Nonlinear diffusion and phase separation

Nauman, E. Bruce; He, David Qiwei

doi:10.1016/s0009-2509(01)00005-7

Cited by 193 publications

(178 citation statements)

References 59 publications

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“…We showed that a necessary and sufficient condition for species spinodal decomposition occurrence is that the particular species be initially present in both streams; this is why heptane, nitrogen and oxygen never experienced spinodal decomposition during the physical time of the simulation. We also found that there is no requirement that each species undergoing spinodal decomposition be initially uniformly distributed, as it is usually specified in the literature (Nauman & He 2001); in fact, non-uniformity will promote, through gradients, the diffusion causing spinodal decomposition. Because chemicalcomposition uniformity is not a requirement for species spinodal decomposition, we conjecture that the high-density-gradient magnitude regions observed even when species were initially segregated, are the precursors to eventual spinodal decomposition in the mixture which is formed by molecular and turbulent processes undergone by the initially segregated species, i.e.…”

Section: Irreversible Entropy Productionmentioning

confidence: 60%

Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition

et al. 2013

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A model is developed for describing mixing of several species under high-pressure conditions. The model includes the Peng-Robinson equation of state, a full massdiffusion matrix, a full thermal-diffusion-factor matrix necessary to incorporate the Soret and Dufour effects and both thermal conductivity and viscosity computed for the species mixture using mixing rules. Direct numerical simulations (DNSs) are conducted in a temporal mixing layer configuration. The initial mean flow is perturbed using an analytical perturbation which is consistent with the definition of vorticity and is divergence free. Simulations are performed for a set of five species relevant to hydrocarbon combustion and an ensemble of realizations is created to explore the effect of the initial Reynolds number and of the initial pressure. Each simulation reaches a transitional state having turbulent characteristics and most of the data analysis is performed on that state. A mathematical reformulation of the flux terms in the conservation equations allows the definition of effective species-specific Schmidt numbers (Sc) and of an effective Prandtl number (Pr) based on effective speciesspecific diffusivities and an effective thermal conductivity, respectively. Because these effective species-specific diffusivities and the effective thermal conductivity are not directly computable from the DNS solution, we develop models for both of these quantities that prove very accurate when compared with the DNS database. For two of the five species, values of the effective species-specific diffusivities are negative at some locations indicating that these species experience spinodal decomposition; we determine the necessary and sufficient condition for spinodal decomposition to occur. We also show that flows displaying spinodal decomposition have enhanced vortical characteristics and trace this aspect to the specific features of high-density-gradient magnitude regions formed in the flows. The largest values of the effective speciesspecific Sc numbers can be well in excess of those known for gases but almost two orders of magnitude smaller than those of liquids at atmospheric pressure. The effective thermal conductivity also exhibits negative values at some locations and the effective Pr displays values that can be as high as those of a liquid refrigerant. Examination of the equivalence ratio indicates that the stoichiometric region is thin and coincides with regions where the mixture effective species-specific Lewis number values are well in excess of unity. Very lean and very rich regions coexist in the vicinity of the stoichiometric region. Analysis of the dissipation indicates that it is † Email address for correspondence: josette.bellan@jpl.nasa.govMulti-species supercritical-pressure mixing 579 dominated by mass diffusion, with viscous dissipation being the smallest among the three dissipation modes. The sum of the heat and species (i.e. scalar) dissipation is functionally modelled using the effective species-specific diffusivities and the effective the...

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Section: Irreversible Entropy Productionmentioning

confidence: 60%

Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition

et al. 2013

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“…1 In contrast, phase-field models provide a more general, thermodynamically consistent treatment of nucleation and growth without resorting to the artificial placement of phase boundaries. 18,19 Considering the excitement surrounding LiFePO 4 as a phase-separating cathode material, phase-field methods have received relatively little attention. Tang et al modeled phase separation and crystallineto-amorphous transformations in spherical isotropic LiFePO 4 particles with a phase-field model, 20 prompting experiments to seek the predicted amorphous surface layers.…”

mentioning

confidence: 99%

Suppression of Phase Separation in LiFePO₄ Nanoparticles During Battery Discharge

Bai

Cogswell²,

Bazant³

2011

Nano Lett.

