Long range forces, elasticity theory

The DMT theory describes the adhesion between elastic spheres by assuming a Hertzian shape of the contact and taking surface forces outside the contact zone into account. It is best applied in the case of hard materials, small sphere radii, and more long-ranged forces. The adhesion force between 2 spheres with reduced radius R in the JKR theory is... 

In the absence of a field, previous theoretical predictions based on a long-range calculation predicted that the elastic quadrupolar repulsion force should follow the power law Prepukion° l [4> 7]. Under the present experimental conditions, i.e., in the presence of an electric field, we observe a steeper repulsion as shown by the log-log plot in the inset of Fig. 13. Two reasons might explain the discrepancy between the experimental measurements and the theory. First, since the electric field is likely to distort the ordering of the liquid crystal molecules in the vicinity of the drops, the measured quadrupolar repulsion may intrinsically depend on Eq. Second, short-range effects, not considered in the theoretical approach, may come into play in the experiments. Indeed, the maximum measured separation between two drops is of the order D. 

DLVO theory explained major principles of coagulation of hydrosols by electrolytes and brought to common grounds all previous observations (primarily of qualitative nature) that related to individual cases and often seemed to be contradictory. In years that followed further extensions of DLVO theory that took into account the possibility of reversible particle aggregation were developed. At very small distances between particles in addition to the usual long-range interaction, molecular attraction and electrostatic repulsion, one must account for other factors that play role at a direct particle contact. The formation of peculiarly structured hydration layers in the vicinity of solid surface, the appearance of elastic forces that are responsible for the Born repulsion between surface atoms at the point of contact, the repulsion between the adsorbed surfactant molecules in contact zone between two particles, all represent the so-called non-DLVO stability factors . This means that more or less deep primary minimum remains finite. 

The function f contains all the constitutive (material-dependent) properties and describes how the internal forces depend on the deformation. A standard assumption is that for a given material, f = 0 for all u when jr -rj > S for some > 0 called the horizon. This characteristic distance represents a length scale for the nonlocality of force. Nonlocal models allow to incorporate directly the description of atomistic effects and long-range interactions into a continuum theory. In contrast, classical elasticity theory does not have a length scale - the horizon consists of a point because of the assumption of a contact force. 

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