Debye Relaxation Mechanism Research Articles

Numerical evaluation of the ferrofluid behaviour under the influence of three-dimensional non-uniform magnetic field

Ferrofluids have always been the centre of interest for a broad range of applications where the flow manipulation is achieved using different types of magnetic fields. In the present work, a Finite Volume Method based numerical study is performed to investigate the ferrofluid behaviour in the laminar flow regime using the complete set of Ferrohydrodynamics equations. Four distinct single layer finite solenoids of different Ls/Ds (length to diameter ratio) are considered to replicate a 3D (three-dimensional) non-uniform magnetic field, and a twofold validation is also reported to authenticate the generated field distributions. Moreover, a magnetic field dependent viscosity model is used to take into account the variation of ferrofluid viscosity in the presence of a non-uniform magnetic field. To accommodate the varying particle size distribution of ferrofluid, an effective relaxation time constant is used that can accurately predict the magnetization using Debye relaxation mechanism. The obtained flow characteristics are then further discussed and compared along with the case of stationary ferrofluid for all solenoid configurations. New insights about the flow structures are provided using the λ2 criteria of vortex identification technique and the critical point theory analysis. It is observed that each solenoid arrangement have a distinct magnetic field distribution which leads to the occurrence of unique vortex structures and fluid deformations. Also, different flow trajectories are noticed within the fluid domain owing to the peculiar distribution of Kelvin force density. Results from the present work have direct implications in all ferrofluid based momentum transport devices and can be effectively used to further improve our understanding about their performances.

Dielectric relaxation study of propylene carbonate from susceptibility and conductivity measurement under broadband electric field

Dielectric relaxation of propylene carbonate (j) dissolved in p-xylene, cyclohexane and n-heptane (i) at different weight fractions ($$ w_{j}^{{\prime }} $$ s) of solutes for 28, 33 and 38 °C temperatures is studied under 3.8 GHz (S-Band), 7.2 GHz (C-Band), 10.5 GHz (X-Band) and 17.6 GHz (Ku-Band) electric field using simultaneously susceptibility ($$ \chi_{ij}^{{\prime }} $$ s) and conductivity ($$ \sigma_{ij}^{{\prime }} $$ s) measurement technique within the framework of Debye model. The existence of double relaxation times τ2 and τ1 due to inter- and intramolecular rotation of the polar molecules is studied from measured data of $$ \chi_{ij}^{{\prime }} \left( { = \varepsilon_{ij}^{{\prime }} - \varepsilon_{\infty ij} } \right),\chi_{ij}^{\prime \prime } \left( { = \varepsilon_{ij}^{\prime \prime } } \right) $$ and $$ \chi_{0ij} \left( { = \varepsilon_{0ij} - \varepsilon_{\infty ij} } \right) $$ at different weight fractions $$ w_{j}^{{\prime }} $$ s using slope and intercept of $$ \frac{{\chi_{oij - } \chi_{ij}^{\prime } }}{{\chi_{ij}^{\prime } }} $$ against $$ \left( {\frac{{\chi_{ij}^{\prime \prime } }}{{\chi_{ij}^{\prime } }}} \right) $$ linear equation to show the monorelaxation behaviour τ2 only. τ’s are also estimated from the ratio of slopes of imaginary $$ \sigma_{ij}^{\prime \prime } ( = w \in_{0} \in_{ij}^{{\prime }} ) $$ and real $$ \sigma_{ij}^{\prime } ( = \omega \in_{0} \in_{ij}^{\prime \prime } ) $$ parts of complex conductivity $$ \sigma_{ij}^{*} $$ as well as $$ \chi_{ij}^{'} $$ and $$ \chi_{ij}^{\prime \prime } $$ parts of complex susceptibility $$ \chi_{ij}^{*} $$ with wj curves along with linear slope of imaginary against real parts of both the measured data. The dipole moments $$ \mu_{j}^{{\prime }} $$ s are measured at all the frequencies in terms of graphically obtained τ’s from susceptibility measurement technique as well as τ’s from conductivity measurement technique. The solute–solvent molecular associations are also predicted. Thermodynamic energy parameters are ascertained from ln(τjT) against 1/T to predict the state of molecular environment surrounding the polar molecules. The estimated Debye factors reveal that the polar–non-polar mixture obeys the Debye relaxation mechanism. Sufficient penetration depth indicates development of a new simple and rapid sensor for determination of propylene carbonate concentration.

