Particle size, measurement motion

The terminal velocity in the case of fine particles is approached so quickly that in practical engineering calculations the settling is taken as a constant velocity motion and the acceleration period is neglected. Equation 7 can also be appHed to nonspherical particles if the particle size x is the equivalent Stokes diameter as deterrnined by sedimentation or elutriation methods of particle-size measurement. 

PCS measures the diffusion coefficient of particles in the size range between 3 nm and a few micrometres. Particle size measurements for particles and/or aggregates smaller than 1 pm were performed on a Malvern Photon Correlation Spectrometer (PCS) Autosizer 4700 (633 nm, 5 mW, He-Ne laser). It is essentuial to use a red laser due to the fluorescence spectra of the humic substances (Goldberg and Weiner (1989)). A round quartz cell was used and temperature adjusted to 25 C. The method measures the diffusion coefficient (Brownian motion) of particles and is limited to about 3 nm... 

Berg, S. Determination of particle size distribution by examining gravitational and centrifugal sedimentation to the pipett method and with divers. Symp. PSA, June 1958, Boston, ASTM STP 234 (1959), p. 143 - 171 /4/ Chung, H. S. Hogg, R. The effect of Brownian motion on particle size analysis by sedimentation. Powder Techn. 41 (1985) 3, p. 211 - 216 /5/ Allen, T. Sedimentation techniques of particle size measurement. Conf. PSA Sept. 1985, Bradford, Proceed, p. 24 - 45... 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

Information on particle size may be obtained from the sedimentation of particles in dilute suspensions. The use of pipette techniques can be rather tedious and care is required to ensure that measurements are sufficiently precise. Instruments such as X-ray or photo-sedimentometers serve to automate this method in a non-intrusive manner. The attenuation of a narrow collimated beam of radiation passing horizontally through a sample of suspension is related to the mass of solid material in the path of the beam. This attenuation can be monitored at a fixed height in the suspension, or can be monitored as the beam is raised at a known rate. This latter procedure serves to reduce the time required to obtain sufficient data from which the particle size distribution may be calculated. This technique is limited to the analysis of particles whose settling behaviour follows Stokes law, as discussed in Section 3.3.4, and to conditions where any diffusive motion of particles is negligible. 

A common method of assessing the relative importance of internal diffusion and point adsorption resistances is to measure, as a function of time, the uptake of adsorbent from a solution containing solid particles. Batch data of this type taken at different temperatures and particle sizes can usually be analyzed so as to establish the importance of internal resistances. However, some types of diffusion have relatively high activation energies so that the separation is complex. Also, in such methods care must be taken to ensure rapid motion of the fluid with respect to the particles, for example by stirring, in order to eliminate external diffusion... 

This section contains a general description of the principles by which the Coulter Model N4 Sub-Micron Particle Analyzer, used in this study to characterize artificial gas-in-water emulsions (see Section 10.4), determines sample particle size. The measuring principles are based on the theory of Brownian motion and photon correlation spectroscopy (ref. 464,465 see also Sections 10.2 and 10.4). 

In this chapter the thermal motion of dissolved macromolecules and dispersed colloidal particles will be considered, as will their motion under the influence of gravitational and centrifugal fields. Thermal motion manifests itself on the microscopic scale in the form of Brownian motion, and on the macroscopic scale in the forms of diffusion and osmosis. Gravity (or a centrifugal field) provides the driving force in sedimentation. Among the techniques for determining molecular or particle size and shape are those which involve the measurement of these simple properties. 

Applications of optical methods to study dilute colloidal dispersions subject to flow were pioneered by Mason and coworkers. These authors used simple turbidity measurements to follow the orientation dynamics of ellipsoidal particles during transient shear flow experiments [175,176], In addition, the superposition of shear and electric fields were studied. The goal of this work was to verify the predictions of theories predicting the orientation distributions of prolate and oblate particles, such as that discussed in section 7.2.I.2. This simple technique clearly demonstrated the phenomena of particle rotations within Jeffery orbits, as well as the effects of Brownian motion and particle size distributions. The method employed a parallel plate flow cell with the light sent down the velocity gradient axis. 

