Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres

The chemical potentials of multicomponent fluids are derived in terms of the pair correlation functions for arbitrary number of components, interaction potentials, and dimensionality. The formally exact result is particularized to hard-sphere mixtures with zero or positive nonadditivity. As a simple application, the chemical potentials of three-dimensional additive hard-sphere mixtures are derived from the Percus-Yevick theory and the associated equation of state is obtained. This Percus-Yevick chemical-route equation of state is shown to be more accurate than the virial equation of state. An interpolation between the chemical-potential and compressibility routes exhibits a better performance than the well-known Boublík-Mansoori-Carnahan-Starling-Leland equation of state.

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“…This extends to multicomponent systems, the work recently reported in Ref. [9]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 78%

“…In the one-component case [9], values of the interpolation parameter α ≈ 0.4 were seen to provide a better equation of state than the standard Carnahan-Starling equation [21]. In particular, the values α = 2 5 and α = 7 18 were explicitly considered.…”

Section: Application To Hard-sphere Mixtures In the Py And Spt Appmentioning

confidence: 99%

Chemical-potential route for multicomponent fluids

Santos

Rohrmann

2013

Phys. Rev. E

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“…Henderson formulas, Eqs. ( 9) or (46) [9,92]). The conductivity also takes the separable form κ(ρ, T ) = √ T k(ρ), where again k(ρ) is generally unknown (though a reasonably good approximation is obtained from Enskog kinetic theory [34,93], see Eq.…”

Section: Scaling In Fourier's Lawmentioning

confidence: 99%

Simulations of Transport in Hard Particle Systems

Hurtado

Garrido

2020

J Stat Phys

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Hard particle systems are among the most successful, inspiring and prolific models of physics. They contain the essential ingredients to understand a large class of complex phenomena, from phase transitions to glassy dynamics, jamming, or the physics of liquid crystals and granular materials, to mention just a few. As we discuss in this paper, their study also provides crucial insights on the problem of transport out of equilibrium. A main tool in this endeavour are computer simulations of hard particles. Here we review some of our work in this direction, focusing on the hard disks fluid as a model system. In this quest we will address, using extensive numerical simulations, some of the key open problems in the physics of transport, ranging from local equilibrium and Fourier's law to the transition to convective flow in the presence of gravity, the efficiency of boundary dissipation, or the universality of anomalous transport in low dimensions. In particular, we probe numerically the macroscopic local equilibrium hypothesis, which allows to measure the fluid's equation of state in nonequilibrium simulations, uncovering along the way subtle nonlocal corrections to local equilibrium and a remarkable bulk-boundary decoupling phenomenon in fluids out of equilibrium. We further show that the the hydrodynamic profiles that a system develops when driven out of equilibrium by an arbitrary temperature gradient obey universal scaling laws, a result that allows the determination of transport coefficients with unprecedented precission and proves that Fourier's law remains valid in highly nonlinear regimes. Switching on a gravity field against the temperature gradient, we investigate numerically the transition to convective flow. We uncover a surprising two-step transition scenario with two different critical thresholds for the hot bath temperature, a first one where convection kicks but gravity hinders heat transport, and a second critical temperature where a percolation transition of streamlines connecting the hot and cold baths triggers efficient convective heat transport. We also address numerically the efficiency of boundary heat baths to dissipate the energy provided by a bulk driving mechanism. As a bonus track, we depart from the hard disks model to study anomalous transport in a related hard-particle system, the 1d diatomic hard-point gas. We show unambiguously that the universality conjectured for anomalous transport in 1d breaks down for this model, calling into question recent theoretical predictions and offering a new perspective on anomalous transport in low dimensions. Our results show how carefully-crafted numerical simulations Dedicated to Joel L. Lebowitz to celebrate his key role as leading editor of the Journal of Statistical Physics.

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“…8,23 The exact solution [24][25][26] of the Percus-Yevick (PY) integral equation 27 leads to explicit expressions for Z by different thermodynamic routes. Specifically, the virial (PY-v), compressibility (PY-c), and chemical-potential (PY-µ) routes in the PY approximation have a common structure, [24][25][26][28][29][30]…”

Section: A Equation Of State Of Multicomponent Hard-sphere Fluidsmentioning

confidence: 99%

“…Given that the PY-µ route is slightly more accurate than the PY-v one, 29,30 an alternative interpolation formula is…”

Section: A Equation Of State Of Multicomponent Hard-sphere Fluidsmentioning

confidence: 99%

Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures

Heyes

Santos

2018

The Journal of Chemical Physics

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A detailed comparison between the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state of hard-sphere mixtures is made with Molecular Dynamics (MD) simulations of the same compositions. The Labík and Smith simulation technique [S. Labík and W. R. Smith, Mol. Simul. 12, 23-31 (1994)] was used to implement the Widom particle insertion method to calculate the excess chemical potential, βμ, of a test particle of variable diameter, σ, immersed in a hard-sphere fluid mixture with different compositions and values of the packing fraction, η. Use is made of the fact that the only polynomial representation of βμ which is consistent with the limits σ → 0 and σ → ∞ has to be of the cubic form, i.e., c(η)+c¯(η)σ/M+c¯(η)(σ/M)+c¯(η)(σ/M), where M is the first moment of the distribution. The first two coefficients, c(η) and c¯(η), are known analytically, while c¯(η) and c¯(η) were obtained by fitting the MD data to this expression. This in turn provides a method to determine the excess free energy per particle, βa, in terms of c¯, c¯, and the compressibility factor, Z. Very good agreement between the BMCSL formulas and the MD data is found for βμ, Z, and βa for binary mixtures and continuous particle size distributions with the top-hat analytic form. However, the BMCSL theory typically slightly underestimates the simulation values, especially for Z, differences which the Boublík-Carnahan-Starling-Kolafa formulas and an interpolation between two Percus-Yevick routes capture well in different ranges of the system parameter space.

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Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres

Cited by 22 publications

References 31 publications

Chemical-potential route for multicomponent fluids

Chemical-potential route for multicomponent fluids

Simulations of Transport in Hard Particle Systems

Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures

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