Penetration depth of microwave into the mixture of goethite with graphite estimated by permittivity and conductivity

A study has been conducted to understand the penetration behavior of microwave into the mixture of goethite with carbon (C) aiming at providing an appropriate guidance to dehydrate the substances with hydroxides occasionally contained in industrial sludge. At first, it was observed that microwave could not sufficiently penetrate into the specimen with C/goethite molar ratios greater than 2, giving incomplete dehydration. To understand the penetration behavior of microwave, permittivity and conductivity were measured. Permittivity measurements were successfully made below 9 vol pct C. For carbon content greater than 8.56 vol pct C, the conductivity of the mixture abruptly increased by four orders of magnitude because of the occurrence of the conductivity percolation. Above 13.7 vol pct C close to an inflection point approximating 10 vol pct C, the mixture became sufficiently conductive. Transition from dielectric to conductive behavior occurred between 8.56 and 13.7 vol pct C. The Generalized Effective Medium approximation could satisfactorily express the variation of the conductivity values in the whole range of vol pct C measured. The penetration depth of microwave was determined by the above two measurements. It was found that penetration depth decreased with the increasing vol pct of C contained in the mixture specimen. Finally, guidance could be provided as for the blend ratio of C to treated material along with the size of a briquette or a pellet referring to the obtained relation between penetration depth and vol pct of C. Furthermore, it was proved that the numerical simulation was quite helpful to predict how microwave behaves in the mixture under given conditions.