Method of induced forces

Mazur (1982) and Mazur and van Saarloos (1982) developed the so-called method of induced forces in order to examine hydrodynamic interactions among many spheres. These forces are expanded in irreducible induced-force multipoles and in a hierarchy of equations obtained for these multipoles when the boundary conditions on each sphere were employed. Mobilities are subsequently derived as a power series-expansion in p 1. In principle, calculations may be performed to any order, having been carried out by the above authors through terms of 0(p 7) for a suspension in a quiescent fluid. To that order, hydrodynamic interactions between two, three, and four spheres all contribute to the final result. This work is reviewed by Mazur (1987). 

Electrically induced migration of ions and water is a proven method of externally forced mass transport in clay soils for contaminant remediation purposes (Pamukcu and Wittle, 1992 Acar and Alshawabkeh, 1993,1996 Lageman, 1993 Probstein and... 

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

Specific properties of polysilanes have been linked to the method of synthesis.35 For example, in the case of anionic polymerization of poly[l-(6-methoxy-hexyl)-l,2,3-trimethyldisilanylene] a new type of chromism was induced in the polysilane film by the difference in the surface properties of substrates and was termed a surface-mediated chromism. The polysilane exhibited thermochromism with an absorption maximum at 306 nm at 23°C, but <15°C a band at 328 nm began to appear. A monolayer of the polysilane was transferred onto both a clean hydrophilic quartz plate and a hydrophobic one treated with hexamethyldisilazane by the vertical dipping method. With the hydrophobic plate, a broad UV absorption at 306 nm is obtained, whereas the absorption on a hydrophilic plate shifts to 322 nm. The conformation of the polysilane is preserved by hydrogen bonding between the silica surface and the ether section of the substituent on the hydrophilic plate. The polysilane is attached to the hydrophobic surface only by van der Waals forces, and this weaker interaction would not sustain the thermodynamically unstable conformational state that is attained on the water surface. 

An effective method of controlling concentration polarization and sustaining productivity involves inducing turbulent vortices on the membrane surface to counteract the forces of solute or particle deposition. The rotating... 

Experimentally, one of the main methods of distinction between the Forster and Dexter mechanisms in an energy transfer is a study of the distance dependence of the observed process. From Equation (2.32) it is evident that the rate of dipole-induced energy transfer, kfen/ decreases as d 6. This is typical of dipolar interactions and is reminiscent of the distance dependence of other such mechanisms, e.g. London dispersion forces. Therefore, the Forster mechanism can operate over large distances, whereas, in contrast, the rate of Dexter energy transfer, kden, falls off exponentially with distance. 

---