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The main difference between the effects of single and multiple scattering is that single scattering can usually be treated as a random phenomenon, whereas multiple scattering, somewhat counterintuitively, can be modeled as a more deterministic process because the combined results of a large number of scattering events tend to average out.
Dispersion is a process by which (in the case of solid dispersing in a liquid) agglomerated particles are separated from each other, and a new interface between the inner surface of the liquid dispersion medium and the surface of the dispersed particles is generated. This process is facilitated by molecular diffusion and convection. [4]
Dispersion of waves on water was studied by Pierre-Simon Laplace in 1776. [7] The universality of the Kramers–Kronig relations (1926–27) became apparent with subsequent papers on the dispersion relation's connection to causality in the scattering theory of all types of waves and particles. [8]
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics , scattering theory and quantum field theory (QFT).
Multiple light scattering coupled with vertical scanning is one of many techniques monitor the dispersion state of a product, identifying and quantifying destabilisation phenomena. [2] [3] [4] It works on concentrated dispersions without dilution. When light is sent through the sample, it is backscattered by the particles / droplets.
Multiple-scattering effects of light scattering by particles are treated by radiative transfer techniques (see, e.g. atmospheric radiative transfer codes). The relative size of a scattering particle is defined by its size parameter x, which is the ratio of its characteristic dimension to its wavelength:
Tyndall scattering, i.e. colloidal particle scattering, [7] is much more intense than Rayleigh scattering due to the bigger particle sizes involved. [ citation needed ] The importance of the particle size factor for intensity can be seen in the large exponent it has in the mathematical statement of the intensity of Rayleigh scattering.
The simple but crucial difference between the Teorell formula and the Onsager laws is the concentration factor in the Teorell expression for the flux. In the Einstein–Teorell approach, if for the finite force the concentration tends to zero then the flux also tends to zero, whereas the Onsager equations violate this simple and physically ...