Relaxation phenomena of nicotinamide and benzamide with 1-propanol and 1-butanol in C6H6 under static and 9.385 GHz electric field

Dielectric relaxation behaviors of nicotinamide+1-propanol, benzamide+1-propanol, and nicotinamide+1-butanol dissolved in C6H6 at 0.990, 0.985, 0.980, 0.975, 0.970; 0.990, 0.985, 0.980, and 0.980 mol fraction xj of 1-propanol or 1-butanol at temperature 30 °C and 30, 40, 50, and 60 °C, respectively, are studied using the Debye model of binary polar–non-polar liquid mixture to predict double relaxation times τ2 and τ1 and dipole moments μ2 and μ1 from susceptibility measurement of concentration variation solution data under static and 9.385 GHz electric fields. Nineteen systems exhibit τ2, τ1 and μ2, μ1. τ2 are found to increase with temperature for all the binary polar mixtures, whereas τ1, most probable τ0, and measured τ from slope methods are almost the same. They agree well with the τ reported by Higasi. The plots of τjk–xj and μjk–xj curves reveal solute–solute and solute–solvent molecular association through H-bonding, and variation of μ with t (°C) is noted from the μjk–t curve. The associational aspects are taken into consideration from theoretical μtheo from the standpoint of inductive, mesomeric, and electromeric effects within the polar groups of the molecules. The estimated Debye factor τjkT/η and Kalman factor τjkT/ηγ reveal that the polar mixture obeys the Debye relaxation mechanism.

Dielectric properties of Yb3+ and Nb5+ doped RbTiOPO4 single crystals

The influence of niobium and ytterbium doping in the electrical properties of the RbTiOPO4 (RTP) crystals has been analyzed along the three crystallographic axes. While Yb3+ does not change the ionic conductivity of RTP, Nb5+ increases it considerably. These effects are also observed for the activation energies of these samples doped with Yb3+ and Nb5+, and different relaxation mechanisms have been observed for the different dopants. RTP and Nb:RTP sample show a non-Debye relaxation mechanism, while Yb:RTP and Nb,Yb:RTP samples show a Debye relaxation mechanism.

Debye relaxation mechanisms of microwave heating of near-critical polar gases

In this work, the average time of slow dielectric relaxation in sub- and supercritical polar gases is considered in terms of a combination of two Debye relaxation mechanisms. Under the assumption of thermal equilibrium, the corresponding relaxation times are theoretically predicted to be proportional to the mean binary collision time and mean translational deceleration time of free molecules with the proportionality factor close to unity. The microwave heating rate for pressurized pure gases and gas mixtures in constant-pressure and constant-density conditions is found from the Poynting formula. Temperature-dependent frequency spectra of the isobaric and isochoric heating rates for sub- and supercritical water are obtained with an allowance for non-Debye high-frequency relaxations. Perceptible temperature effects in the supercritical water heating rates at relaxation frequency are predicted when pressures/densities are high enough and considerable reduction of the heating time for higher pressures/densities is expected.

Electrical and petrophysical modeling of Ferron Sandstone data

As part of the 3D characterization of a fluvial reservoir analog site in the Ferron Sandstone in east-central Utah, new lab measurements of porosity, permeability, water content, and complex dielectric permittivity are collected and analyzed. Petrographic analysis of thin sections extracted from the same samples produced data on bulk, macro- and microporosity, lithology, and cementation. Thus, we have an unusually comprehensive data base for analysis. Debye models of complex dielectric permittivities are fitted using three frequency-dependent Debye relaxation mechanisms. Most ambient and dry samples are dominated by low-frequency relaxation mechanisms. The average dielectric constant and electrical conductivity at the typical ground-penetrating radar (GPR) frequency of [Formula: see text] are directly related to volumetric water content and are 3.86 and [Formula: see text] for oven-dried samples, 4.50 and [Formula: see text] for ambient saturated sam-ples, and 15.42 and [Formula: see text] for fully saturated samples. Electrical conductivity is poorly estimated from the oven-dried samples (for all clay content) because ion mobility is significantly reduced; thus, the dry conductivity is less useful for estimating petrophysical variations. Multivariate regressions with the petrophysical parameters estimate the electrical properties at [Formula: see text] and [Formula: see text] with average correlation coefficients of [Formula: see text] and [Formula: see text], respectively. Empirically derived predictions of dielectric constant as a function of water content will always provide better fits to the observed values than either generic models (such as the CRIM model) or fits to other data sets (such as the Topp formula, which was derived for soils). The Topp model consistently underestimates the dielectric constant, while the CRIM model generally overestimates it, at both 75 and [Formula: see text]. The overall regression procedures can be applied to data from other sites and potentially used as the basis of inversion of petrophysical properties from measurements of electric and dielectric properties.

