Estimating the Normalized Polarizability of a Dusty Medium by Using Elliptic Integrals

Abstract

An expression is developed to estimate the normalized polarizability of a dusty medium by taking into account the geometry factor of dust particles, the dust dielectric constant, and the probability of dust particles' axial ratios. This normalized polarizability reflects the overall impact of factors affecting the dusty medium's dielectric constant. The study assumes that the dust particles are ellipsoidal in shape with specific dimensions suggested by previous researchers. Elliptical integrals are used to determine the geometry factor of the dusty medium based on the distribution of axial ratios of the ellipsoidal dust particles. The Maxwell-Granett mixture model is utilized to determine the dusty medium's dielectric constant. Understanding the dielectric constant and particle geometry factor is crucial for effectively utilizing this model. The relationships between the geometry factors on the different semi-axis of the ellipsoidal dust particles are examined, and their respective domains are identified, along with an empirical relation connecting them. Numerical values are provided for the normalized polarizability at various frequencies within different frequency bands.