Particle mobility, determination

Figure 6. Electrical transient from LC colloid corresponding to the optical transient in Figure 5. Solid line is based on calculations using an estimate of ionic mobility and the particle mobilities determined by optical transients. (Reproduced, with permission, from Ref. 29.)...

The angle of repose is defined as the angle between a line of repose of loose material and a horizontal plane. Its value depends on the magnitude of friction and adhesion between particles and determines the mobility of loose solids, which is a critical parameter in designing conical discharge and feeding nozzles and in... 

The impact strength increases almost linearly with gel content and thus with the degree of crosslinking (17). Figure 9.3 shows the increase of the molecular mobility with the impact strength for ABS. For HIPS it is claimed that the situation is quite similar. The molecular mobility of the soft phase particles is determined by nuclear magnetic-resonance spectroscopy relaxation measurements (16). 

Electrophoretic mobilities of the alumina particles were determined for the same conditions as were used to obtain the adsorption isotherms. For this purpose, a sample of the alumina suspension was transferred to the electrophoresis cell for measurement of the electrophoretic mobilities. A Zeta-Meter was used for this part of the program. 

Model particle mobility has been determinated with the Tiselius method (Tiselius, 1937, 1938). This method also allows the integration of the mobility of a large number of particles even if the refractive index is very close to that of the electrolyte medium, allowing to minimize the experimental errors inherent to the classical microelectrophoretic techniques. The electrophoretic mobilities will not be transformed into surface charges because the theoretical relationship between these parameters is highly dependant on the particle radius of curvature and the electrolyte concentration in the vicinity of the particle (Hunter and Wright, 1971). For both methods, the analytical error falls below 5 %, however, it increases up to 10 % for natural composite samples and/or low mobilities. 

Figure 4. Experimental setup for determination of particle mobility using both optical and electrical transients (10).

Features of PEPT of particular benefit to engineering studies include the fact that the actual particles of interest may be used as tracers, rather than dissimilar materials of unknown behaviour, and that y-rays are sufficiently penetrating that location is unimpaired by the presence of metal walls, for example. In recent developments, the minimum size of particles which can be tracked has been reduced to approximately 60 pm. It is now possible to track multiple particles, to determine particle rotation and to track motion within real industrial equipment by use of a mobile modular positron camera. These developments are described later. 

In the theory of diffusion in liquids, the mobility of a Brownian particle is determined using Stokes s law. Consequently,... 

Electrophoresis of nonconducting colloidal particles has been reviewed in this chapter. One important parameter determining the electrophoretic velocity of a particle is the ratio of the double layer thickness to the particle dimension. This leads to Smoluchowski s equation and Huckel s prediction for the particle mobility at the two extrema of the ratio when deformation of the double layer is negligible. Distortion of the ion cloud arising from application of the external electric field becomes significant for high zeta potential. An opposite electric field is therefore induced in the deformed double layer so as to retard the particle s migration. 

If the particle mobility is known, it is easy to determine the electric force acting on the particle, provided the field strength is also known. However, the field strength may not be constant but may have some spatial or temporal distribution, that is, ft = f[x,y,z,t). In addition, q may vary from particle to particle and may vary on a single particle with time in a discontinuous, stochastic manner. Thus, except for quite simple cases, it is exceedingly difficult to predict particle motion in an electric field with accuracy. 

Baker pioneered direct measurements of the onset of particle mobility on substrates using controlled atmosphere electron microscopy (17). He has pointed out the close relationship between the onset of particle motion as determined in his studies and the Tammann temperature (18). It is important to establish whether melting temperature decreases monotonically with particle size as indicated by the data of Buffat and Borel (7) or is equal to the Tammann temperature as hypothesized by Baker (18). 

A scanning mobility particle sizer (SMPS) was applied to analyze nanoparticles [2][4]. Size distributions and total number concentrations (TNC) of particles in the range from 0.01-0.7 pm are determined by analysis of particle mobility. An impactor with a cut-off size of 1 pm is used to withdraw the coarse particle fraction. Exhaust gas is taken with a probe, which is also fed with particle free air. The resulting dilution factor is adjusted by the flow rate of the diluting air and the total flow. To prevent condensation of water onto the particle surface, the dilution factor is chosen high enough, to achieve a dew point below ambient temperature. The analytical set-up is shown in Figure I. 

As shown earlier, the direct conversion from retention time to particle diameter values [Eq. (1)] requires that the correction factor y is predicted or experimentally estimated. It is known that, in GrFFF, y can be influenced by either hydrodynamic or other effects as those due to the mobile phase [8] and the channel walls nature [9]. All of these effects can influence particle size determination by GrFFF. 

Electrical transients (12) can also be used to evaluate particle mobilities in special circumstances. Charged particles, their counterions and other excess ions present in the suspending fluid contribute to the electrical current. When the concentration of excess ions is very low compared to the concentration of counterions, it is sometimes possible to determine the current contributed by particles versus that contributed by ions. Ionic concentrations define the extent of double layers in colloids. Transient and AC conductivities can be related most directly to the ionic concentrations and mobilities. But, again, the measurements in low conductivity fluids have to be performed in planar cells with narrow electrode spacings in order to ensure well defined electric fields. 

Monodispersed polystyrene latex particles 1.049 pm in diameter (std dev = 0.0587 pm) were captured utilizing a radial flow parallel-plate mobility analyzer (Tardos et. al. 1984). The mobility of the particles was determined from measurements of the collection efficiency of the analyzer by sampling particle number density for the inlet and exit flows (Figure 3-10). The principle was fundamentally that of electrostatic precipitation. The particles were charged by a corona discharge. The particles capture efficiency in the mobility... 

The lipoproteins are macromolecules with varying complexes of lipids where the hydrophobic lipid portions—cholesterol esters and triglycerides—are localized at the core of the molecules. The amphipathic surface layers surrounding the core contain the apolipoproteins and phospholipids. The lipoproteins vary in size, density, lipid composition, and apolipoprotein constituents, and they ean be classihed by size, the flotation rate determined by ultracentrifugation, or their electrophoretic mobilities. Put simply, the density of a lipoprotein particle is determined by the relative amounts of lipid and protein contained in the particle. Chylomicrons and very low density lipoproteins have the highest lipid content and the lowest protein content thus, very excessive amounts of chylomicrons float on the surface of plasma. In descending order of size, the broad lipoprotein fractions (with their electrophoretic mobility) are... 

That the electrophoretic mobility is independent of the nature and concentration of the above ions, and depends solely on pH, is almost conclusive proof that the charge on L-myosin particles is determined exclusively by the binding (and release) of H ions. This means that the other ions, including sodium and potassium, are not bound, but are free in solution as gegenions. The agreement between the alkali content of salt-free myosin gel and the amount of protons given up on the alkaline side of the I.P. leads to the same conclusion (Hollwede and Weber, 1938) and finally, the pH-mobility curve found by Erdos and Snellman (1948)... 

The electrophoretic mobility of the particles was determined to confirm the buildup of negative charge on the colloid. In these measurements, the potential difference across the liquid liquid interface was controlled by potential-determining ions. It was shown that the charge on the colloid was dependent on the concentration of the electron-donor DCMFc. The results clearly showed that the metal colloid was charged in the two-phase process. 

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