Homogeneous nucleation and growth in simple fluids. I. Fundamental issues and free energy surfaces of bubble and droplet formation

Uline, Mark J.; Torabi, Korosh; Corti, David S.

doi:10.1063/1.3499313

Cited by 17 publications

(15 citation statements)

References 34 publications

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“…Previous studies have investigated the minimum work for a bubble formation with two variables, taking into account bubble compressibility [41][42][43][44][45][46]. Here we use the two variables r and P g .…”

Section: B Free Energy For Bubble Formation and The Poynting Correctionmentioning

confidence: 99%

“…In bubble nucleation, additional detail in the treatment of the process is required, in comparison to droplet nucleation, because of the variable vapor pressure and density in bubbles as they grow [41][42][43][44][45][46]. The vapor pressure in bubbles varies as they grow and has a significant effect on their growth rates and on the pre-exponential factor in the CNT formula for the nucleation rate.…”

Section: Introductionmentioning

confidence: 99%

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Simple improvements to classical bubble nucleation models

Tanaka

Angélil

et al. 2015

Phys. Rev. E

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We revisit classical nucleation theory (CNT) for the homogeneous bubble nucleation rate and improve the classical formula using a correct prefactor in the nucleation rate. Most of the previous theoretical studies have used the constant prefactor determined by the bubble growth due to the evaporation process from the bubble surface. However, the growth of bubbles is also regulated by the thermal conduction, the viscosity, and the inertia of liquid motion. These effects can decrease the prefactor significantly, especially when the liquid pressure is much smaller than the equilibrium one. The deviation in the nucleation rate between the improved formula and the CNT can be as large as several orders of magnitude. Our improved, accurate prefactor and recent advances in molecular dynamics simulations and laboratory experiments for argon bubble nucleation enable us to precisely constrain the free energy barrier for bubble nucleation. Assuming the correction to the CNT free energy is of the functional form suggested by Tolman, the precise evaluations of the free energy barriers suggest the Tolman length is 0.3σ independently of the temperature for argon bubble nucleation, where σ is the unit length of the Lennard-Jones potential. With this Tolman correction and our prefactor one gets accurate bubble nucleation rate predictions in the parameter range probed by current experiments and molecular dynamics simulations.

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Section: B Free Energy For Bubble Formation and The Poynting Correctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simple improvements to classical bubble nucleation models

Tanaka

Angélil

et al. 2015

Phys. Rev. E

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“…In other words, for the critical nucleus, the solution of the constrained system is equivalent to that for the nonconstrined system. Note that κ = 0 in this work corresponds to the situations that κ equals chemical potential in the work by Uline et al, 42,43 in which In general, the use of constraints in the constrained LDFT affects the free energy cost for the formation of a small nucleus, although the bias on our system introduced by the constraint must be very small since the differences are very small for both κ[N 0 L − N L ] and κ[N 0 S − N S ]. The constraint introduces an undesirable bias which depends on the nucleus size.…”

Section: B Equivalence Between the Constrained System And The Unconsmentioning

confidence: 93%

Physical basis for constrained lattice density functional theory

Men

Zhang

2012

The Journal of Chemical Physics

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To study nucleation phenomena in an open system, a constrained lattice density functional theory (LDFT) method has been developed before to identify the unstable directions of grand potential functional and to stabilize nuclei by imposing a suitable constraint. In this work, we answer several questions about the method on a fundamental level, and give a firmer basis for the constrained LDFT method. First, we demonstrate that the nucleus structure and free energy barrier from a volume constraint method are equivalent to those from a surface constraint method. Then, we show that for the critical nucleus, the constrained LDFT method in fact produces a bias-free solution for both the nucleus structure and nucleation barrier. Finally, we give a physical interpretation of the Lagrange multiplier in the constraint method, which provides the generalized force to stabilize a nucleus in an open system. The Lagrange multiplier is found to consist of two parts: part I of the constraint produces an effective pressure, and part II imposes a constraint to counteract the supersaturation.

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“…The residual or excess Helmholtz free energy that follows from the CS equation of state (

) for a pure component hard sphere fluid is given by [ 8 , 17 , 18 ]

where

is the Boltzmann constant,

is the absolute temperature, V is the volume of the system,

is the number density, and

is the packing fraction. To use Equation (4) to model liquid crystals, Lee redefined the packing fraction to be

.…”

Section: Theoretical Methodsmentioning

confidence: 99%

On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Ohadi

Corti

Uline

2021

Entropy

Self Cite

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Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

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Homogeneous nucleation and growth in simple fluids. I. Fundamental issues and free energy surfaces of bubble and droplet formation

Cited by 17 publications

References 34 publications

Simple improvements to classical bubble nucleation models

Simple improvements to classical bubble nucleation models

Physical basis for constrained lattice density functional theory

On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

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