Interparticle force

Tadros (1986) describes four types of interparticle forces hard sphere, soft (electrostatic), van der Waals, and steric. Hard-sphere interactions, which are repulsive, become significant only when particles approach each other at distances slightly less than twice the hard-sphere radius. They are not commonly encountered. 

Soft (Electrostatic) and van der Waals Forces DLVO Theory 

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

Surfactants and Interfacial Phenomena, Third Edition. Milton J. Rosen ISBN 0-471-47818-0 2004 John Wiley Sons, Inc. 

The total potential energy of interaction V is the sum of the potential energy of attraction VA and that of repulsion Vr  

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Marlow and Rowell discuss the deviation from Eq. V-47 when electrostatic and hydrodynamic interactions between the particles must be considered [78]. In a suspension of glass spheres, beyond a volume fraction of 0.018, these interparticle forces cause nonlinearities in Eq. V-47, diminishing the induced potential E. 

In the region where > 1 then if the interparticle force is assumed to be constant over thi integration time step the following result is obtained [van Gunsteren et al. 1981] ... 

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

Equations 3 to 7 indicate the method by which terminal velocity may be calculated. Erom a hydrodynamic force balance that considers gravity, buoyancy, and drag, but neglects interparticle forces, the single particle terminal velocity is... 

This equation indicates that, for small particles, viscosity is the dorninant gas property and that for large particles density is more important. Both equations neglect interparticle forces. 

Interparticle Forces. Interparticle forces are often neglected in the fluidization Hterature, although in many cases these forces are stronger than the hydrodynamic ones used in most correlations. The most common interparticle forces encountered in gas fluidized beds are van der Waals, electrostatic, and capillary. 

Transport Disengaging Height. When the drag and buoyancy forces exerted by the gas on a particle exceed the gravitational and interparticle forces at the surface of the bed, particles ate thrown into the freeboard. The ejected particles can be coarser and more numerous than the saturation carrying capacity of the gas, and some coarse particles and clusters of fines particles fall back into the bed. Some particles also coUect near the wall and fall back into the fluidized bed. 

Glassification. Classification (2,12,26,28) or elutriation processes separate particles by the differences in how they settle in a Hquid or moving gas stream. Classification can be used to eliminate fine or coarse particles, or to produce a narrow particle size distribution powder. Classification by sedimentation iavolves particle settling in a Hquid for a predetermined time to achieve the desired particle size and size distribution or cut. Below - 10 fim, where interparticle forces can be significant, gravitational-induced separation becomes inefficient, and cyclone and centrifugation techniques must be used. Classification also separates particles by density and shape. Raw material separation by differential sedimentation is commonly used in mineral processiag. 

Deflocculants. Deflocculants (34), dispersants (qv), or anticoagulants are added to slurries to improve dispersion and dispersion stabiHty. Dispersants break up floes in a slurry by lowering van der Waals interparticle forces. Deflocculants adsorb on particle surfaces and prevent the approach of particles either by electrostatic or steric stabilization. Deflocculation by electrostatic stabilization is common in clay slurries, as weU as with ceramic particles dispersed in polar Hquids such as water. 

Monovalent cations are good deflocculants for clay—water sHps and produce deflocculation by a cation exchange process, eg, Na" for Ca ". Low molecular weight polymer electrolytes and polyelectrolytes such as ammonium salts (see Ammonium compounds) are also good deflocculants for polar Hquids. Acids and bases can be used to control pH, surface charge, and the interparticle forces in most oxide ceramic—water suspensions. 

J. E. Lane, T. H. Spurling. Monte Carlo simulation of the effects of adsorption on interparticle forces. Aust J Chem 55 231-239, 1980. 

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... 

This describes the motion of a single particle having the reduced mass of the two-particle system, whose position is that of particle two with respect to particle one, and which is acted upon by the interparticle force. 

Angle of Deflection for Some Simple Cases.—If, as is often assumed for simplicity, the interparticle force law is given by... 

In the derivation of the Boltzmann equation, it was noted that the distribution function must not change significantly in times of the order of a collision time, nor in distances of the order of the maximum range of the interparticle force. For the usual interatomic force laws (but not the Coulomb force, which is of importance in ionized gases), this distance is less than about 10 T cm the corresponding collision times, which are of the order of the force range divided by a characteristic particle velocity (of the order of 10 cm/sec for hydrogen at 300° C), is about 10 12 seconds. 

If the effect of the external force on the particles during a collision is small in comparison to the interparticle forces, the solution of Eq. (1-129) is ... 

New experimental techniqnes for the direct measurement of interparticle forces are now available and can be nsed to nnderstand the physicochemical factors that control adhesion, coating phenomena, tribology, and others. 

Although we have explained Bose-Einstein condensation as a characteristic of an ideal or nearly ideal gas, i.e., a system of non-interacting or weakly interacting particles, systems of strongly interacting bosons also undergo similar transitions. Eiquid helium-4, as an example, has a phase transition at 2.18 K and below that temperature exhibits very unusual behavior. The properties of helium-4 at and near this phase transition correlate with those of an ideal Bose-Einstein gas at and near its condensation temperature. Although the actual behavior of helium-4 is due to a combination of the effects of quantum statistics and interparticle forces, its qualitative behavior is related to Bose-Einstein condensation. 

Po Total number of pellets Reduced interparticle force per... 

For larger particles, the nature of interparticle forces is still unresolved. A typical operating condition for most commercial gas solid beds is well beyond the point of minimum bubbling. It might be expected that... 

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