Academic literature on the topic 'Relaxation time in fluid binary mixtures'

We investigate the structural relaxation in a binary fluid over the time scales of β-relaxation regime. For this we have used a recently proposed self-consistent mode-coupling theory (MCT) formulated from the fluctuating nonlinear hydrodynamics approach. We have considered here both the hard sphere as well as the Kob–Andersen Lennard–Jones1 binary mixtures. From the solution of the MCT equations obtained here the initial power law decay t-a appears to be very weak. For the later part of the β-relaxation regime, the density correlation functions follow von Schweidler (VS) power law decay tb. The validity of the so-called factorization property of the MCT over the β-relaxation is also analyzed. We find the exponent b to be in qualitative agreement with the findings from the computer simulations of the same system by Kob and Andersen.

We propose a non-equilibrium framework for modelling the evolution of cities, which describes intra-urban migration as an irreversible diffusive process. We validate this framework using the actual migration data for the Australian capital cities. With respect to the residential relocation, the population is shown to be composed of two distinct groups, exhibiting different relocation frequencies. In the context of the developed framework, these groups can be interpreted as two components of a binary fluid mixture, each with its own diffusive relaxation time. Using this approach, we obtain long-term predictions of the cities’ spatial structures, which define their equilibrium population distribution.

Abstract The dielectric spectra of diethylsulfoxide (DESO)/tetrachloromethane mixtures have been measured from 0.5 to 72 GHz at 20 °C. On the basis of the relation between the relaxation time and the DESO concentration a complex formation between DESO and tetrachloromethane is suggested.

Using standard standing wave microwave X-band techniques, and by following Gopala Krishna’s single frequency (9.90 GHz) concentration variational method, the dielectric relaxation times (τ) and dipole moments (μ) of binary mixtures of different molar concentrations of ethanol (EtOH) in binary mixtures of N-methylacetamide (NMA) and ethanol in benzene solutions at 25, 30, 35 and 40 ◦C have been calculated. The activation parameters (ΔHε , ΔFε , ΔSε ) for the dielectric relaxation process of binary mixtures containing 30 mol% of EtOH have been calculated at 25, 30, 35 and 40 ◦C and compared with the corresponding viscosity parameters. A good agreement between the free energy of activation from these two sets of values shows that the dielectric relaxation process, like the viscous flow, can be treated as a rate process. From relaxation time behaviour of NMA and EtOH binary mixtures in benzene solution, solute-solute and solute-solvent types of the molecular association have been predicted.

The dielectric properties of binary mixtures of benzylamine-1,2,6-hexantriol mixtures at different volume fractions of 1,2,6-hexanetriol have been measured using Time Domain Reflectometry (TDR) technique in the frequency range of 10 MHz to 30 GHz. Complex permittivity spectra were fitted using Havriliak–Negami equation. By using least square fit method the dielectric parameters such as static dielectric constant ([Formula: see text]), dielectric constant at high frequency ([Formula: see text]), relaxation time [Formula: see text] (ps) and relaxation distribution parameter ([Formula: see text]) were extracted from complex permittivity spectra at 25[Formula: see text]C. The intramolecular interaction of different molecules has been discussed using the Kirkwood correlation factor, Bruggeman factor. The Kirkwood correlation factor ([Formula: see text]) and effective Kirkwood correlation factor ([Formula: see text]) indicate the dipole ordering of the binary mixtures.

The dielectric relaxation time (τ ) and dipole moment (μ) of binary mixtures of different molar concentrations of N-methylformamide (NMF) in binary mixtures of NMF and tetramethylurea (TMU) in benzene have been calculated at 25, 30, 35 and 40 ◦C using standard standing wave microwave techniques and following the single frequency (9.885 GHz) concentration variational method of Gopala Krishna. The energy parameters (ΔHε , ΔFε , ΔSε ) for the dielectric relaxation process of binary mixtures containing 30 mol% of NMF have been calculated at different temperatures, and comparison has been made with the corresponding energy parameters (ΔHη , ΔFη , ΔSη ) for the viscous flow process. Based on these studies, it was inferred that the dielectric relaxation process can be treated as a rate process just like the viscous flow process. Solute-solvent and solute-solute molecular associations have been proposed.

