is therefore of great importance to have experimental evidence for the validity of these theories. One approach to this is to study the forces between macroscopic objects, to which the same theoretical equations should apply. Since these forces arc exceedingly small until the bodies come into very close proximity, work in this area has faced considerable experimental difficulties. Experiments on the force between two plates and between a plate and a lens have been of limited validity because of the difficulty in achieving adequate surface smoothness and in completely eliminating dust. The... 

The classical DLVO theory of interparticle forces considers the interaction between two charged particles in terms of the overlap of their electric double layers leading to a repulsive force which is combined with the attractive London-van der Waals term to give the total potential energy as a function of distance for the system. To calculate the potential energy of attraction Va between solid spherical particles we may use the Hamaker expression ... 

Interparticle forces are a determinant factor for most properties of dispersions, including rheological behavior. They are produced by the molecular forces on the surfaces of the particles, due to their nature or to adsorbed molecules, that modify the interface. These are electrical forces arising from charges on the particles and London-van der Waals attraction forces. The role of these forces on suspension stability has been extensively study and is known as the DLVO theory. In addition, sterical forces encountered on dispersions stabilized with nonionic species also exert an important influence on rheological behavior. The nature of these forces will not be considered since they are matters of discussion in Chapters 1-4. However, from a rheological point of view it is impwtant to understand how these factors modify the flow characteristics of dispersions. 

In contrast, particle adhesion can be a problem in certain areas powders may refuse to flow out of hoppers, pigments may form intractable sediments in paints and dust grains may wreck electronic micro-circuitry by adhering strongly to the chips. Perhaps the most dramatic consequences of problematic particle adhesion are found during earthquakes or mudslides, when the relatively weak interparticle forces are overcome by vibration or by fluid flow. The theory of powder adhesion attempts to describe and predict snch problems from first principles. 

Adopting a different point of view, we tried to fit the variation of D versus (p at low (j) with existing theories taking into account the role of hydrodynamic interactions and interparticle forces. This has been done for microemulsions A and B, using Felderhof theory (11) with an interaction potential sum of hard sphere repulsion and W = A(2R/r), A = B. The agreement with experimental a values is quite satisfactory. 

We are trying to increase the understanding of the role of inierparticle forces in the processing of ceramics. The effects of electrolyte addition and pH changes on the rheological properties of dispersions, tho kinetics of pressure filtration, and the miechanical properties and microstructure of the resulting bodies will be compared to each other and to existing models of interparticle forces i.e. DLVO theory). 

The fact that the origin and mechanisms of particle aggregation are principally understood and can even be quantitatively predicted by means of aggregation kernels and stability ratio (cf. Sect. 5.2.3) does not imply that such a prediction is easy to accomplish or that the interfacial properties can be easily derived from stability measurements. Indeed, the stability theory ignores the origin of interparticle forces and is indifferent towards their temporal evolutions. If, however. 

The most important feature to realize in a discussion of the theories of adhesion is that the phenomenon of adhesion can be considered in both a theoretical and a practical sense. Practical adhesion refers to determining the strength of a bond, usually by stressing it to failure. Theoretical adhesion is concerned with the magnitude of interparticle forces which cause materials... 

The authors postulate that a solid and a liquid of similar polarity will give a minimum value of y%. Kitazaki and Hata also discuss the ramifications of their postulates and experimeiital results on adhesion measurements. Overall their conclusion is that a maximum is achieved when the polarities of the solid surface and the adhesive are as similar as possible. From the Good and Girifalco theory, a maximum in would also be expected when the interparticle forces across the interface are at a maximum. Wu has also analyzed the separation of the force components of the interfacial and surface tensions. Wu, however, chooses to make an arithmetic mean approximation rather than the geometric mean approximation used by Good and by Fowkes. He bases this choice on an analogy with the form of the expressions for the interparticle forces, which are more closely mimicked by an arithmetic mean. Wu contends that his use of the arithmetic mean yields results closer to measured values. 

JKR Elastic-Adhesive Normal Contact Model The theory of Johnson et al. [22], referred to as JKR model, assumes that the attractive forces are confined within the area of contact and are zero outside. In other words, the attractive interparticle forces are of infinitely short range. JKR model extends the Hertz model to two elastic-adhesive spheres by using an energy balance approach. The contact area predicted by the JKR model is larger than that by Hertz. Consequently, there is an outer annulus in the contact area that experiences tensile stresses. This annulus surrounds an inner circular region over which a Hertzian compressive distribution acts [23]. Figure 7.9 shows schematieally the force-overlap response of the JKR model. 

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