Polydisperse suspensions particle size measurements

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]. 

The particle size analysis techniques outlined earlier show promise in the measurement of polydispersed particle suspensions. The asumption of Gaussian instrumental spreading function is valid except when the chromatograms of standard latices are appreciably skewed. Calc ll.ation of diameter averages indicate a fair degree of insensitivity to the value of the extinction coefficient. 

An approximate mathematical correction of a measured polydisperse size distribution has been carried out using a deconvolution technique [170]. This was verified with suspension droplets the advantage being that it can measure such distributions the disadvantages being that the correlation between particle size and velocity is lost and at least 5,000 data points are required for deconvolution [171]... 

For a monodisperse suspension the decay rate can be described by a first order rate equation. For a polydisperse suspension the decay rate is a sum of exponentials. Measurement of the decay rate permits computation of particle size [338]. 

The above equations can be used to deduce the properties of the suspension from observations of the front speeds, typically the one separating the clarified layer from the suspension. For example, knowing the fall speed (Eq. 5.4.6), we can determine the effective particle size if the particle density has been found independently. The extension of the results to infinitely dilute systems containing particles of two or more sizes (polydisperse systems) is straightforward and will not be discussed further here. It may only be mentioned that with different fall speeds there will be as many distinct downward-moving fronts as there are particle sizes. From measurements of these front speeds the particle sizes can be determined as for the monodisperse system. 

The bimodal model has also been applied to polydisperse suspensions (Probstein et al. 1994), which in practice generally have particle sizes ranging from the submicrometer to hundreds of micrometers. In order to apply the bimodal model to a suspension with a continuous size distribution, a rational procedure is required for the separation of the distribution into fine and coarse fractions. Such a procedure has not been developed so that an inverse method had to be used wherein the separating size was selected which resulted in the best agreement with the measured viscosity. Again, however, the relatively small fraction of colloidal size particles was identified as the principal agent that acts independently of the rest of the system and characterizes the shear thinning nature of the suspension viscosity. 

Using the formulas (8.147) and (8.148), it is possible to determine experimentally the properties of infinite diluted suspensions containing same-sized particles (a monodisperse suspension), for example, the mass concentration and size of particles. If the suspension contains particles of different sizes (a polydisperse suspension), then dividing the entire spectrum of particle sizes from amin to amax into a finite number of fractions, it is possible to carry out the argumentation stated above for each fraction, and to determine the laws of motion for the corresponding discontinuity surfaces. Measuring the velocities of discontinuity surfaces in an experiment, it is possible to determine the characteristics of each fraction and thereby the size distribution of particles. 

It is probably the most widespread method it is based on the direct observation, with a suitable magnifying optics, of individual particles in their electrophoretic motion. In fact, it is not the particle what is seen but its scattering pattern when illuminated in a dark background field. It allows direct observation of particles in their medium and the observer can in principle select a range of sizes to be tracked in case of polydispersed suspensions [29,30], As the observations are possible only if the suspensions are dilute enough, even moderately unstable systems can be measured, as aggregation times are expectedly large for such dilute systems. 

The experiment of Kumar et al (2000) consists of continuously feeding the polydisperse suspension through a vertical column in the well-mixed state and allowing the relative motion of particles to exit at an outlet located at a suitable distance from the point of entry. The relative motion of particles will have established a steady state, spatially uniform distribution of particles with an exit number density that can be measured by a device such as a Coulter counter. The population density, / (z, v) in vertical coordinate z and particle size described by volume v, satisfies the population balance equation... 

For our experiments we used a charge stabilized suspension of polystyrene spheres dispersed in ultrapure water (Batch No. PS-F-3390, Berlin Microparticles GmbH Germany). The diameter was determined by electron microscopy to be 590 nm. The size polydispersity was determined to be 5.8%. The particles are stabilized with CCX)H- and HSOq-groups and the effective charge was measured by conductivity to be Z = 3(XX) 100. For diluting of the stock solution to a definite volume fraction deionized water of a MilliQ water system was used. To adjust the salt concentration of the suspension NaCl was added to screen the interaction of the particles (typically 1 mM). 

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