A theory of the quadrupolar relaxation rate,RQ , for ideal liquid binary metallic mixtures ispresented. The theory predicts cancellation after a few tenths of a picosecond of the two andthree particle correlation terms in the fluctuation of the electric field gradient (EFG) for puremetals, and prevailing of the three particle term for binary mixtures. This is due to the highsymmetry in the arrangement of the atoms around a probe nucleus. The prevailing of the threeparticle term in binary systems leads to a longer correlation time (a few picoseconds) of thefluctuating EFG and explains the experimentally observed higher values of RQ and theirquadratic concentration dependence. The validity of the theory has been confirmed by experimentaldata. Deviations for some real systems are discussed.

The dielectric constant ε´ and dielectric loss ε´´ of the binary mixtures of tetramethylurea (TMU) and chlorobenzene (CB) have been calculated at 9.883 GHz by using standard standing microwave techniques. Gopalakrishna’s single frequency concentration variation method has been used to calculate dipole moment μ and dielectric relaxation time τ for different mole fractions of TMU in the binary mixture at different temperatures of 25 °C, 30 °C, 35 °C, and 40 °C. The variation of dielectric relaxation time with the mole fraction of TMU in the whole concentration range of the binary mixtures was found to be non-monotonic. The solute-solute and solute-solvent type of molecular associations may be proposed based upon above observations. Using Eyring rate equations the energy parameters ΔH, ΔF, and ΔS for the dielectric relaxation process and the viscous flow process have been calculated at the given temperatures. It is found from the comparison of energy parameters that, just like the viscous flow process, the dielectric relaxation process can also be treated as a rate process.

