Diffusion colloidal particles

This model has been successful in describing flux decline during dead-end filtration of particulate suspensions, but is not appropriate for application to crossflow filtration where the feed solution continuously recirculates [158]. Also, neither the occurrence of macromolecules and colloidal particles diffusion nor the influence of solute-solute and solute-membrane interactions on flux decline is considered in this model [42,59,159]. 

Contents indude contaminant vapors, adherence of Squids to "Water-dry" and "Water-wet" soil particles, contaminants in pore spaces, floating contaminants, dissolved contaminants, contaminants sorbed onto colloidal particles, diffusion into mineral grains or rock, contaminants sorbed onto or into soil microbiota, and fractured or karstic limestone. 

Schwartz (1962) proposed a model with a tightly bound layer of adsorbed counterions on the sphere surface to explain the high permittivity increment found (hundreds of 8q) in a suspension of colloidal particles. Diffusion, and not migration, may govern ionic motion in a double layer. Diffusion processes are not necessarily exponential, but as an... 

As a colloidal particle diffuses or sediments through a solution containing nonadsorbing polymer chains, one may naively expect that the friction experienced by the particle is set by the bulk viscosity. In practice, it is smaller. An analysis of the... 

In this case the colloid particle diffusion contribution is small and only 4% of the total. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Ohshima, H Kondo, T, Electrophoretic Mobility and Donnan Potential of a Large Colloidal Particle with a Surface Charge Layer, Journal of Colloid and Interface Science 116, 305, 1987. O Neil, GA Torkelson, JM, Modeling Insight into the Diffusion-Limited Cause of the Gel Effect in Free Radical Polymerization, Macromolecules 32,411, 1999. 

The rate of MV formation was also dependent on pH. The bimolecular rate constant, as calculated from the first order rate constant of the MV build-up and the concentration of colloidal particles, was substantially smaller than expected for a diffusion controlled reaction Eq. (10). The electrochemical rate constant k Eq. (9) which largely determines the rate of reaction was calculated using a diffusion coefficient of of 10 cm s A plot of log k vs. pH is shown in Fig. 24. 

In the pulse radiolysis studies on the reaction of MV with TiOj, the sol contained propanol-2 or formate and methyl viologen, MV Ionizing radiation produces reducing organic radicals, i.e. (CH3)2COH or C02 , respectively, and these radicals react rapidly with MV to form MV. The reaction of MV with the colloidal particles was then followed by recording the 600 nm absorption of MV . The rate of reaction was found to be slower than predicted for a diffusion controlled reaction. 

Pulse radiolysis studies showed that the rate of the reaction of MV with a-Fc203, in which an electron is transferred to the colloidal particles, is slower than predicted for a diffusion controlled reaction. For pH > 8, the reaction is incomplete as the reverse reaction Fe203 - - - Fe203 - - MV takes place more efficiently... 

Routh and Russel [10] proposed a dimensionless Peclet number to gauge the balance between the two dominant processes controlling the uniformity of drying of a colloidal dispersion layer evaporation of solvent from the air interface, which serves to concentrate particles at the surface, and particle diffusion which serves to equilibrate the concentration across the depth of the layer. The Peclet number, Pe is defined for a film of initial thickness H with an evaporation rate E (units of velocity) as HE/D0, where D0 = kBT/6jT ir- the Stokes-Einstein diffusion coefficient for the particles in the colloid. Here, r is the particle radius, p is the viscosity of the continuous phase, T is the absolute temperature and kB is the Boltzmann constant. When Pe 1, evaporation dominates and particles concentrate near the surface and a skin forms, Figure 2.3.5, lower left. Conversely, when Pe l, diffusion dominates and a more uniform distribution of particles is expected, Figure 2.3.5, upper left. 

Most descriptions of the dynamics of molecular or particle motion in solution require a knowledge of the frictional properties of the system. This is especially true for polymer solutions, colloidal suspensions, molecular transport processes, and biomolecular conformational changes. Particle friction also plays an important role in the calculation of diffusion-influenced reaction rates, which will be discussed later. Solvent multiparticle collision dynamics, in conjunction with molecular dynamics of solute particles, provides a means to study such systems. In this section we show how the frictional properties and hydrodynamic interactions among solute or colloidal particles can be studied using hybrid MPC-MD schemes. 

If the electric field E is applied to a system of colloidal particles in a closed cuvette where no streaming of the liquid can occur, the particles will move with velocity v. This phenomenon is termed electrophoresis. The force acting on a spherical colloidal particle with radius r in the electric field E is 4jrerE02 (for simplicity, the potential in the diffuse electric layer is identified with the electrokinetic potential). The resistance of the medium is given by the Stokes equation (2.6.2) and equals 6jtr]r. At a steady state of motion these two forces are equal and, to a first approximation, the electrophoretic mobility v/E is... 

