Brownian motion and

Woessner D E 1996 Brownian motion and correlation times Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 1068-84... 

Acid mist eliminators use three aerosol collection mechanisms inertial impaction, interception, and Brownian motion. Inertial impaction works well for aerosols having particle diameters larger than 3 p.m Brownian motion and interception work well with aerosols having smaller particle diameters. 

Ions of an electrolyte are free to move about in solution by Brownian motion and, depending on the charge, have specific direction of motion under the influence of an external electric field. The movement of the ions under the influence of an electric field is responsible for the current flow through the electrolyte. The velocity of migration of an ion is given by ... 

In view of the facts that three-dimensional coUoids are common and that Brownian motion and gravity nearly always operate on them and the dispersiag medium, a comparison of the effects of particle size on the distance over which a particle translationaUy diffuses and that over which it settles elucidates the coUoidal size range. The distances traversed ia 1 h by spherical particles with specific gravity 2.0, and suspended ia a fluid with specific gravity 1.0, each at 293 K, are given ia Table 1. The dashed lines are arbitrary boundaries between which the particles are usuaUy deemed coUoidal because the... 

Factors which adversely influence the separation of veiy fine particle systems are brownian motion and London forces. However, it is possible to counter these forces by the use of dispersants, temperature control, and so on. 

Dickinson, E., 1986. Brownian motion and aggregation from hard spheres to proteins. 

McConnell J. Rotational Brownian Motion and Dielectric Theory. (Academic Press, New York) (1980). 

Liquid-solid transitions in suspensions are especially complicated to study since they are accompanied by additional phenomena such as order-disorder transition of particulates [98,106,107], anisotropy [108], particle-particle interactions [109], Brownian motion, and sedimentation-particle convection [109], Furthermore, the size, size distribution, and shape of the filler particles strongly influence the rheological properties [108,110]. More comprehensive reviews on the rheology of suspensions and rubber modified polymer melts were presented by Metzner [111] and Masuda et al. [112], respectively. 

First, consider the solvent. The characterization of the solute-solvent coupling by a relaxation time is based on analogy to Brownian motion, and the relaxation time is called the frictional relaxational time Xp. It is the relaxation time for momentum decay of a Brownian motion in the solute coordinate of interest when it interacts with the solvent under consideration. If we call the subject solute coordinate s, then the component of frictional force along this coordinate may be written as... 

Molecules in ordinary liquids average out all anisotropic spin interactions due to isotropic Brownian motions, and their NMR spectra are governed by the Hamiltonian in units of Hz due to the Zeeman interaction, the isotropic chemical shift (a) and the isotropic indirect spin-spin coupling (7)... 

In this chapter, we shall first make a brief review of the phenomenological aspect of Brownian motion and we shall then show how the general transport equation derived in Section II allows an exact microscopic theory to be developed. 

Polymerization in microemulsions allows the synthesis of ultrafine latex particles in the size range of 5 to 50 nm with a narrow size distribution [33], The deposition of an ordered monolayer of such spheres is known to be increasingly difficult as the diameter of such particles decreases [34], Vigorous Brownian motion and capillary effects create a state of disorder in the system that is difficult... 

Weber G. (1953) Rotational Brownian Motions and Polarization of the Fluorescence of Solutions, Adv. Protein Chem. 8, 415-459. 

G. Weber, Rotational Brownian motion and polarization of the fluorescence of solutions,... 

The early years of the twentieth century saw giant advances in man s understanding of nature which must be mentioned in any synopsis of the scientific history of this era. Thus, in 1901, M. Planck (NLP 1918 ) published his first paper on the black-body radiation law which ushered in the era of quantum mechanics. In 1905, A. Einstein (NLP 1918 ) published his Anna Mirabilis Papers on the photo effect, on Brownian motion, and on the theory of special relativity and the equivalence of matter and energy. 

The relationships follow from considerations of Brownian motions and thermal fiuctuations which also infiuence the internal motions in flexible objects. is the translation coefficient of the particle s center of mass where the subscript indicates the z-average over the molar mass distribution. The first bracket in Eq. (12) describes the concentration dependence which often is well represented by a linear dependence... 

Rotational Brownian Motion and Polarization of the Fluorescence of Solutions Gregorio Weber... 

In this section, we have considered four possible ways of formulating and interpreting a set of SDE to describe Brownian motion, and tried to clarify the relationships among them. Because each interpretation may be defined as the At 0 limit of a discrete Markov processes, this discussion of SDEs provides a useful starting point for the discussion of possible simulation algorithms. 

Figure 2 Relative adsorption rates due to collisions resulting from Brownian motion and mechanical agitation. The lines represent conditions where the rates are equal. Agitation dominates to the right of the lines...

It is somewhat surprising that despite all of his contributions to science and engineering, including his work on Brownian motion and the theory of relativity, Albert Einstein (1879-1955) won his only Nobel Prize in 1921 for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect. ... 

Jean Perrin s 1913 monograph, Les Atomes, on Brownian motion and some of the related topics on the molecular nature of matter has been reprinted recently (Perrin 1990) and is an interesting source of information on the evolution of ideas on diffusion and determination of Avogadro s number. This monograph also contains some of Perrin s sketches of random walks executed by colloidal spheres in his experiments. 

A critical comparison by van Konyenberg and Steele [230] and Jones et al. [231] of extended diffusion models with Brownian motion and other continuum models strongly favours the former treatment. More detailed analysis is given by Berne and Pecora [232]. 

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