Modelling of Transport Properties of Hard Sphere Fluids and Related Systems, and its Applications

Silva, Carlos M.; Liu, H.

doi:10.1007/978-3-540-78767-9_9

Cited by 26 publications

(54 citation statements)

References 166 publications

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“…There is no simple theory that accurately predicts the concentration dependence of the viscosity of a hard disk mixture at higher densities [68]. To our knowledge there is no published Enskog kinetic theory calculations for hard-disk mixtures in two dimensions, even for the simpler case of equal diameters.…”

Section: Viscosity νmentioning

confidence: 99%

“…In the hydrodynamic simulations we used bare transport coefficient values based on Enskog kinetic theory for the hard-sphere fluid [68]. For the single-component fluid with molecular mass m = 1, this theory gives η 0 ≈ 2.32 and χ 0 ≈ 0.053, which corresponds to a bare Schmidt number…”

Section: Hard Sphere Fluctuating Hydrodynamics Simulationsmentioning

confidence: 99%

“…For the inter-species diffusion coefficient χ, which we emphasize is distinct from the self-diffusion coefficients for particles of either species, Enskog kinetic theory predicts no concentration dependence and a simple scaling with the mass ratio [68], Figure 8: Estimates of the momentum diffusion coefficient (viscosity) ν = η/ρ obtained from the width of the central peak in the dynamic structure factor of vorticity. A collection of 24 distinct discrete wavenumbers k were used and the width of the peaks estimated using a nonlinear least squares Lorentzian fit.…”

Section: Diffusion Coefficient χmentioning

confidence: 99%

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Low Mach number fluctuating hydrodynamics of diffusively mixing fluids

Donev

Nonaka

Sun

et al. 2014

Commun. Appl. Math. Comput. Sci.

133

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We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations represent a coarse-graining of the microscopic dynamics of the fluid molecules in both space and time, and eliminate the fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach number model preserves the spatiotemporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach number fluctuating equations in both two and three dimensions and construct several explicit Runge-Kutta temporal integrators that strictly maintain the equation of state constraint. The resulting spatio-temporal discretization is second-order accurate deterministically and maintains fluctuation-dissipation balance in the linearized stochastic equations. We apply our algorithms to model the development of giant concentration fluctuations in the presence of concentration gradients, and investigate the validity of common simplifications such as neglecting the spatial non-homogeneity of density and transport properties. We perform simulations of diffusive mixing of two fluids of different densities in two dimensions and compare the results of low Mach number continuum simulations to hard-disk molecular dynamics simulations. Excellent agreement is observed between the particle and continuum simulations of giant fluctuations during time-dependent diffusive mixing.

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Section: Viscosity νmentioning

confidence: 99%

Section: Hard Sphere Fluctuating Hydrodynamics Simulationsmentioning

confidence: 99%

Section: Diffusion Coefficient χmentioning

confidence: 99%

See 1 more Smart Citation

Low Mach number fluctuating hydrodynamics of diffusively mixing fluids

Donev

Nonaka

Sun

et al. 2014

Commun. Appl. Math. Comput. Sci.

133

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“…Since the effect of solvent viscosity on the rate of diffusion also depends on the size of diffusing molecules, the solute molar volume should also be introduced, being evaluated at its normal boiling point (V bp,2 ). In addition, the diffusivities in SCFs get values between those of liquids and gases, which means that an additional dependence on the molecular weight of the solute (M 2 ) should be taken into account, as suggested by the kinetic theory of gases [22,24]. Consequently, the following relationship is embodied in this work:…”

Section: New Hydrodynamic Models For D 12mentioning

confidence: 99%

“…(2) and (5) , ˇ universal constants in Eqs. (2) and (5) [22,24], the effective hard sphere diameter method [24][25][26][27], the free-volume theories [24,[28][29][30], the van der Waals [24,31,32] and rough hard sphere principles [24,[33][34][35][36][37][38][39], the hydrodynamic models based on the Stokes-Einstein equation [3,40], the Eyring activated-state theory [41], and excess entropy scaling laws [24,[42][43][44]. Most of these models and approaches were described and reviewed by Reid et al [40], Liong et al [3], Silva and Liu [24], and Medina [45].…”

Section: Introductionmentioning

confidence: 99%

Accurate hydrodynamic models for the prediction of tracer diffusivities in supercritical carbon dioxide

Magalhães

Vaz

Gonçalves

et al. 2013

The Journal of Supercritical Fluids

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Preparative Chromatography: Batch and Continuous

Aniceto

Silva

2015

Analytical Separation Science

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Chromatography, although initially prevalent in the analytical field, is increasingly extended as a preparative process for the commercial scale production of several chemicals whose separation from feed streams is difficult to achieve by conventional methods. In this chapter, the most relevant and recent preparative chromatography approaches are presented and discussed, divided in terms of batch and continuous processes. The fundamental conservation equations, kinetic laws, and equilibrium relations governing chromatographic systems are presented in detail as they are common to all processes modeling. Several models and approaches are presented in an order of higher approximation to reality that necessarily results in an increasing degree of mathematical sophistication. This complexity trend is linked to the sequential introduction of the various phenomena that take place inside the adsorption bed. In particular, the influence of finite mass transfer resistances and axial dispersion upon the dynamic behavior of the chromatographic system is highlighted. With regard to batch chromatography, the most frequent techniques, such as preparative HPLC and supercritical fluid chromatography are covered, along with key chromatography concepts. Closed loop recycling chromatography and steady‐state recycling chromatography are recycling techniques that may be situated between batch and continuous strategies, being able to enhance the performance of batch systems while avoiding the higher complexity inherent to continuous approaches. Regarding continuous chromatography, the development of the simulated moving bed ( SMB ) technology has allowed improved productivity, product's purities, and lower operating costs compared to batch processing. Since its inception, several different strategies and modifications to the conventional SMB have been proposed. The well‐established and the most innovative SMB operation modes, such as intermittent‐ SMB , supercritical SMB , and variable external streams systems, are presented and discussed, along with the necessary equipment designs that allow their implementation. Other continuous chromatographic processes include the high‐speed countercurrent chromatography and the centrifugal partition chromatography, both involving two immiscible liquid phases, and annular chromatography that permits continuous operation while using a stationary phase. Some brief remarks are made on equipment and system designs.

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Modelling of Transport Properties of Hard Sphere Fluids and Related Systems, and its Applications

Cited by 26 publications

References 166 publications

Low Mach number fluctuating hydrodynamics of diffusively mixing fluids

Low Mach number fluctuating hydrodynamics of diffusively mixing fluids

Accurate hydrodynamic models for the prediction of tracer diffusivities in supercritical carbon dioxide

Preparative Chromatography: Batch and Continuous

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