2008/2009
This thesis is aimed to the study of dynamics in binary fluid mixtures by means of inelastic scattering spectroscopies. Nowadays the understanding of these dynamics is still unsatisfactory. In particular, any model is able to adequately describe collective dynamics beyond the hydrodynamic limit. In such a low momentum (k) and frequency () transfer limit, the collective dynamics is characterized by a single (adiabatic) longitudinal acoustic mode accounting for sound propagation. At frequencies above the hydrodynamics ones a transition towards a decoupled dynamic regime is expected. This is characterized by two distinct modes, namely the slow (low-) and fast (high-) sounds. The microscopic mechanisms driving such a transition, so as the related macroscopic quantities, are still unclear, even in an heuristic point of view. In this work the collective dynamics of neutral and ionic mixtures are investigated with the aim to shed light in this debated issue. He/Ne mixtures have been studied by means of Inelastic X-ray Scattering (IXS) spectroscopy. Exploiting the lack of kinematic limitations peculiar of this technique, the high frequency (>THz) dynamics has been analyzed from the mesoscopic up to the high-k range, where the dynamic response of the system can be described using the Impulse Approximation (IA). This kind of study is of particular interest for disparate mass mixtures, since inefficient kinetic energy exchanges between light and heavy particles taking place on very short time scales are expected to greatly influence the phenomenology of the aforementioned dynamic decoupling. The prototype ionic mixture, RbF, also, has been investigated by means of Inelastic Neutron Scattering (INS) spectroscopy. Ionic mixtures are particularly suited to investigate the role played by optic-like excitations (related to concentration fluctuations) in the transition from the hydrodynamics to the decoupled regime. Indeed, these kind of excitations are expected to be emphasized because of the long range Coulomb interactions. Conversely at k’s enough high, i.e. k>k* with k* dependent on the values of the electric conduction coefficient and the adiabatic sound velocity, they are expected to behave like neutral binary mixtures. The study of molten RbF has been, then, focused on the characterization of collective dynamics in the transition region, which is more difficultly accessible by IXS because of instrumental limitations. IXS data on He0.8Ne0.2 mixture have been analyzed using a generalization of the viscoelastic function, which, in our knowledge, has been applied for the first time to this purpose. This kind of data analysis permitted to extrapolate the partial dynamical structure factors related to He-He, Ne-Ne and He-Ne density fluctuations. The adiabatic and high frequency sound velocity as well as the relaxation time associated to each mixture component has been calculated from fitting parameters. The analysis of the extrapolated relaxation times permitted to define, in the probed range, two k-region depending on the behavior of such quantity. At the higher k probed the relaxation times of single components can be well described by the respective single specie collision time, indicating a complete dynamics decoupling. At lower k, conversely, the relaxation times show a deviation to respect the collisional times. The study of the same mixture in three different thermodynamic conditions, revealed a common k trend of the single component relaxation times once proper normalization, made by means of kinetic parameters, has been done. An empirical expression has then been proposed. The result can be interpreted in the framework of ‘two temperature theory’, based on the assumption that in disparate mass binary mixtures inefficient kinetic energy exchanges induce a two step process for the relaxation of density fluctuations towards the thermodynamic equilibrium. These processes are characterized by two distinct timescales: the intra-specie collision time, where each specie subsystem reaches a condition of ‘local’ equilibrium associated with a ‘local’ temperature and a characteristic time for the equilibration of the microscopic temperatures to the thermodynamic temperature trough inter-specie collisions. A further corroboration of the above picture has been found from the analysis of IXS spectra in the IA region, which allowed extrapolating the momentum distribution functions of the specie subsets. An anomalous behavior has been noticed on the He momentum distribution function, i.e. the apparent temperature associated to the momentum distribution is about 40 K higher than the macroscopic one. This striking result can be straightforwardly interpreted as a fingerprint of the peculiar ‘two temperature’ equilibration process. INS experiment on molten RbF permitted to reveal the simultaneous presence of two dispersive collective modes in the transition region. The dispersive behavior (linear with k) and the characteristic energies permitted to exclude an optic-like nature for both excitations. The performed data analysis permitted also to extrapolate the value of the electrical conduction coefficient, founding a quite low value as compared with typical values of molten salts. An estimation of k* for the studied system emphasize the possibility that at the probed k it may be isomorphous to a neutral mixture. The observed phenomenology can be thus interpreted in terms of double sound propagation phenomenon, observed in rarefied non-ionic gaseous mixtures. Finally, an alternative interpretation of these experimental results can be qualitatively provided within the frame of the generalized collective mode approach. In this case the high frequency mode is identified with the extension of the adiabatic longitudinal sound mode beyond hydrodynamic limit that, in analogy to what observed in several fluids, follows a linear dispersion with an associated sound velocity larger than the adiabatic one. The low frequency mode could instead be associated with a propagating kinetic mode related to energy fluctuations (heat waves). In conclusion, an extensive analysis of high-frequency dynamics in binary mixtures has been reported. Particular emphasis has been devoted to the study of the sound decoupling phenomenon manifesting beyond the hydrodynamic region. The experimental results indicate that such a phenomenon is manifested in both neutral and ionic disparate mass binary mixtures. It can be related to microscopic dynamics, e.g. thermalization effects related to the inefficient kinetic exchange between lighter and heavier particles.
XXI Ciclo
1978

Abstract Mixing characteristics of supercritical injection studies were analyzed with regard to the necessity to include diffusive fluxes. Therefore, speed of sound data from mixing jets were investigated using an adiabatic mixing model and compared to an analytic solution. In this work, we show that the generalized application of the adiabatic mixing model may become inappropriate for subsonic submerged jets at high-pressure conditions. Two cases are discussed where thermal and concentration driven fluxes are seen to have significant influence. To which extent the adiabatic mixing model is valid depends on the relative importance of local diffusive fluxes, namely Fourier, Fick and Dufour diffusion. This is inter alia influenced by different time and length scales. The experimental data from a high-pressure n-hexane/nitrogen jet injection were investigated numerically. Finally, based on recent numerical findings, the plausibility of different thermodynamic mixing models for binary mixtures under high pressure conditions is analyzed.

Spiral wound membrane is used in several industrial purification processes such as desalination, food industries and gas separation. It has been shown that membrane performance could be greatly enhanced by momentum mixing in the feed channel induced by spacers. Square shaped spacers will be considered in inline geometries for the Reynolds number, Re, of 300 and 500. A separation of CO2 from CH4 will be investigated. A computational fluid dynamics simulation will be conducted for flows of a binary mixture of CO2 and CH4. The mass flux through the membrane will be determined based on the local partial pressures of each species, the permeability, and the selectivity of the membrane. Shear Stress Transport turbulence model will be employed to capture the steady state velocity and concentration field. The transient effect on the momentum mixing will be studied using lattice Boltzmann method. Two dimensional nine velocity directional, D2Q9, lattice arrangement with multi-relaxation time (MRT) lattice Boltzmann method is used to simulate transient flow field while single relaxation time (SRT) lattice Boltzmann method is employed to simulate concentration field for Re = 100 and 300. The bounding surfaces are treated as impermeable walls for simulations conducted using the lattice Boltzmann method. The results predicted by lattice Boltzmann and SST turbulence model agree well.

