Suspensions, monodisperse, particle size measurements

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. 

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. 

For the measurements, suspensions of spherical quasi monodisperse particles in distilled water are used (particle sizes specified by the manufacturer (Xspec) 522, 214, 70.6, 39.63, and 19.98 pm). The measurements are carried out in a cuvette with a measurement length of 10 mm. The movement of the particles through the light beam is ensured by a stirring rod in the cuvette. 

In colloidal suspensions, the sound propagation is typically governed by the acoustophoretic motion of particles. For monodisperse spheroids that do not deviate too much from spherical shape (aspect ratio <10/1), the attenuation spectrum essentially reflects the volume specific surface area of the particles (Babick and Richter 2006). Similar results would probably be obtained for any convex particle shape. For particle aggregates, the inner structure is decisive. Regarding the type of quantity, acoustically measured size distributions are ideally volume weighted distributions (see comments in Sect. 2.2). 

There the relation is shdwn between the relative solid concentration and the sedimentation path for quartz particles in water. The measuring plane is in the middle of the vessel. After the sedimentation time for a particle of 0.1 pm size has passed, concentration distributions are found, which only near the measuring plane and also near the suspension level are described with sufficient accuracy by the approximation equation. As shown in /6/, the latter, however, is only applicable, if the particles are greater than 0.1 pm. If only the mechanisms in the middle of a sufficiently big sedimentation vessel are considered, then the theory gives the following expression for the measured apparent distributions of monodisperse particles ... 

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