Change In Effective Conductivity Research Articles

Low-Frequency Electrical Conductivity of Trabecular Bone: Insights from In Silico Modeling

Background: The electrical conductivity of trabecular bone at 100 kHz has recently been reported as a good predictor of bone volume fraction. However, quantifying its relationship with free water (or physiological solution) content and the conductivities of its constituents is still difficult. Methods: In this contribution, in silico models inspired by microCT images of trabecular bovine samples were used to build realistic geometries. The finite element method was applied to solve the electrical problem and to robustly fit the conductivity of the constituents to the literature data. The obtained effective electrical conductivity was compared with the Bruggeman three-medium mixture model using a physiological solution, bone marrow and a bone matrix. Results: The values for the physiological solution plus bone marrow (together as one material) and the bone matrix that best captured the bone volume fraction in the two-medium finite element model were σps+bm = 298.4 mS/m and σb = 21.0 mS/m, respectively. Additionally, relatively good results were obtained with the three-medium Bruggeman mixture model, with σbm= 103 mS/m, σb= 21.0 mS/m and σps= 1200 mS/m. Simple linear relationships between the proportions of constituents depending on bone volume fraction were tested. Degree of anisotropy and fractal dimension do not show detectable changes in effective conductivity. Conclusions: These results provided some useful findings for simulation purposes. First, a higher value for the electrical conductivity of bone marrow has to be used in order to obtain similar values to those of experimental published data. Second, anisotropy is not detectable with conductivity measurements for small trabecular samples (5 mm cube). Finally, the simulations presented here showed relatively good fitting of the Bruggeman mixture model, which would potentially account for the free water content and could rescale the model for whole-bone electrical simulations.

Effective thermal conductivity in BCC and FCC lattices for all volume fractions and conductivity ratios: Analyses by microstructural efficiency and morphology factor and analytic models

The effective thermal conductivity of composite materials is of great interest for thermal storage applications demanding rapid charge and discharge behaviour. Open cell porous metal foams filled with phase change material are one class of composite in which small changes in morphology lead to large changes in effective conductivity. Regular lattices can be easily built by additive manufacturing techniques, but are often used as simple analogues of composites materials with randomly distributed particles or irregular foams, that can thus be studied using computational techniques. Through procedural steady state simulation of heat transfer through unit cells, the impact of morphology on the thermal response of spheres upon BCC and FCC lattices is quantified. The indices of normalised effective thermal conductivity, microstructural efficiency and morphology factor are given for all volume fractions and conductivity ratio 10−4 to 104. Simple empirical models are developed and are compared to experimental data. Recommendations are made on the most optimal morphology for combinations of volume fraction and conductivity ratio.

Broadband Dielectric Properties of Ex Vivo Bovine Liver Tissue Characterized at Ablative Temperatures

To investigate the thermal and frequency dependence of dielectric properties of ex vivo liver tissue - relative permittivity and effective conductivity - over the frequency range 500 MHz to 6GHz and temperatures ranging from 20 to 130°C. We measured the dielectric properties of fresh ex vivo bovine liver tissue using the open-ended coaxial probe method (n = 15 samples). Numerical optimization techniques were utilized to obtain parametric models for characterizing changes in broadband dielectric properties as a function of temperature and thermal isoeffective dose. The effect of heating tissue at rates over the range 6.4-16.9°C/min was studied. The measured dielectric properties were used in simulations of microwave ablation to assess changes in simulated antenna return loss compared to experimental measurements. Across all frequencies, both relative permittivity and effective conductivity dropped sharply over the temperature range 89 - 107°C. Below 91°C, the slope of the effective conductivity changes from positive values at lower frequencies (0.5-1.64GHz) to negative values at higher frequencies (1.64-6GHz). The maximum achieved correlation values between transient reflection coefficients from measurements and simulations ranged between 0.83 - 0.89 and 0.68 - 0.91, respectively, when using temperature-dependent and thermal-dose dependent dielectric property parameterizations. We have presented experimental measurements and parametric models for characterizing changes in dielectric properties of bovine liver tissue at ablative temperatures. The presented dielectric property models will contribute to the development of ablation systems operating at frequencies other than 2.45GHz, as well as broadband techniques for monitoring growth of microwave ablation zones.