453

734

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Using a novel electrochemical phase-field model, we question the common belief that Li x FePO 4 nanoparticles separate into Li-rich and Li-poor phases during battery discharge. For small currents, spinodal decomposition or nucleation leads to moving phase boundaries. Above a critical current density (in the Tafel regime), the spinodal disappears, and particles fill homogeneously, which may explain the superior rate capability and long cycle life of nano-LiFePO 4 cathodes.

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“…Indeed, local inhomogeneities affect turbulence production 7,27 as well as phase separation. 26,28,29 These arguments lead to the analysis being focussed on the state obtained at t * tr . In analyzing the numerical results, we first perform a statistical analysis of the large-scale distortion of the mixing layers at t * tr .…”

Section: Resultsmentioning

confidence: 99%

A priori and a posteriori investigations for developing large eddy simulations of multi-species turbulent mixing under high-pressure conditions

Borghesi

Bellan

2015

Physics of Fluids

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A Direct Numerical Simulation (DNS) database was created representing mixing of species under high-pressure conditions. The configuration considered is that of a temporally evolving mixing layer. The database was examined and analyzed for the purpose of modeling some of the unclosed terms that appear in the Large Eddy Simulation (LES) equations. Several metrics are used to understand the LES modeling requirements. First, a statistical analysis of the DNS-database large-scale flow structures was performed to provide a metric for probing the accuracy of the proposed LES models as the flow fields obtained from accurate LESs should contain structures of morphology statistically similar to those observed in the filtered-and-coarsened DNS (FC-DNS) fields. To characterize the morphology of the large-scales structures, the Minkowski functionals of the iso-surfaces were evaluated for two different fields: the second-invariant of the rate of deformation tensor and the irreversible entropy production rate. To remove the presence of the small flow scales, both of these fields were computed using the FC-DNS solutions. It was found that the large-scale structures of the irreversible entropy production rate exhibit higher morphological complexity than those of the second invariant of the rate of deformation tensor, indicating that the burden of modeling will be on recovering the thermodynamic fields. Second, to evaluate the physical effects which must be modeled at the subfilter scale, an a priori analysis was conducted. This a priori analysis, conducted in the coarse-grid LES regime, revealed that standard closures for the filtered pressure, the filtered heat flux, and the filtered species mass fluxes, in which a filtered function of a variable is equal to the function of the filtered variable, may no longer be valid for the high-pressure flows considered in this study. The terms requiring modeling are the filtered pressure, the filtered heat flux, the filtered pressure work, and the filtered species mass fluxes. Improved models were developed based on a scale-similarity approach and were found to perform considerably better than the classical ones. These improved models were also assessed in an a posteriori study. Different combinations of the standard models and the improved ones were tested. At the relatively small Reynolds numbers achievable in DNS and at the relatively small filter widths used here, the standard models for the filtered pressure, the filtered heat flux, and the filtered species fluxes were found to yield accurate results for the morphology of the large-scale structures present in the flow. Analysis of the temporal evolution of several volume-averaged quantities representative of the mixing layer growth, and of the cross-stream variation of homogeneous-plane averages and second-order correlations, as well as of visualizations, indicated that the models performed equivalently for the conditions of the simulations. The expectation is that at the much larger Reynolds numbers and much larger filter widths used in practical applications, the improved models will have much more accurate performance than the standard one.

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Nonlinear diffusion and phase separation

Cited by 193 publications

References 59 publications

Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition

Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition

Suppression of Phase Separation in LiFePO₄ Nanoparticles During Battery Discharge

A priori and a posteriori investigations for developing large eddy simulations of multi-species turbulent mixing under high-pressure conditions

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Nonlinear diffusion and phase separation

Cited by 193 publications

References 59 publications

Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition

Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition

Suppression of Phase Separation in LiFePO4 Nanoparticles During Battery Discharge

A priori and a posteriori investigations for developing large eddy simulations of multi-species turbulent mixing under high-pressure conditions

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Product

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Suppression of Phase Separation in LiFePO₄ Nanoparticles During Battery Discharge