For small colloidal particles, which are subject to random Brownian motion, a stochastic approach is more appropriate. These methods are based on the formulation and solution of the diffusion equation in a force field, in the presence of convection... 

In any case, exceptions to the FIAM have been pointed out [2,11,38,44,74,76,78]. For example, the uptake has been shown to depend on the Cj M or rMI (e.g. in the case of siderophores [11] or hydrophobic complexes [43,50]), rather than on the free c M. Several authors [11,12,15] showed that a scheme taking into account the kinetics of parallel transfer of M from several solution complexes to the internalisation transporter ( ligand exchange ) can lead to exceptions to the FIAM, even if there is no diffusion limitation. Adsorption equilibrium has been assumed in all the models discussed so far in this chapter, and the consideration of adsorption kinetics is kept for Section 4. Within the framework of the usual hypotheses in this Section 3, we would expect that the FIAM is less likely to apply for larger radii and smaller diffusion coefficients (perhaps arising from D due to the labile complexation of M with a large macromolecule or a colloid particle, see Section 3.3). 

Photon correlation spectroscopy (PCS) has been used extensively for the sizing of submicrometer particles and is now the accepted technique in most sizing determinations. PCS is based on the Brownian motion that colloidal particles undergo, where they are in constant, random motion due to the bombardment of solvent (or gas) molecules surrounding them. The time dependence of the fluctuations in intensity of scattered light from particles undergoing Brownian motion is a function of the size of the particles. Smaller particles move more rapidly than larger ones and the amount of movement is defined by the diffusion coefficient or translational diffusion coefficient, which can be related to size by the Stokes-Einstein equation, as described by... 

Relaxation studies have shown that the attachment of an ion to a surface is very fast, but the establishment of equilibrium in wel1-dispersed suspensions of colloidal particles is much slower. Adsorption of cations by hydrous oxides may approach equilibrium within a matter of minutes in some systems (39-40). However, cation and anion sorption processes often exhibit a rapid initial stage of adsorption that is followed by a much slower rate of uptake (24,41-43). Several studies of short-term isotopic exchange of phosphate ions between aqueous solutions and oxide surfaces have demonstrated that the kinetics of phosphate desorption are very slow (43-45). Numerous hypotheses have been suggested for this slow attainment of equilibrium including 1) the formation of binuclear complexes on the surface (44) 2) dynamic particle-particle interactions in which an adsorbing ion enhances contact adhesion between particles (43,45-46) 3) diffusion of ions into adsorbents (47) and 4) surface precipitation (48-50). 

Smoluchowski, who worked on the rate of coagulation of colloidal particles, was a pioneer in the development of the theory of diffusion-controlled reactions. His theory is based on the assumption that the probability of reaction is equal to 1 when A and B are at the distance of closest approach (Rc) ( absorbing boundary condition ), which corresponds to an infinite value of the intrinsic rate constant kR. The rate constant k for the dissociation of the encounter pair can thus be ignored. As a result of this boundary condition, the concentration of B is equal to zero on the surface of a sphere of radius Rc, and consequently, there is a concentration gradient of B. The rate constant for reaction k (t) can be obtained from the flux of B, in the concentration gradient, through the surface of contact with A. This flux depends on the radial distribution function of B, p(r, t), which is a solution of Fick s equation... 

Particles of a size of less than 2 turn are of particular interest in Process Engineering because of their large specific surface and colloidal properties, as discussed in Section 5.2. The diffusive velocities of such particles are significant in comparison with their settling velocities. Provided that the particles scatter light, dynamic light scattering techniques, such as photon correlation spectroscopy (PCS), may be used to provide information about particle diffusion. 

The literature suggests that the toxic effects of Thorotrast are due to the alpha radiation effects of thorium and not to the chemical effects of thorium or of the colloid (Faber 1973 BEIR IV 1988 Taylor et al. 1986 Wesch et al. 1983). Wesch et al. (1983) injected Thorotrast enriched with thorium-230 into rats and found a linear relationship between radiation level and tumor incidence. At a constant radioactive level, an increase in the injected colloidal volume had little influence on the number of liver tumors, but resulted in a decrease in tumor appearance time and, therefore, a decrease in lifespan. The larger colloidal volume may result in a more diffuse organ dose and a less "hot spot" distribution. Injection of the nonradioactive colloid resulted in no appreciable incidence of liver tumors. It is not known whether the colloidal particles induce the liver tumors when given in... 

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