Interparticle force/distance

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. 

To measure the force-extension law of a small biomolecule, these authors employed a two-step strategy. First, the background repulsive force-distance profile, in the absence of biomolecules, Fbg(h), is measured, h being the interparticle spacing. Then, once the biocomplexes have been properly attached within each interval between colloids, the same measurement is repeated, allowing determination of the force-distance profile of this irreversible assembly The force / >(/t)... 

Stabilising a colloidal suspension implies that the total interparticle potential decreases with increasing inter particle distance. The different kinds of stabilisation all use some of the above-mentioned interparticle forces. 

FIGURE 12.1 (a) Hydrophilic colloid encased in bound water (b) interparticle forces as a function of interparticle distance. 

The textural properties of a fat are influenced by all levels of structure, particularly microstructure. The microstmcture includes the spatial distribution of mass, particle size, interparticle separation distance, particle shape, and interparticle interaction forces (49-51). Methods that can be used for the characterization of microstructure in fat systems include, among others, small deformation rheology and polarized light microscopy, employing a fractal approach (49-51). 

DLVO [2,3] theory estimates the repulsive and attractive force due to the overlap of electric double layers and London-van der Waals force in terms of inter particle distance, respectively. The summation of them gives the total interaction force and can be used for the interpretation of colloid stability in terms of the nature of interaction force-distance curve. If a small interparticle separation (H) is assumed, van der Waals forces for a sphere and substrate can be expressed to... 

Second is that the results of Figs. 21-117 and 21-118 do not clearly depict the role of saturation and compact porosity. Decreases in compact porosity generally increase compact strength through increases in interparticle friction, whereas increases in saturation lower strength (e.g.. Figs. 21-112 and 21-113 and Holm et al. [Parts V and VI, Pow-der Technol., 43, 213—233 (1985)]). Hence, the curve of Fig. 21-118 should be expected to shift with these variables, particularly since the viscous force for axial approach is singular in the interparticle gap distance [Eq. 21-111)]. 

Here, a and )3 indicate the different Cartesian components of the interfacial stress tensor S, the interparticle distance r, and the interparticle force Fy, respectively. We assume that the contribution to the stress tensor due to particles that are completely desorbed from the interface is negligible, and therefore we sum over all particles in the system. 

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. 

We can at this stage state that we are now in possession of a very accurate theoretical and numerical tool to calculate properties of any three-body system where the interparticle forces may be expressed as a function of the three interparticle distances. 

A theoretical derivation of the Schulze-Hardy rule can be developed on the basis of the interparticle forces described in Sec. 6.2. Each of the three forces is associated with a potential energy that contributes additively to the total potential energy between two planar particle surfaces a distance d apart. If (p(d) is the total potential energy per unit area of planar surface, then... 

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 include the van der Waals attractive forces, electrostatic r ul-sive forces arising firom surface chaiges on the particles, and entropic repulsive forces due to water-soluble polymera adsoibed/anchored to the particle surface and/or due to adsorbed surfactants. These interparticle forces become important as the interparticle distance, h, becomes smaller, and are significant factors at h < 10 nm. Both smaller particle diameter, d, and higher volume fracfion, < >, lead to decreasing values of h, as shown in Equation (13.8). As already seen in Section 13.2.4, the thickness of adsorbed surfactant layers can be an appreciable fraction of the interparticle distance. Adsorbed polymer layers can be of the order of 10 nm in thickness, and in systons with low ionic strength, electrical charge effects can extend much further. 

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