Dielectric relaxation of para polar liquids under high frequency electric field

Abstract The structural and associational aspects of nonspherical para polar liquids (j) in nonpolar solvents (i) are studied through high frequency conductivities σij's of solutions. The relaxation time τ of the respective liquids under 3cm. wavelength electric field at various experimental temperatures in °C are estimated from the slope of individual variations of real σ′ij and imaginary σ″ij parts of hf complex conductivity σ ∗ ij with weight fractions wj's of polar liquid. The temperature variation of τ for comparatively larger nonspherical para molecules in dioxane are not strictly obeyed by the Debye model unlike other simpler para di- or tri-substituted benzene in benzene. Thermodynamic energy parameters ΔHτ, ΔSτ and ΔFτ are obtained from Eyring's rate process equation with the estimated τ's in order to get information on the solvent environment around them. The higher values of γ obtained from lnτjT against lnη equation indicate the solid phase rotators for the liquids. The estimated Kalman and Debye factors τjT/ηγ and τjT/η establish the Debye relaxation mechanism for almost all the para-molecules. The obtained dipole moments μj's in terms of slope β of σij-wj curve and dimensionless parameter ‘b’ involved with estimated τ are then compared with the reported μ and μtheo obtained from bond angles and bond moments. The μj's of para liquids are often zero but at other temperatures they show net moments. The slight disagreement between the measured and theoretical μ's reveals the presence of the inductive and mesomeric moments of substituted polar groups in molecules at different temperatures.

Association of normal alcohols in the presence of some aniline derivatives

Abstract The specific absorption Δe ″/ x for chloro and bromo anilines and also for N-N diethyl aniline were measured in carbon tetrachloride at microwave (0.2–18 GHz). Two Debye relaxation mechanisms were considered. The relaxation which is associated with the relaxation of the molecule as a whole and that ascribed to the rotation of the amino group which may be restricted by replacing the hydrogen atoms in both sides of nitrogen by two ethyl groups. From the apparent dipole moment measurements, the tendency to self-association in some normal alcohols, n-butanol, n-octanol, n-dodecanol is discussed in terms of the restriction which may happen by the addition of aniline derivatives. The critical concentration, which may lead to a complete restriction has been determined.

Waves in elastic and anelastic stratified microstructure: A numerical comparison

Burridge et al. [J. Acoust. Soc. Am. 94, 2884–2894 (1993)] presented a fast algorithm to compute wave propagation through a stack of finely layered elastic or anelastic microstructure. The method goes beyond previous work in two aspects: (a) the sample autocorrelation is used so that the coda of the computed response is preserved; and (b) the anelastic effect due to intrinsic attenuation is incorporated and by order-of-magnitude argument, the terms governing the scattering and anelastic effects enter separately but in a similar way. The present work is a numerical justification of the perturbation theory. Using a standard linear solid model with a single Debye relaxation mechanism, a finely layered microstructure was made anelastic. Using the SH case as an example, impulse responses were computed using two methods: the approximate method and an exact method for both elastic and anelastic media at normal and oblique angles of incidence. The impulse responses obtained by the two methods agree well for both elastic and anelastic cases. The results of the investigation can be summarized in several points: (a) accuracy is best for the head of the pulse; (b) the presence of anelasticity increases the time delay and dispersion of the broad pulse; and (c) the perturbation code is 30–54 times faster than the exact code.

Elasticity study on lattice instability in BiSrCaCuO

The frequency dependences of heights and positions of the attenuation peaks at 95K and 250K for Bi 2Sr 2CaCu 2O 8 single crystal (T c=84K) show the characters of phase transitions. The pseudo-static ferroelastic σ-ϵ loops of Pb doped BiSrCaCuO polycrystal (T c=107K) always appear around 130K and 250K. The energy loss (loop area) is independent of the strain rate and increases with the strain amplitude, which also exhibits the characteristics of static hysteresis loss related to phase transitions instead of the Debye relaxation mechanism. Some discrepancies in elasticity measurements so far observed for high Tc superconductors have been analyzed.

On the Rayleigh dissipation function for dielectric media

Explicit expressions are obtained for the Rayleigh dissipation function for stationary dielectric media having either a discrete set of Debye relaxation mechanisms or a discrete set of Lorentz absorption mechanisms.

On the energy loss of slow electrons due to dielectric relaxation

We derive an approximate formula for a novel form of energy loss experienced by 1–10 eV electrons passing through polar liquids. This loss mechanism, which depends on the translational motions of polar molecules in the Coulomb field of an electron is shown to yield a dissipation rate comparable in magnitude with the prediction of the Fröhlich-Platzman theory, which allows only for the rotational motion of polar molecules (Debye relaxation mechanism).

Dispersion of the dielectric permittivity in mixtures of nematic liquid crystals

The spectrum of relaxation time for the low-frequency dispersion has been found to become wider in mixtures of nematic liquid crystals, which can be interpreted as a superposition of two Debye relaxation mechanisms.

Cole-Cole diagrams of ionic hopping systems

A hopping conduction mechanism is proposed for the mobile ions in evaporated silicon oxide films. The Cole-Cole diagram, calculated numerically, is identical to that of a simple Debye relaxation mechanism. The hopping conduction mechanism can also be combined with surface trapping, which gives rise to Cole-Cole diagrams similar to those found experimentally. Lastly it is shown that the hopping conduction model is closely related to a drift-diffusion mechanism, which has also been used to describe ion transport phenomena in thin insulating films.