Separation factor-particle size modeling

A number of publications (6-10) have demonstrated that the size separation mechanism In HDC can be described by the parallel capillary model for the bed Interstices. The relevant expression for the separation factor, Rj., (ratio of eluant tracer to particle mean residence times) Is given by. 

A presentation for a theoretical model of constant rate and falling rate drying is available in work by Yang et al. (19) in a study of a vibro-separator. Major factors discussed include the role of vacuum level, air bleeding rate, the critical moisture content, vibratory energy transfer, and particle size. The modeled drying rates are compared to experimental values. 

Table 5 summarizes the effect of operating parameters (particle size, solution concentration, separation factor, stirring rate, resin exchange capacity, and temperature) on ion exchange kinetics described by these different models in batch reactors. 

As a second benchmark problem, the motion of spherical and elliptical particles are analyzed in a channel with a hurdle at the middle. The results for spherical (Fig. 6) and elliptical particles (Fig. 7) are shown in the figures below. The rotation of the particles can also be realized. The particles realesed from 10 pm follows a streamline which is different than that of 10 pm after the hurdle due to hydrodynamic interaction of the particles at the comers and within the hurdle section. As the released location increases, this issue diminishes. Although, it is not simulated, the interaction of the particles with the comers has size dependence. So, the location of the particles after the hurdle depends on the size of the particle. BEM has clearly the ability to model this hydrodynamic interaction with the wall without any need for correction factor. The dependence of the equilibrium position after the hurdle on particle size is the key ingredient for the microfluidic devices for hydrodynamic separation of bioparticles. With the ability of BEM, this issue can be explored in details to come up with efficient microfluidics bioparticle separators. 

The form factor and structure factor can often be separated. Then we can obtain information on the particle size and shape from P q) using appropriate models. Modelling is necessary because the density distribution within a particle cannot be obtained directly due to the phase problem, i.e. information on the phase shift of waves upon diffraction is lost because intensities are measured. The structure factor is related by a Fourier transformation to the radial distribution function, g(r) ... 

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