Multiple scattering, particle-particl

Thanks to a low sensitivity to disturbances from multiple scattering, particle size measurements by ultrasonic spectrometry can be extended to extremely high particle concentrations. An evaluation of the measurements based on Lambert-Beer s law can provide results of sufficient quality for particle concentrations up to about 20 % by volume. An extension of ultrasonic measurements to even higher concentrations will require a more thorough understanding of steric interactions, including steric interactions between particles of different size. 

Clouds of Nonblack Particles The correction for nonblackness of the particles is complicated by multiple scatter of the radiation reflected by each particle. The emissivity . of a cloud of gray particles of individual surface emissivity 1 can be estimated by the use of Eq. (5-151), with its exponent multiplied by 1, if the optical thickness alv)L does not exceed about 2. Modified Eq. (5-151) would predict an approach of . to 1 as L 0°, an impossibihty in a scattering system the asymptotic value of . can be read from Fig. 5-14 as /, with albedo (0 given by particle-surface refleclance 1 — 1. Particles with a perimeter lying between 0.5 and 5 times the wavelength of interest can be handledwith difficulty by use of the Mie equations (see Hottel and Sarofim, op. cit., chaps. 12 and 13). 

Another popular form of data pre-processing with near-infrared data is the application of the Multiplicative Scatter Correction (MSC, [28]). It is well known that particle size distribution of non-homogeneous powders has an overall effect on the spectrum, raising all intensities as the average particle size increases. Individual spectra x, are approximated by a general offset plus a multiple of a reference spectrum, z. 

Fig. 22. The diagrams contributing to electrophoresis and the definition of lithe box. The reason why we only retain this class of terms is that we want to allow long-range propagation by the fluid— as shown in Fig. 21—which is clearly impossible if ions a and fi overlap in the box, because this would correspond to multiple scattering processes on particles a and fi.

The propagation of light in multiple scattering media is quantified usually on the level of radiative transfer or particle diffusion. Scattering, absorption, and emission are considered as independent statistical processes, and the consequences of wave character are either ignored, like polarization, or added as an additional parameter, like the phase function P(ji n) that describes the angular distribution of scattered... 

Image formation in a transmission electron microscope can be considered as a two-step process. In the first step, the electron beam is interacting with the specimen. This interaction is very strong compared to X-ray or neutron scattering and causes multiple scattering events. In order to understand this process, the classical particle description of the electron is not adequate, and the quantum mechanical wave formalism has to be used. Thus, assuming the... 

ELNES on Si L ionisation edge can be used to reveal the change in coordination of Si atoms due to the reductive treatment. After background subtraction and removal of multiple scattering [49], the spectra from different areas for both samples are plotted in Fig. 5. Before reduction, the Si L ELNES from as-grown silica and from the area with Pt particles exhibit the typical Si L ELNES of Si02, identical with the one measured from the Si02 substrate after the treatment. Some new features appear in the Si L ELNES spectrum obtained from particle after the reduction. This is a... 

A necessary condition for the correctness of the multiple-scattering explanation of the observed circular polarization is that scattering by noctilucent cloud particles does not appreciably reduce the degree of circular polarization of the incident light. That this is so for randomly oriented Rayleigh ellipsoids is readily shown. M in (5.52) is nearly unity for ice ellipsoids, so to good approximation... 

There are several possible explanations for the circular polarization data they are in error the particles are small, aligned, and highly absorbing the light illuminating the clouds has acquired a degree of circular polarization by multiple scattering. 

Standard static and dynamic light scattering methods assume that there is very little multiple scattering by the particles, that is, the dispersion has to be sufficiently dilute so that the photons are scattered only once as they pass through the sample. Is there a way to look inside a dispersion that is cloudy or milky, such as a foam, and to extract information on the local structure and its kinetics and relaxation Or, is it possible to tailor a dispersion so that... 

In contrast to traditional dynamic light scattering (which, as we discuss in Section 5.8, probes the continuous random motion of the particles), DWS here probes spatially localized, temporally intermittent events that are characterized by relatively larger length scales. Despite this, the basic quantity measured (g,(trf) in the notation of Section 5.8 there is no angular dependence in DWS because of multiple scattering) is essentially the same, only the method of analysis is different. 

Chu 1991 Schmitz 1990). For example, the dynamic version of the diffusing wave spectroscopy described in Vignette V is a form of DLS, although in diffusing wave spectroscopy the method of analysis is different in view of multiple scattering. Most of the advanced developments are beyond the scope of this book. However, DLS is currently a routine laboratory technique for measuring diffusion coefficients, particle size, and particle size distributions in colloidal dispersions, and our objective in this section is to present the most essential ideas behind the method and show how they are used for particle size and size distribution measurements. 

The theory of multiple scattering (scattering interaction) relates the scattering coefficient S to the pigment volume concentration o and to the scattering diameter Qs of the individual particle. The absorption coefficient K is directly proportional to the absorption diameter gA and the concentration a. 

Further development of this analogy leads to the non-Hermitian Hamiltonian problem describing the Bose particles. Proceeding in this way, the classical diffusion problem could be related to quantum theory of multiple scattering [115-118]. 

For the reasons described above, the droplet size distribution of the same emulsion measured on different laser diffraction instruments can be significantly different, depending on the precise design of the optical system and the mathematical theory used to interpret the diffraction pattern. It should be noted, however, that the most common source of error in particle size analysis is incorrect operation of the instrument by the user. Common sources of user error are introduction of air bubbles into the sample, use of the wrong refractive index, insufficient dilution of emulsion to prevent multiple scattering. and use of an unclean optical system. 

For small particles the specific turbidity increased with dilution which was explained by decreased intensity loss from the primary and scattered beams due to particle turbidity. For certain particles of a size around the first turbidity maximum where the scattering is strongest, the specific turbidity decreased with dilution as the stray light from multiple scattering decreased. 

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