Expressions for the Evaporation and Condensation Coefficients in the Hertz-Knudsen Relation

Persad, Aaron H.; Ward, C. A.

doi:10.1021/acs.chemrev.5b00511

Cited by 317 publications

(251 citation statements)

References 255 publications

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“…However, the classical diffusion flow of vapour starts beyond the Knudsen layer. The Hertz-Knudsen-Schrage (HKS) relation (Schrage 1953) can be applied to model the mass flux across the interface, along with the NSF equations in the bulk, provided Kn is sufficiently small (Persad & Ward 2016). Fuchs (1959) obtained a semi-empirical formula to account for the Knudsen layer by matching the free molecular solution, valid at the interface, with the diffusion solution valid at the edge of the Knudsen layer, the width of which is used as a fitting parameter to give a good match for all Kn.…”

Section: Modelling Evaporation and Condensationmentioning

confidence: 99%

Evaporation-driven vapour microflows: analytical solutions from moment methods

2018

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Macroscopic models based on moment equations are developed to describe the transport of mass and energy near the phase boundary between a liquid and its rarefied vapour due to evaporation and hence, in this study, condensation. For evaporation from a spherical droplet, analytic solutions are obtained to the linearised equations from the Navier-Stokes-Fourier, regularised 13-moment and regularised 26-moment frameworks. Results are shown to approach computational solutions to the Boltzmann equation as the number of moments are increased, with good agreement for Knudsen number 1, whilst providing clear insight into non-equilibrium phenomena occurring adjacent to the interface.

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Section: Modelling Evaporation and Condensationmentioning

confidence: 99%

Evaporation-driven vapour microflows: analytical solutions from moment methods

2018

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“…Normally, and are measured at the range of 0.001 to 1 and very close to each other [44][45][46]. is slightly higher than when water is heated to evaporate.…”

Section: Svii Evaporation Enhancement Calculationmentioning

confidence: 66%

Ultra-fast vapor generation by a graphene nano-ratchet: a theoretical and simulation study

Ding

Peng

et al. 2017

Nanoscale

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Vapor generation is of prime importance for a broad range of applications: domestic water heating, desalination and wastewater treatment, etc. However, the natural evaporation is slow and low efficiency. Ratchet effect can give rise to nonzero mass flux under a zero-mean time-dependent drive. In this paper, we proposed a nano-ratchet, multilayer graphene with cone-shaped nanopores (MGCN), to accelerate the vapor generation. By performing molecular dynamics simulations, we found that the air molecules spontaneously transport across MGCN and form a remarkable pressure difference between the two sides of MGCN. Besides, we studied the dependence of pressure difference on the ambient temperature and the geometry of MGCN in detail.By further analysis of the diffusive transport, we identified that the pressure difference relates to the competition between ratchet transport and Knudsen diffusion. The pressure difference could give rise to 15 times enhancement of vapor generation at least, which shows there is a widely potential application of the ratchet effect of MGCN.

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“…This boundary condition is essentially controlled by the evaporation coefficient (see review [9] for the details). A theoretical estimation of this coefficient requires the application of molecular dynamics (MD) methods [1].…”

Section: United Atom Modelmentioning

confidence: 99%

Kinetic and MD modelling of automotive fuel droplets heating and evaporation: recent results

Sazhin

Shishkova

2017

Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems

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Recent results of the investigation of kinetic and molecular dynamics (MD) models for automotive fuel droplet heating and evaporation are summarised. The kinetic model is based on the consideration of the kinetic region in the close vicinity of the surface of the heated and evaporating droplets, where the motion of molecules is described in terms of the Boltzmann equations for vapour components and air, and the hydrodynamic region away from this surface. The effects of finite thermal conductivity and species diffusivity inside the droplets and inelastic collisions in the kinetic region are taken into account. A new self-consistent kinetic model for heating and evaporation of Diesel fuel droplets is briefly described. The values of temperature and vapour densities at the outer boundary of the kinetic region are inferred from the requirement that both heat flux and mass flux of vapour components in the kinetic and hydrodynamic regions in the vicinity of the interface between these regions are equal. At first, the heat and mass fluxes in the hydrodynamic region are calculated based on the values of temperature and vapour density at the surface of the droplet. Then the values of temperature and vapour density at the outer boundary of the kinetic region, obtained following this procedure, are used to calculate the corrected values of hydrodynamic heat and species mass fluxes. The latter in their turn lead to new corrected values of temperature and vapour density at the outer boundary of the kinetic region. It is shown that this process quickly converges and leads to self-consistent values for both heat and mass fluxes. Boundary conditions at the surface of the droplet for kinetic calculations are inferred from the MD calculations. These calculations are based on the observation that methyl (CH3) or methylene (CH2) groups in n-dodecane (approximation of Diesel fuel) molecules can be regarded as separate atom-like structures in a relatively simple United Atom Model. Some results of the application of quantum chemical methods to the estimation of the evaporation/condensation coefficient are discussed. KeywordsDiesel fuel, droplets, heating, evaporation, kinetic modelling. IntroductionIn most applications, including those focused on automotive fuel droplets, the modelling of heating and evaporation processes has been based on the assumption that vapour at the liquid surface is saturated and the problem of evaporation reduces to the analysis of diffusion of vapour from the liquid (droplet) surface to the ambient gas [1]. The limitations of this approximation have been well known for over a century (see the references in [2]). In a number of studies, summarised in [1], the evaporation of n-dodecane C12H26 or a mixture of n-dodecane and pdipropylbenzene C12H18 (approximating alkanes and aromatics in Diesel fuel) was studied and a new model based on a combination of the kinetic and hydrodynamic approaches was developed. In the close vicinity of droplet surfaces (up to one hundred molecular mean free paths), the vapou...

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Expressions for the Evaporation and Condensation Coefficients in the Hertz-Knudsen Relation

Cited by 317 publications

References 255 publications

Evaporation-driven vapour microflows: analytical solutions from moment methods

Evaporation-driven vapour microflows: analytical solutions from moment methods

Ultra-fast vapor generation by a graphene nano-ratchet: a theoretical and simulation study

Kinetic and MD modelling of automotive fuel droplets heating and evaporation: recent results

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