Physical properties Brownian motion

Behavior. Diffusion, Brownian motion, electrophoresis, osmosis, rheology, mechanics, and optical and electrical properties are among the general physical properties and phenomena that are primarily important in coUoidal systems (21,24—27). Of course, chemical reactivity and adsorption often play important, if not dominant, roles. Any physical and chemical feature may ultimately govern a specific industrial process and determine final product characteristics. 

Equation (17) indicates that the entire distribution may be determined if one parameter, av, is known as a function of the physical properties of the system and the operating variables. It is constant for a particular system under constant operating conditions. This equation has been checked in a batch system of hydrosols coagulating in Brownian motion, where a changes with time due to coalescence and breakup of particles, and in a liquid-liquid dispersion, in which av is not a function of time (B4, G5). The agreement in both cases is good. The deviation in Fig. 2 probably results from the distortion of the bubbles from spherical shape and a departure from random collisions, coalescence, and breakup of bubbles. 

Throughout this section, we will use the notation X (t),..., X t) to denote a unspecified set of L Markov diffusion processes when discussing mathematical properties that are unrelated to the physics of constrained Brownian motion, or that are not specific to a particular set of variables. The variables refer specifically to soft coordinates, generalized coordinates for a system of N point particles, and Cartesian particle positions, respectively. The generic variables X, ..., X will be indexed by integer variables a, p,... = 1,...,L. 

Chemical parameters determine the surface characteristics of the suspended colloids, the concentration of the coagulant and its effects upon the surface properties of the destabilized particles, and the influence of other constituents of the ionic medium upon the coagulant and the colloids. The extent of the chemical and physical interactions between the colloidal phase and the solution phase determines the relative stability of the suspended colloids. One speaks of stable suspensions when all collisions between the colloids induced by Brownian motion or by velocity gradients are completely elastic the colloidal particles continue their... 

The majority of the different chemical and physical properties, as well as the morphology of microemulsions, is determined mostly by the micro-Brownian motions of its components. Such motions cover a very wide spectrum of relaxation times ranging from tens of seconds to a few picoseconds. Given the complexity of the chemical makeup of microemulsions, there are many various kinetic units in the system. Depending on their nature, the dynamic processes in the microemulsions can be classified into three types ... 

Wc note that P E,t) must have the property that i Efi) = 0 and P(Eyt) —> 1 as > oo. H. A. Kramers, Physics 7,284 (1940), has given an approximate solution to this problem based on a simplified analogy to a model for brownian motion in one dimension. 

In looking at the various physical properties of these cations (cf. Table 1) one realizes especially the differences in size, which manifest themselves clearly in energy parameters. However, the effective sizes of the solvated ions — i. e. the Stokes radii — apart from showing a reversed order do not differ greatly. Any simple model based on Brownian motion of totally solvated metal ions under the influence of an electric field gradient could not explain pronounced specificities of electric transport across membranes. In realizing this fact physiologists proposed the idea of a carrier, which via its peculiar molecular architecture could specifically interact with an ion of a... 

Many macroscopic phenomena of colloidal suspensions arc related to the light scattering and the Brownian motion of the single particles. Both properties depend largely on particle size they are, therefore, frequently employed for the characterisation of particle systems (cf. previous chapter). Additionally, the small size of colloids enhances the significance of the interface to the particles physical behaviour. The interfacial properties additionally affect the interaction between particles and are, thus, cmcial for the macroscopic suspension behaviour (e.g. stability). A particular characteristic of interfaces is the electric double layer (EDL), which camiot be ignored in most situations. Its formation and sttucture is closely related to dissolved ionic species and their interaction with the particle surface (e.g. adsorption, precipitation). Last but not least, the interfacial properties can be affected by the solubility behaviour of the particle phase. 

Albert Einstein (1879-1955). .. was a German-bom theoretical physicist who is mainly renowned for his special theory of relativity and its extension to the general theory of relativity. In addition to this, he worked on statistical mechanics and quantum theory and investigated the thermal properties of light. At the beginning of his scientific career he also set important landmarks for colloid science. This applies particularly to his explanation of Brownian motion, but is also valid for the calculation of suspension viscosity as well as his theory of critical opalescence. In 1921, he was given the Nobel Prize in Physics Tor his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect . 

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