Potential dipole solution

The Stokes quadrapole solutions are more complicated however, one component turns out to be particularly useful in the solution of Stokes flow problems, and that is the potential dipole solution, namely,... 

Hence when (8-139) and (8-140) are compared, it is obvious that a superposition of the stokeslet and potential dipole solutions will satisfy the creeping-flow equations and also the boundary condition (8 138). Specifically,... 

In view of the properties of the stokeslet and potential dipole solutions, the force acting on the spheroid is simply represented by the accumulative strength of the stokeslet distribution along the centerline of the spheroid. Thus, in dimensionless terms,... 

We will describe integral equation approximations for the two-particle correlation fiinctions. There is no single approximation that is equally good for all interatomic potentials in the 3D world, but the solutions for a few important models can be obtained analytically. These include the Percus-Yevick (PY) approximation [27, 28] for hard spheres and the mean spherical (MS) approximation for charged hard spheres, for hard spheres with point dipoles and for atoms interacting with a Yukawa potential. Numerical solutions for other approximations, such as the hypemetted chain (EfNC) approximation for charged systems, are readily obtained by fast Fourier transfonn methods... 

Coulomb or static dipole potentials should be included in the model potential whose solutions wo, w are used to construct the Green function. 

Hence it is clear that the stokeslet solution alone cannot satisfy (8 138). However, it has already been suggested that the stokeslet is most often accompanied by the potential dipole uc. At the sphere surface, the potential dipole field becomes... 

Although this completes the formal solution and demonstrates that the distribution of stokeslets and potential dipoles proposed in (8 167) is sufficient to solve the problem, it is of interest to calculate the force on the body. 

An aqueous electrolyte solution consists of a variety of charged and uncharged species, e.g. cations, anions, water dipoles, organic molecules, trace impurities, etc. which under equilibrium conditions are randomly oriented so that within the solution there is no net preferentially directed field. However, under the influence of a potential difference, the charge will be transported through the solution by cations and anions that migrate to... 

Thus the potential difference at the interface between a metal and electrolyte solution is due to both the charges at the interface (electrostatic potential difference) and the surface dipole layers the latter is referred to as the surface or adsorption potential difference. On the basis of the above considerations it might appear that adsorption at a metal surface with an excess charge is solely due to electrostatic interaction with charged species in the solution, i.e. if the metal surface has an excess negative charge the cations... 

Complete and Incomplete Ionic Dissociation. Brownian Motion in Liquids. The Mechanism of Electrical Conduction. Electrolytic Conduction. The Structure of Ice and Water. The Mutual Potential Energy of Dipoles. Substitutional and Interstitial Solutions. Diffusion in Liquids. 

I Calculates the potential from the solvent I dipoles at the sites of the solute atoms. 

In the previous chapter we considered a rather simple solvent model, treating each solvent molecule as a Langevin-type dipole. Although this model represents the key solvent effects, it is important to examine more realistic models that include explicitly all the solvent atoms. In principle, we should adopt a model where both the solvent and the solute atoms are treated quantum mechanically. Such a model, however, is entirely impractical for studying large molecules in solution. Furthermore, we are interested here in the effect of the solvent on the solute potential surface and not in quantum mechanical effects of the pure solvent. Fortunately, the contributions to the Born-Oppenheimer potential surface that describe the solvent-solvent and solute-solvent interactions can be approximated by some type of analytical potential functions (rather than by the actual solution of the Schrodinger equation for the entire solute-solvent system). For example, the simplest way to describe the potential surface of a collection of water molecules is to represent it as a sum of two-body interactions (the interac-... 

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