On the role of microgeometry in conductivity substitution

Conductivity substitution is the process of predicting the change in the effective electrical conductivity of a rock upon a change in conductivity of the mineral or fluid phase. Conductivity substitution is nonunique — only a range of conductivities can be predicted from knowledge of the initial effective conductivity, the porosity, and the initial and final compositions. The precise change depends strongly on the rock microstructure, which is seldom adequately known. Rigorous bounds on the change in effective conductivity upon changes in the phase conductivities for two-phase isotropic composites are used to gain insights into the roles of microgeometry and phase conductivity contrast. When the conductivity contrast between phases is high, the conductivity substitution predicted by Archie’s law corresponds approximately to the upper bound on the change of conductivity upon substitution. Inclusion modeling suggests that vuggy, highly tortuous, or partially disconnected pore space could account for conductivity changes smaller than those predicted by Archie’s law. Substitution behavior computed analytically for known microgeometries correlates with measures of microgeometry, including the fraction of connected fluid phase and variance of electric field strength in each phase. Comparison of the conductivity substitution bounds with brine-saturated sandstone data reveals that the position of measured data with respect to the conductivity substitution bounds can be indicative of the effective clay content. The bounds provide a template for better prediction of effective conductivity if we have at least some knowledge of the pore microstructure. Similarly, multiple conductivity measurements on the same rock might be used to extract more information about the rock and pore space properties than is possible with only a single measurement.

Effective Conductivity of a Suspension of Permeabilized Cells: A Theoretical Analysis

During the electroporation cell membrane undergoes structural changes, which increase the membrane conductivity and consequently lead to a change in effective conductivity of a cell suspension. To correlate microscopic membrane changes to macroscopic changes in conductivity of a suspension, we analyzed the effective conductivity theoretically, using two different approaches: numerically, using the finite elements method; and analytically, by using the equivalence principle. We derived the equation, which connects membrane conductivity with effective conductivity of the cell suspension. The changes in effective conductivity were analyzed for different parameters: cell volume fraction, membrane and medium conductivity, critical transmembrane potential, and cell orientation. In our analysis we used a tensor form of the effective conductivity, thus taking into account the anisotropic nature of the cell electropermeabilization and rotation of the cells. To determine the effect of cell rotation, as questioned by some authors, the difference between conductivity of a cell suspension with normally distributed orientations and parallel orientation was also calculated, and determined to be <10%. The presented theory provides a theoretical basis for the analysis of measurements of the effective conductivity during electroporation.

Dielectric analysis of hen egg white with denaturation and in cool storage

Dielectric relaxation spectra (DRS) of fresh hen raw egg white solutions and thermally denatured gels were measured at frequencies between 1 MHz and 3 GHz by using the coaxial line reflection method with a network analyser and an open‐ended coaxial probe. The values of the dielectric constant ε of the denatured gels were higher than those of the raw solutions at frequencies lower than 100 MHz and then became close to each other with the increase in the frequency. No significant change in effective conductivity σ was found on denaturation, implying that this process does not affect the binding of water. The gels were stored at 5°C for 13 days to be subjected to a dehydration process that led to a corresponding decrease in dielectric constant and conductivity. When the dielectric data had been measured, the molecular motions and water status in the egg whites were analysed.

Analytical compensation between DTM grid resolution and effective values of staurated hydraulic conductivity within the TOPMODEL framework

The recent widespread availability of digital terrain data has resulted in increasing use, in a variety of hydrological models, of different degrees of complexity. Previous experience suggests that neither model results nor effective parameter values are independent of the resolution of the digital terrain data used. Calibration of parameter values can compensate for lack of resolution in the digital terrain data. This paper will show, for one particular model, TOPMODEL, how an analytical link can be established between the grid size of a raster digital terrain model and the effective saturated hydraulic conductivity value used in the model. The work generalizes the results of the recent study by Franchini et al. (1996) and allows the change in effective conductivity to be estimated on the basis of keeping a realistic simulation of saturated contributing areas as the DTM grid size changes.

The AC magnetoresistance in inhomogeneous solids

The theory of AC magnetoresistance in inhomogeneous solids is developed using the effective-medium theory. Calculations are performed for systems which consist of random high- and low-conductivity regions. The weak magnetic field H is directed along the z axis. The effective conductivity changes Delta sigma mxx and Delta sigma mzz and the magnetoresistance Delta rho mxx and Delta rho mzz in both the low- and the high-frequency regions are calculated up to the H2 approximation. The calculations show that, owing to inhomogeneities, plateaux of the finite values Delta sigma mzz and Delta rho mzz in the low-frequency region occur. It is possible to have both Delta rho mxx> Delta rho mzz and Delta rho mxx< Delta rho mzz. In the high-frequency limit the equalities Delta sigma mzz= Delta rho mzz=0 hold as in homogeneous solids.