Rayleigh’s ratio

The scattered light techniques determine cither Rayleigh s ratio (with nephelome-ters) (Fabelinski, 1965 Eskin, 1973) or turbidity t (with colorimeters and spectrophotometers). The former quantity... 

In view of Equation 37, r is referred to as a full optical cross-section (in the atmosphere optics literature), and Rayleigh s ratio differential optical cross-section... 

Accepting n fn riy, we derive the traditional formula for Rayleigh s ratio for polymer solutions of moderate molecular weights, which is applied to determine the molecular weights of polymers... 

The concentration at the maximum of Rayleigh s ratio, Ria.9o,max> slightly differs from the critical one owing to the influence of the concentration dependence of other optical... 

II expression for Rayleigh s ratio for ]>olymolecular polymer solution results from Kconversion formulae in lable 2.3) (Scliollc, 1970b, 1971)... 

An expression for Rayleigh s ratio /f,> wllli duo account of polymolecularily. intra- and intcrmolecular interference, the spiuodal proximity, and appropriate dependence, of the interaction parameter has been derived by Vrij (197 1, 1978) and will be rlisciissetl later. 

In light-scattering investigations, one measures the reduced scattering intensity at a scattering angle 0,sometimes simply referred to as Rayleigh s ratio, which is defined as [27] ... 

Light scattering from solutions depends on concentration fluctuations and thus can be related to thermodynamics by standard statistical mechanical methods. The ratio c/R(0,c), where R(0, c) is the reduced scattered intensity (or Rayleigh s ratio) due to the solute, is extrapolated to zero scattering angle 6. For a binary system, R(0,c) is related very simply to the osmotic pressure by... 

The limiting dilute-solution behavior of the reduced intensity R q, c) (Rayleigh s ratio) of light scattered through an angle 9 is given by (3)... 

When the size parameter x is sufficiently small, that is, when the particle is small compared with the wavelength of light, only the leading term in the normal mode expansion for the spherical harmonic functions is needed. In this case Eq. (76) reduces to Rayleigh s result, Eq. (47), for the ratio of the scattered irradiance to the incident irradiance. 

Thus we see that within the limitations of Rayleigh s assumptions, asd increases the ratio of residual to initial intensity, I/I0 diminishes, as it also does when l and N increase, although not at as great a rate. The influence of any variation in X is also evident. 

This formula is crude, and it does not account for differences in shear rates between the droplet and the medium (which are large when the viscosity ratio differs greatly from unity). Nevertheless, because of the shear-rate-dependence of, Eq. (9-22) can predict a.minimum in droplet size as a function of shear rate that is observed in some cases (Sundararaj and Macosko 1995 Plochocki et al. 1990 Favis and Chalifoux 1987). Viscoelastic forces have indeed been shown to suppress the breakup of thin liquid filaments that would otherwise rapidly occur via Rayleigh s instability (Goldin et al. 1969 Hoyt and Taylor 1977 Bousfield et al. 1986). Elongated filaments, for example, are observed in polymer blends (Sondergaard... 

The dimensionless equation describing the transfer phenomena may be obtained either by direct reference to the ratios of the physical quantities or by recourse to the classical techniques of dimensional analysis, i.e., the Buckingham n Theorem or Rayleigh s method of indices. In addition, the basic differential equations governing the process may be reduced to dimensionless form and the coefficients identified. In general, the dimensionless equation for heat transfer through the combined film is... 

For a given weight (or volume) of material, initially composed of monodisperse singlets of very small size so that Rayleigh s law is obeyed (dsuspension turbidity will increase as the third power of the ratio of the aggregate radius to the... 

The Rayleigh wave propagation velocity urw = f Ut is determined by the sound velocity of the transverse-polarized phonons. The factor depends on the ratio of the longitudinal to transverse sound velocities, that is, depends on the Poisson s ratio, which may vary between 0 and 0.5 for the various materials. This results in a range of between 0.874 and 0.955. For Si, the Poisson ratio is 0.27, and = 0.918 is obtained. In any case, the velocity of the Rayleigh wave is smaller than the transverse sound velocity. Consequently, the branch of the Rayleigh... 

The parameter a is the ratio of the conductivity of the dispersed phase to that of the continuous phase. Meredith and Tobias extended this result to higher-order terms. Zuzovsky and Brenner used a multipole expansion technique to calculate the effective conductivity of simple cubic, body-centered cubic, and face-centered cubic arrays of spheres. Their technique allowed for fourfold symmetry in the arrays, while those of previous authors did not. McPhe-dran and McKenzie and McKenzie, McPhedran, and Derrick extended Rayleigh s method for calculating the conductivities of lattices of spheres. Their method includes the effects of multipoles of arbitrarily high order specifically, their equation gives the numerical value of the / -order term referred to by Zuzovsky and Brenner. Sangani and Acrivos also used a fourfold potential to calculate effective conductivities of simple cubic, body-centered cubic, and face-centered cubic lattices to 0(/ ). They corrected a numerical slip in the work of Zuzovsky and Brenner. Their equation is... 

As mentioned in Chap. 3, for depfli/diameter ratios less than 0.5, such as in large cylindrical LPG and LNG tanks, flie boundary layer flow across the base may be broken by the creation of vertical fliermals spaced horizontally at intervals approximating to the liquid depth according to Rayleigh s instability criteria for natural convection. In aU cases, the heat in-flow is carried by boundary layer flows, and thermals, to the liquid surface. 

---