Nearly spherical spheroidal particle

We give below a simple method to derive an approximate solution to the hnear-ized Poisson-Boltzmann equation (1.9) for the potential distribution i/ (r) around a nearly spherical spheroidal particle immersed in an electrolyte solution [12]. This method is based on Maxwell s method [13] to derive an approximate solution to the Laplace equation for the potential distribution around a nearly spherical particle. 

Closed wakes have been modeled as completing the sphere or spheroid of which the particle forms the cap [e.g. (C5, P2)]. However, the wake is smaller than that required to complete a spheroid for Re < 5 and greater for larger Re (B3). The wake becomes more nearly spherical as Re 100, but is still somewhat egg-shaped (B3, H5). Wake volumes, normalized with respect to the volume of the fluid particle, are shown in Fig. 8.6 for Re up to 110. Note the close agreement with results (Kl) for solid spherical caps of the same aspect ratio. This is not surprising since separation necessarily occurs at the rim of the... 

For nonspherical particles, the diameter, to be used in Eq. (1) should be the diameter of a sphere with equal volume. For closely sized near-spherical particles, the volume-surface mean diameter should be employed. For prolate spheroids, the smaller of the two principal dimensions is best used as the particle diameter in Eq (1). 

FIG. 28 Various monolayers near the jamming state generated in the RSA simulations (a) spherical particles at homogeneous surfaces (b) spherical particles at precovered smfaces (c) spheroidal particles (ellipses) adsorbing side-on (d) spherocylinders adsorbing side-on (e) prolate spheroids (unoriented adsorption) (f) oblate spheroids (unoriented adsorption). 

To examine the role of the LDOS modification near a metal nanobody and to look for a rationale for single molecule detection by means of SERS, Raman scattering cross-sections have been calculated for a hypothetical molecule with polarizability 10 placed in a close vicinity near a silver prolate spheroid with the length of 80 nm and diameter of 50 nm and near a silver spherical particle with the same volume. Polarization of incident light has been chosen so as the electric field vector is parallel to the axis connecting a molecule and the center of the silver particle. Maximal enhancement has been found to occur for molecule dipole moment oriented along electric field vector of Incident light. The position of maximal values of Raman cross-section is approximately by the position of maximal absolute value of nanoparticle s polarizability. For selected silver nanoparticles it corresponds to 83.5 nm and 347.8 nm for spheroid, and 354.9 nm for sphere. To account for local incident field enhancement factor the approach described by M. Stockman in [4] has been applied. To account for the local density of states enhancement factor, the approach used for calculation of a radiative decay rate of an excited atom near a metal body [9] was used. We... 

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