Spheroids, conduction

The spheroidal modulus (So) is defined as the ratio of conduction heat flux through the vapor film to the evaporation heat flux ... 

A commercial controlled release, polymer coated spheroid/bead product (Slophyllin, Rona) was used as received. The spheroids were microtomed to expose a cross-sectional area of the inner drugladen core and the surrounding polymer film coating, and subsequently mounted on the sample holder using conductive silver paint with the microtomed surface uppermost. 

Boxer s group [2] first made a ns-laser photolysis apparatus with a super-conducting magnet. The sample was excited at 532 or 600 nm with a frequency-doubled YAG pumped dye laser (8ns, fwhm) and was probed at 860 nm with a laser diode. The maximum field of their magnet was 5 T. With this apparatus, they measured the quantum yield of triplet states (detected optically in quinone-depleted photosynthetic reaction centers (RCs) from R. spheroids, R-26 mutant, as a function of applied magnetic strength and temperature. The reaction scheme for qinone-depleted RCs is shown in Fig. 12.1. Here, the singlet and triplet radical-ion pair (RIP) are represented by [D" A ] and [D A ], respectively, and the rate constants of the S-T conversion of RIP, the recombination from [D A ], and the recombination from [D A ] are denoted by hsT, ks, and kj, respectively. 

Transport properties of ionomer blends, characterized by a given type of spheroids and the aspect ratio, e/a, can now be analyzed by the effective medium theory discussed in the previous section. In this theory, the two phases are assumed randomly mixed and the probability of finding each phase is equal to its volume fraction f.. The effective conductivity, o, of the composite for either Na+ of OH ions is given by (15) ... 

H. Fricke, A mathematical treatment of the electric conductivity and capacity of disperse systems, I. The electric conductivity of a suspension of homogeneous spheroids, Phys., Rev., 24, 575-587 (1924). 

Below we present a new uniform approach to the solution of the problem by perturbation method. The suggested perturbation formula, valid over the whole conductivity range, follows from the electrodynamic problem of a prolate spheroid immersed in a time-harmonic locally uniform field. The detailed... 

Fig. 4.6a considers a spherical core-shell particle in which the core is taken to be vacuum and the shell is silver. The particle radius is 50 nm, so when the shell thickness is 50 nm we recover the solid particle result. As the shell becomes thinner, the plasmon resonance red-shifts considerably, very much like we see for highly oblate spheroids. Fig. 4.6a assumes that the dielectric constant of silver is independent of shell thickness, so the resonance width does not change much when the shell becomes thin. However, the correct dielectric response needs to include for finite size effects (as noted above) when the shell thickness is smaller than the conduction electron mean free path. Fig. 4.6b shows what happens to the spectrum in Fig. 4.6a when the finite size effect is incorporated, and we see that it has a significant effect for shells below 10 nm thickness, leading to much broader plasmon lineshapes. 

External transient conduction from an isothermal convex body into a surrounding space has been solved numerically (Yovanovich et al. [149]) for several axisymmetric bodies circular disks, oblate and prolate spheroids, and cuboids such as square disks, cubes, and tall square cuboids (Fig. 3.10). The sphere has a complete analytical solution [11] that is applicable for all dimensionless times Fovr = all A. The dimensionless instantaneous heat transfer rate is QVa = Q AI(kAQn), where k is the thermal conductivity of the surrounding space, A is the total area of the convex body, and 0O = T0 - T, is the temperature excess of the body relative to the initial temperature of the surrounding space. The analytical solution for the sphere is given by... 

V r, V, z r, V- 6 Tl. V, z Tl, V, z T1,0, V 0 0 0,1 0, oo OQ 1,0 1, OO 1,2 1,2,3 12 ID constant volume condition cylindrical coordinates spherical coordinates elliptical cylinder coordinates bicylinder coordinates oblate and spheroidal coordinates zero thickness limit based on centroid temperature zeroeth order, first order value on the surface and at infinity infinite thickness limit first eigenvalue value at zero Biot number limit first eigenvalue value at infinite Biot number limit solids 1 and 2 surfaces 1 and 2 cuboid side dimensions net radiative transfer one-dimensional conduction... 

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