Padé approximations for identification of air bubble volume from temperature- or frequency-dependent permittivity of a two-component mixture

Abstract

The article presents a numerical method developed for identification of information about structural parameters of a two-component mixture from effective complex permittivity measurements. The identification is based on the reconstruction of the spectral function in the analytic Stieltjes representation of the effective permittivity using Padé approximation. The spectral function contains all information about the microgeometry of the mixture, it is used to calculate volume fractions of the components in the mixture. Padé approximation is derived from a constrained minimization problem. Numerical results of recovering volume fraction of air in mixtures of air prolate and oblate spheroidal inclusions in water and in ethanol show good agreement of theoretical and predicted values. The proposed method can be used for estimating volume fractions and other structural parameters using the effective complex permittivity of two-component composite materials.

Keywords:

• Spectral representation
• Effective complex permittivity
• Two-component composite
• Ellipsoidal inclusion
• Padé approximations

Mathematics Subject Classifications::

• 41A20
• 45Q05
• 78A48

Acknowledgement

This work was supported by NSF grants DMS-0508901 and DMS-0411035.