(468e) Representation of a Continuous Particle Size Distribution Using a New Polydisperse Kinetic Theory

Flows of polydisperse particles are common in nature as well as in industrial applications. In the past, kinetic theories for monodisperse systems have not only been successful in predicting the rapid flow of particles but have also been extended to gas-solid systems. Previous kinetic theories for polydisperse systems have been based on the assumptions of a Maxwellian velocity distribution or an equipartition of energy. Recently, a kinetic theory for an s-component mixture of inelastic, smooth hard disks (2D) and spheres (3D) has been derived that rigorously incorporates the non-Maxwellian and non-equipartition (Garzó, Dufty, and Hrenya, 2007 and Garzó, Hrenya & Dufty, 2007) effects. It is applicable to wide range of restitution coefficients and a wide range of concentrations (dilute and moderately dense). At the center of the current effort is using this new theory to represent a continuous size distribution. Two questions are considered: (i) What technique should be used to choose discrete particle sizes to represent the continuous size distribution, and (ii) How many discrete sizes are appropriate for an accurate representation? Regarding the first question, a representation of a continuous particle size distribution (PSD) using discrete species is attempted via the method of moments. To answer the second question, all transport coefficients are evaluated using an increasing number (s) of discrete species. The results show that s = 3 (three discrete particle sizes chosen according to the method of moments) provides an accurate description of a continuous PSD for both Gaussian and lognormal distributions.

References:

Garzó, V., Dufty, J. & Hrenya, C. M. (2007) Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport. Physical Review E, 76, art. no. 031303.

Garzó, V., Hrenya, C. M. and Dufty, J. W. (2007) Enskog theory for polydisperse granular mixtures. II. Sonine polynomial approximation. Physical Review E, 76, art. no. 031304.