Particle Brownian motion

In general, increasing the temperature within the stability range of a single crystal structure modification leads to a smooth change in all three parameters of vibration spectra frequency, half-width and intensity. The dependency of the frequency (wave number) on the temperature is usually related to variations in bond lengths and force constants [370] the half-width of the band represents parameters of the particles Brownian motion [371] and the intensity of the bands is related to characteristics of the chemical bonds [372]. 

Increasing the radius of the suspended particles, Brownian motion becomes less important and sedimentation becomes more dominant. These larger particles therefore settle gradually under gravitational forces. The basic equation describing the sedimentation of spherical, monodisperse particles in a suspension is Stokes law. It states that the velocity of sedimentation, v, can be calculated as follows ... 

Dynamic light scattering (DLS) techniques measure the fluctuations in the scattered light intensity caused by the random Brownian motion of the dispersed particles. The use of a theoretical model of particle Brownian motion enables us to extract particle size from DLS data. Other dynamic light scattering techniques such as electrophoretic light scattering (ELS) study collective particle motions. Theoretical interpretation of ELS data leads to other particle properties such as electrophoretic mobility fi and zeta potential f. These techniques will be discussed in more detail in subsequent sections. 

Let us summarize the obtained results. From the expression for the viscosity of an infinite diluted suspension, it follows that the viscosity factor does not depend on the size distribution of particles. The physical explanation of this fact is that in an infinite diluted suspension W 1), particles are spaced far apart (in comparison with the particle size), and the mutual influence of particles may be ignored. Besides, under the condition a/h 1, we can neglect the interaction of particles with the walls. It is also possible to show that in an infinite diluted suspension containing spherical particles. Brownian motion of particles does not influence the viscosity of the suspension. However, if the shape of particles is not spherical, then Brownian motion can influence the viscosity of the suspension. It is explained by the primary orientation of non-spherical particles in the flow. For example, thin elongated cylinders in a shear flow have the preferential orientation parallel to the flow velocity, in spite of random fluctuations in their orientation caused by Brownian rotational motion. 

When the particles are deposited from solution (see Fig. VI. 1 curve 2 and Fig. VI.2 curves 3 and 4), the gap is maximized, and in this case the minimum force of adhesion is realized, corresponding to the second minimum F m-Estimation of the limiting value of the second minimum can be approached by starting with the quantity kT(k is Boltzmann s constant Tis the absolute temperature). Free movement of the particles (Brownian motion) can be expressed by the equation [169]... 

Every particle or molecule in suspension is constantly in contact with solvent molecules that are moving due to thermal energy. In turn, this causes the molecules or particles to move in a particular manner, called Brownian motion, which depends on their size. When the sample is illuminated with a laser, the intensity of scattered light fluctuates depending on particle Brownian motion velocities—and, therefore, then-size. Through the analysis of intensity fluctuations. Brownian motion velocity can be acquired and the radius of the particle can then be determined by the Stokes-Ein-stein relationship. He and co-workers have developed a technique for hierarchical DNA self-assembly into polyhedral architectures, and, using DLS, they compared the hydrodynamic radius of the assembled complexes with the predicted ones. ... 

Gravitational settling of particles is enhanced by increased particle size, which occurs spontaneously by coagulation (see Chapter 6, Figure 6.11). Thus, over time, the size of particles increases and the number of particles decreases in a mass of air that contains particles. Brownian motion of particles less than about 0.1 mi in size is primarily responsible for their contact, enabling coagulation to occur. Particles greater than about 0.3 pm in radius do not diffuse appreciably and serve primarily as receptors of smaller particles. 

In eq. (1) A is a, in principle constant, background signal and B is an instrumental factor. Note that eq. (1) applies only to scattered fields with Gaussian statistics an hypothesis which is not always fulfilled experimentally. Especially for particles larger than roughly 0.5 to 1 im additional time delay dependent factors can be distinguished in eq. (1) In a second step the time decay of the field autocorrelation function is related to the particles Brownian motion. Thereby it is assumed that the particles scatter independently. In particular for monodisperse samples gi(0,x) is an exponentially decaying function ... 

Smoluhovsky, M. Three reports on Brownian molecular motion and concretion of colloidal particles Brownian motion. M ONTl. 1936b, 332-417, (in Russian). 