The effect of particle size and spinning of the NMR tube were studied for the latex state 13C-NMR of natural rubber latex fractionated by particle size [134], High-resolution spectrum was obtained by measurement without sample spinning. The diffusion constant of Brownian motion was found to be a dominant factor governing the intensity and halfwidth of the signals. As the particle size decreased and temperature of measurement was raised, the intensity of signals increased and was comparable to the theoretical value, which was observed by the addition of triethylene glycol as an internal standard. 

Photon correlation spectroscopy (PCS), also referred to as dynamic light scattering, is a technique that is used to measure particles in the size range of 1 -0.001 p,m. Unlike particle sizing by laser diffraction, the sample, dispersed in a diluent, is not circulated, stirred, or sonicated during the measurement. The technique is dependent upon a stable suspension of particles that are in constant random motion due to collisions with molecules of the suspending liquid. 

Adequate dispersion must be obtained for the measurement to be successful because the technique is based upon the Brownian motion of the particles in a liquid medium. If the particles should flocculate in the liquid, gravitational settling will occur, thereby removing the particles from the measurement zone in the sample cell. For this measurement to be successful, the refractive index of the material, both the real and the imaginary component, must be known. In the particle size regime where PCS can be employed, the refractive index has a very significant effect on the measured average particle size. 

Many excellent introductions to quasi-elastic light scattering can be found in the literature describing the theory and experimental technique (e.g. 3-6). The use of QELS to determine particle size is based on the measurement, via the autocorrelation of the time dependence of the scattered light, of the diffusion coefficients of suspended particles undergoing Brownian motion. The measured autocorrelation function, G<2>(t), is given by... 

It is not always easy to determine what procedure to follow in making a particle-size distribution. Obviously, if the particles are soluble in water or any other fluid, sedimentation procedures must be applied with caution. It is likewise clear that any sedimentation technique is markedly affected by the shape of the particles used, and that results are subject to interpretation. In other words, determinations depending upon sedimentation (and elutriation) are merely equivalent measures of spheres having the same rate of settling. Greatest reliance naturally applies to that size range whose motion is known to be specified by Stokes law. 

Solid particles are suspended within the gas of a protoplanetary disk and experience motions as a result of their interactions with the gas. These interactions depend on such factors as the particle size and local properties of the gas (pressure, density, and their respective gradients). An important measure of how a solid particle is affected by the gas is its stopping time, which is given by ... 

Eulerian equations for the dispersed phase may be derived by several means. A popular and simple way consists in volume filtering of the separate, local, instantaneous phase equations accounting for the inter-facial jump conditions [274]. Such an averaging approach may be restrictive, because particle sizes and particle distances have to be smaller than the smallest length scale of the turbulence. Besides, it does not account for the Random Uncorrelated Motion (RUM), which measures the deviation of particle velocities compared to the local mean velocity of the dispersed phase [280] (see section 10.1). In the present study, a statistical approach analogous to kinetic theory [265] is used to construct a probability density function (pdf) fp cp,Cp, which gives the local instantaneous probable num-... 

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. 

Heterodyne experiments measure a linear function of g(1) and therefore produce if111 data with improved signal-to-noise ratio due to removal of the errors 113 introduced by the square root in Eq. (50). However, particle sizing applications rarely employ this approach because of experimental difficulties 113,50] and the sensitivity of heterodyne experiments to collective particle motions. 

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). 

Transient turbidity is an optical technique for measuring the size of magnetic particles [63,64], It does this by aligning particles in an electric field, removing the field, and following their return to random orientation induced by Brownian motion. Their relaxation is measured by turbidity and this can be related to particle size distribution if assumptions are made... 

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