Abstract The most common NMR methods in the oil and gas industry are NMR relaxometry and diffusometry. Relaxation times T1 and T2 as well as diffusivity D are determined for characterizing fluids and their surrounding pores in logging applications or laboratory analyses. NMR spectroscopy is rarely used for petrophysical investigations but primarily in medical, food, and material applications. In a joint operator-academia-service company project, we explore opportunities for gas component quantification by low-field NMR spectroscopy with the prospect of rig-site, production-plant, and sea-floor deployment. Using an affordable benchtop device in a production-like environment, we gained a fundamental understanding for a commercially viable application of low-field NMR spectroscopy and translated this knowledge into a practical workflow for online natural gas composition analysis. We measured typical natural gas components (all isomers from methane to n-hexane) with a portable desktop NMR spectrometer working at a proton resonance frequency of 60 MHz A hardware setup was manufactured for mimicking a gas production environment up to 200 bar. A database was populated by NMR signatures of pure gas components, derived from measurements on pure components and binary mixtures. Additional efforts were dedicated to understanding and quantifying systematic effects on the hydrocarbon NMR spectra connected to sample composition and pressure. Pre- and post-processing data procedures were developed and applied for substantially increasing robustness of the method and further improving the gas composition analyses results. Using an indirect hard modeling (IHM) analysis, the constituting pure components in binary, ternary, and more complex gas mixtures were identified and quantified. IHM automatically accounts for small variations and uncertainties in the NMR spectra. The results from the NMR spectrum analysis are in very good agreement with vendor certificates of gas composition obtained from gravimetrics and gas chromatography.

This paper presents research on the evaporation of methanol/water mixtures in uniformly heated, constant cross-section silicon serpentine microchannels. The phase change of a variety of mixtures of methanol and water was observed, characterized and compared to the phase change both of pure water and pure methanol. Seven fluids were tested: pure water, pure methanol and five different molar fractions of methanol mixed with water. Flow rates were varied from Reynolds number five to ten. In the microscale system, it is shown that the flow boiling characteristics of the methanol/water mixtures are markedly different from those of pure liquids. Specifically, for the binary system there is a lack of a clear meniscus that spans the microchannel, which is seen in the pure fluid systems. Rather, the phase change of binary mixtures appears to occur over a much greater length of microchannel than for pure fluids. Unstable, intermittent evaporation fronts were also observed within the channels for moderate levels of superheat that are most likely dictated by the local temperature and pressure variations along the channel. Furthermore, at no time was bubble formation observed, despite the fact that several of the mixtures were subject to superheats as great as 20°C.

The rheological properties and the duration of particle interactions in a dense granular media are closely related to the formation of particle interaction networks. The behavior of particle interaction networks depends not only on the particle volume fractions but also on friction between particles. For examples, for frictionless particles, a particle interaction network may not form at particle volume fraction greater than 0.62, the random dense packing volume fraction for monodisperse spheres. Without network formation, particle interactions are short in time and mostly binary. Under this condition, the granular medium can be modeled as a viscous fluid with variable viscosity as in kinetic theory. Formation of particle interaction networks dramatically increases particle interaction time and results in a phase transition in the constitutive relations of the granular medium. Then, the stress relaxation time is inversely proportional to the macroscopic shear rate in simple shear flows, and the granular medium can be modeled as a viscoelastic material with a stress relaxation time depending on the macroscopic shear rate. For small shear rates, the stresses in the granular medium are independent of macroscopic shear rates in simple shear flows. Thus, as the shear rate approaches zero, the relaxation time approaches infinity, and the shear stress approaches a finite value, the yield stress, instead of zero. We also studied the relaxation behavior of the stress tensor under time-dependent shear rates. The dynamics of the particle interaction network leads to a nonlinear behavior of stress relaxation not exhibited by ordinary viscoelastic materials, such as polymeric fluids.