For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev–Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.

A Zakharov–Kuznetsov (ZK) equation, a modified ZK (mZK) equation, and a coupled ZK (cZK) equation for small but finite amplitude dust acoustic waves in a magnetized two-ion-temperature dusty plasma with dust size distribution have been investigated in this paper. The variations of the linear dispersion relation and group velocity, nonlinear solitary wave amplitude, and width with an arbitrary dust size distribution function are studied numerically. We conclude that they all increase as the total number density of dust grains increases, and they are greater for unusual dusty plasma (the number density of larger dust grains is greater than that of smaller dust grains) than that of usual dusty plasma (the number density of smaller dust grains is greater than that of larger dust grains). It is noted that the frequency of the linear wave increases as the wave number along the magnetic direction increases. Furthermore, the width of the nonlinear waves increases but its amplitude decreases as the wave number along the magnetic direction increases.

Microwave technology has a potential application in the extraction of zinc from sulphide ores, knowledge of the dielectric properties of these ores plays a major role in the microwave design and simulation for any process. The dielectric properties of zinc sulfide concentrate for two different apparent densities-1.54 and 1.63 g/cm3-have been measured by using the resonance cavity perturbation technique at 915 and 2450 MHz during the roasting process for the temperature ranging from room temperature to 850 °C. The variations of dielectric constant, the dielectric loss factor, the dielectric loss tangent and the penetration depth with the temperature, frequency and apparent density have been investigated numerically. The results indicate that the dielectric constant increases as the temperature increases and temperature has a pivotal effect on the dielectric constant, while the dielectric loss factor has a complicated change and all of the temperature, frequency and apparent density have a significant impact to dielectric loss factor. Zinc sulfide concentrate is high loss material from 450 to 800 °C on the basis of theoretical analyses of dielectric loss tangent and penetration depth, its ability of absorbing microwave energy would be enhanced by increasing the apparent density as well. The experimental results also have proved that zinc sulfide concentrate is easy to be heated by microwave energy from 450 to 800 °C. In addition, the experimental date of dielectric constant and loss factor can be fitted perfectly by Boltzmann model and Gauss model, respectively