Derivation of Lichtenecker's Logarithmic Mixture Formula From Maxwell's Equations

Simpkin, Ray

doi:10.1109/tmtt.2010.2040406

Cited by 190 publications

(84 citation statements)

References 8 publications

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“…Another empirical relation is the Lichtenecker (L) or Lichtenecker-Rother equation (Lichtenecker 1926;Lichtenecker and Rother 1931;Heller 1945) which, as Simpkin (2010) showed, in fact, has a theoretical basis and can be derived from Maxwell's equations: while relatively common Newton (N) equation (Newton 1704;Kurtz and Ward 1936;Reis et al 2010) also has a theoretical foundation:…”

Section: Refractive Index Density and Viscosity Tuningmentioning

confidence: 99%

A review of solid–fluid selection options for optical-based measurements in single-phase liquid, two-phase liquid–liquid and multiphase solid–liquid flows

2017

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Experimental techniques based on optical measurement principles have experienced significant growth in recent decades. They are able to provide detailed information with high-spatiotemporal resolution on important scalar (e.g., temperature, concentration, and phase) and vector (e.g., velocity) fields in single-phase or multiphase flows, as well as interfacial characteristics in the latter, which has been instrumental to step-changes in our fundamental understanding of these flows, and the development and validation of advanced models with ever-improving predictive accuracy and reliability. Relevant techniques rely upon well-established optical methods such as direct photography, laser-induced fluorescence, laser Doppler velocimetry/phase Doppler anemometry, particle image/tracking velocimetry, and variants thereof. The accuracy of the resulting data depends on numerous factors including, importantly, the refractive indices of the solids and liquids used. The best results are obtained when the observational materials have closely matched refractive indices, including test-section walls, liquid phases, and any suspended particles. This paper reviews solid–liquid and solid–liquid–liquid refractive-index-matched systems employed in different fields, e.g., multiphase flows, turbomachinery, bio-fluid flows, with an emphasis on liquid–liquid systems. The refractive indices of various aqueous and organic phases found in the literature span the range 1.330–1.620 and 1.251–1.637, respectively, allowing the identification of appropriate combinations to match selected transparent or translucent plastics/polymers, glasses, or custom materials in single-phase liquid or multiphase liquid–liquid flow systems. In addition, the refractive indices of fluids can be further tuned with the use of additives, which also allows for the matching of important flow similarity parameters such as density and viscosity

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Section: Refractive Index Density and Viscosity Tuningmentioning

confidence: 99%

A review of solid–fluid selection options for optical-based measurements in single-phase liquid, two-phase liquid–liquid and multiphase solid–liquid flows

2017

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show abstract

“…As noted in [16], Leichtencker mixture formula is symmetric with respect to its constitutes thus: ε ε 2 = ( ε 1 ε 2 ) 1−α can be written as ε ε 1 = ( ε 2 ε 1 ) α . Based on above relations and the knowledge that biological tissues consist of water (composite 1) and organic material (composite 2), as described on [12], the relative permittivity of child biological tissues may be presented as:…”

Section: Methods: Derivation Of Formula For Calculation Of Permittivimentioning

confidence: 99%

“…Recently, a 2010 study [16] has confirmed that formula can be derived by applying Maxwell's equations and the principle of charge conservation to a mixture for which the spatial distribution of shapes and orientations of the components is randomly distributed.…”

Section: Methods: Derivation Of Formula For Calculation Of Permittivimentioning

confidence: 99%

Derivation of Electromagnetic Properties of Child Biological Tissues at Radio Frequencies

Ibrani

Ahma²,

Hamiti³

et al. 2011

PIER Letters

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Abstract-The knowledge of electromagnetic properties of biological tissues is required to assess the radio frequency energy deposition in children exposed to electromagnetic fields. The issue whether children should be considered a dosimetric sensitive group in comparison to adults, to which the confirmation of age-dependence of human tissue electromagnetic properties potentially may contribute remains debatable at scientific forums. This paper derives the formula for calculation of electromagnetic properties (permittivity and conductivity) of children tissues, as a function of height, weight, and age, respectively. By using the proposed formula, we have calculated and presented electromagnetic properties of the muscle, brain (gray matter) and skin for 1-year-old to 10-year-old children for 900 MHz, 1800 MHz and 2.4 GHz, at which frequencies most of radio frequency devices used by children operate. The trend over the age of child electromagnetic properties has been presented, and electromagnetic properties at different frequencies for the same child age have also been compared. For certain tissues, comparison between the children at various age and adult electromagnetic parameters has been given. A database with electromagnetic properties for children, of all ages, tissues and frequencies may be built up with the proposed approach. It will further advance research on the assessment of children exposure to electromagnetic fields. Formula can also be used for the determination of electromagnetic parameters for children with specific height and weight.

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“…(1)) and μ r (Eq. (2)) of well dispersed composite materials, 24,25 ln(ε composite ) = f ln(ε MnZn )…”

confidence: 99%

Heavily loaded ferrite-polymer composites to produce high refractive index materials at centimetre wavelengths

et al. 2013

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A cold-pressing technique has been developed for fabricating composites composed of a polytetrafluoroethylene-polymer matrix and a wide range of volume-fractions of MnZn-ferrite filler (0%–80%). The electromagnetic properties at centimetre wavelengths of all prepared composites exhibited good reproducibility, with the most heavily loaded composites possessing simultaneously high permittivity (180 ± 10) and permeability (23 ± 2). The natural logarithm of both the relative complex permittivity and permeability shows an approximately linear dependence with the volume fraction of ferrite. Thus, this simple method allows for the manufacture of bespoke materials required in the design and construction of devices based on the principles of transformation optics

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Derivation of Lichtenecker's Logarithmic Mixture Formula From Maxwell's Equations

Cited by 190 publications

References 8 publications

A review of solid–fluid selection options for optical-based measurements in single-phase liquid, two-phase liquid–liquid and multiphase solid–liquid flows

A review of solid–fluid selection options for optical-based measurements in single-phase liquid, two-phase liquid–liquid and multiphase solid–liquid flows

Derivation of Electromagnetic Properties of Child Biological Tissues at Radio Frequencies

Heavily loaded ferrite-polymer composites to produce high refractive index materials at centimetre wavelengths

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