A similar approach was used by the same group to encapsulate MMT platelets using cationic RAFT copolymers composed of randomly distributed BA and quatemized units of 2-dimethylaminoethyl methacrylate (DMAEMA) and a MMA BA (10 1 weight ratio) monomer feed [86]. Despite the successful formatiOTi of flat, comflake-Uke composite particles. Brownian motion prevented them from adopting a specific orientation after deposition on a substrate. 

The invention of the ultramicroscope by Siedentopf and ZsigmoNUy in 1903 placed the fact that gold sols contain particles the siae of which depended on the method of preparation beyond all doubt When soon after this (1908), thanks to the investigations of Perrin the si2 e of molecules and atoms became known and indeed in a way which illustrated continuous transitions between molecules and larger particles (Brownian motion) the character of colloids as a dispersion intermediate between molecular dispersion and that of coarse suspensions was generally accepted. 

The viscosity of a suspension of ellipsoids depends on the orientation of the particle with respect to the flow streamlines. The ellipsoidal particle causes more disruption of the flow when it is perpendicular to the streamlines than when it is aligned with them the viscosity in the former case is greater than in the latter. For small particles the randomizing effect of Brownian motion is assumed to override any tendency to assume a preferred orientation in the flow. 

There is an intimate connection at the molecular level between diffusion and random flight statistics. The diffusing particle, after all, is displaced by random collisions with the surrounding solvent molecules, travels a short distance, experiences another collision which changes its direction, and so on. Such a zigzagged path is called Brownian motion when observed microscopically, describes diffusion when considered in terms of net displacement, and defines a three-dimensional random walk in statistical language. Accordingly, we propose to describe the net displacement of the solute in, say, the x direction as the result of a r -step random walk, in which the number of steps is directly proportional to time ... 

Diffusional interception or Brownian motion, ie, the movement of particles resulting from molecular collisions, increases the probability of particles impacting the filter surface. Diffusional interception also plays a minor role in Hquid filtration. The nature of Hquid flow is to reduce lateral movement of particles away from the fluid flow lines. 

Figure 5 relates N j to collection efficiency particle diffusivity from Stokes-Einstein equation assumes Brownian motion same order of magnitude or greater than mean free path of gas molecules (0.1 pm at... 

The natural process of bringing particles and polyelectrolytes together by Brownian motion, ie, perikinetic flocculation, often is assisted by orthokinetic flocculation which increases particle coUisions through the motion of the fluid and velocity gradients in the flow. This is the idea behind the use of in-line mixers or paddle-type flocculators in front of some separation equipment like gravity clarifiers. The rate of flocculation in clarifiers is also increased by recycling the floes to increase the rate of particle—particle coUisions through the increase in soUds concentration. 

Other Factors Affecting the Viscosity of Dispersions. Factors other than concentration affect the viscosity of dispersions. A dispersion of nonspherical particles tends to be more viscous than predicted if the Brownian motion is great enough to maintain a random orientation of the particles. However, at low temperatures or high solvent viscosities, the Brownian motion is small and the particle alignment in flow (streamlining) results in unexpectedly lower viscosities. This is a form of shear thinning. 

Sols are dispersions of colloidal particles in a Hquid. Sol particles are typically small enough to remain suspended in a Hquid by Brownian motion. 

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. 

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... 

In other words, the lower the mass of the particle, the higher its velocity, because the average energy of any particle at a given temperature is constant, kT. A dispersed particle is always in random thermal motion (Brownian motion) due to coUisions with other particles and with the walls of the container (4). If the particles coUide with enough energy and are not well dispersed, they will coagulate or flocculate. 

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. 

Stokes diameter is defined as the diameter of a sphere having the same density and the same velocity as the particle in a fluid of the same density and viscosity settling under laminar flow conditions. Correction for deviation from Stokes law may be necessary at the large end of the size range. Sedimentation methods are limited to sizes above a [Lm due to the onset of thermal diffusion (Brownian motion) at smaller sizes. 

Fumes are typically formed by processes such as sublimation, condensation, or combustion, generally at relatively high temperatures. They range in particle size from less than 0.1 [Lm to 1 [Lm. Similar to smokes, they settle very slowly and exhibit strong brownian motion. 

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