Deviations from classical droplet evaporation theory

Finneran, Joshua; Garner, Colin P.; Nadal, François

doi:10.1098/rspa.2021.0078

Cited by 16 publications

(15 citation statements)

References 44 publications

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“…When , both (2.11) and (2.13) can be significantly simplified, and one obtains In the case where , and , (2.16) can be further simplified to recover the diffusion-dominated boundary condition (Finneran et al. 2021): …”

Section: Formulation Of the Mixed Boundary Conditionsmentioning

confidence: 99%

“…small Eckert number), constant fluids properties and in the absence of the Soret/Dufour effect and droplet heating, we obtain the following classical formulation of the problem (Spalding 1979; Abramzon & Sirignano 1989; Finneran et al. 2021): where and are the rescaled droplet size and time, respectively, is the Lewis number, is the thermal conductivity and .…”

Section: Quasi-steady Droplet Evaporationmentioning

confidence: 99%

“…However, the paradoxical assumption of the local thermodynamic equilibrium at the interface (net evaporation can occur only when the interface region is out of equilibrium) persists and is still widely adopted in recent theoretical and experimental work (Lu et al. 2017; Finneran, Garner & Nadal 2021). The local thermodynamic equilibrium assumption allows for the determination of the vapour partial pressure in the close vicinity of the droplet surface (hence the vapour concentration), based on the liquid surface temperature.…”

Section: Introductionmentioning

confidence: 99%

“…Over the years, continued efforts have been made to correct for some of the assumptions made by Maxwell, such as the quasi-steady (QS) gas phase, negligible internal and external flow (including the Stefan flow) and negligible droplet heating, as reviewed in detail in the literature (Sazhin 2006;Sirignano 2010). However, the paradoxical assumption of the local thermodynamic equilibrium at the interface (net evaporation can occur only when the interface region is out of equilibrium) persists and is still widely adopted in recent theoretical and experimental work (Lu et al 2017;Finneran, Garner & Nadal 2021). The local thermodynamic equilibrium assumption allows for the determination of the vapour partial pressure in the close vicinity of the droplet surface (hence the vapour concentration), based on the liquid surface temperature.…”

Section: Introductionmentioning

confidence: 99%

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Droplet evaporation in inert gases

Zhao

Nadal²

2023

J. Fluid Mech.

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A general mixed kinetic-diffusion boundary condition is formulated to account for the out-of-equilibrium kinetics in the Knudsen layer. The mixed boundary condition is used to investigate the problem of quasi-steady evaporation of a droplet in an infinite domain containing inert gases. The widely adopted local thermodynamic equilibrium assumption is found to be the limiting case of infinitely large kinetic Péclet number ${{Pe}_k}$ , and it introduces significant error for ${{Pe}_k} \leqslant O(10)$ , which corresponds to a typical droplet radius $a$ of a few micrometres or smaller. When compared with experimental data, solutions based on the mixed boundary condition, which take into account the temperature jump across the Knudsen layer, better predict the time evolution of $a$ than the classical $D^2$ -law (i.e. $a^2 \propto t$ , where $t$ denotes time). In the slow evaporation limit, an analytical solution is obtained by linearising the full formulation about the equilibrium condition, which shows that the $D^2$ -law can be recovered only in the large ${{Pe}_k}$ limit. For small ${{Pe}_k}$ , where the process is dominated by kinetics, a linear relation, i.e. $a \propto t$ , emerges. When the gas phase density approaches the liquid density (e.g. at high-pressure or low-temperature conditions), the increase in the chemical potential of the liquid phase due to the presence of inert gases needs to be accounted for when formulating the mixed boundary condition, an effect largely ignored in the literature so far.

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Section: Formulation Of the Mixed Boundary Conditionsmentioning

confidence: 99%

Section: Quasi-steady Droplet Evaporationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Droplet evaporation in inert gases

Zhao

Nadal²

2023

J. Fluid Mech.

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“…An extra simplification is made in Eq. (2) by neglecting the laminar flow induced by evaporation itself, the so-called Stefan flow, see for example [35] , [41] . The presence of dissolved species in the droplet, which may modify the thermodynamics of water, is also neglected, as well as the variation of physical quantity of air as function of humidity.…”

Section: Transport Of Droplets Evaporation and Sedimentationmentioning

confidence: 99%

Respiratory pandemic and indoor aeraulics of classrooms

Carlotti

Massoulié

Morez

et al. 2022

Building and Environment

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Respiratory pandemics, such as COVID19, may be transmitted by several modes. The present work focuses on the transmission through small droplets released by people from their mouth by breathing, speaking, coughing, sneering, and possibly aspirated by other people around through their respiration. An analysis of droplet evolution in simplified situations shows that the droplets reach very quickly a quasi-equilibrium temperature before encompassing an isothermal evaporation process. The removal of droplets from suspension is thus piloted by balance between evaporation and sedimentation. It is shown that ambient relative humidity is a major factor influencing the lifetime of droplets and the distance they may travel. As a consequence, and independently of any other health consideration linked to ambient humidity, it is seen that a dry air is a favourable factor for limiting risk of contamination from COVID19. Further investigation is made using computational fluid dynamics (CFD) in a classroom geometry. Several ventilation strategies are investigated: classical regulatory mechanical ventilation, open window natural ventilation and displacement natural ventilation. Ventilation has several effects which influence contamination risk: by introducing fresh air, it reduces droplet concentration; humidity released by human occupants is also limited. However, these effects are not uniform in space, and depend on ventilation strategy. Application of a dose–effect model calibrated for COVID19 to CFD results allows to estimate contamination risk. It is shown that contamination risk is higher for regulatory mechanical ventilation, and may be reduced, using natural ventilation in the absence of wind, by a factor 2.3 to nearly 3 when the teacher is sick, and by a factor 6 to 500 when a student is sick. In the presence of wind, the reduction factor is as high as 13 when the teacher is sick and 17 when a student is sick.

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Heating and Evaporation of Mono-component Droplets

Sazhin

2022

Droplets and Sprays: Simple Models of Complex Processes

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Deviations from classical droplet evaporation theory

Cited by 16 publications

References 44 publications

Droplet evaporation in inert gases

Droplet evaporation in inert gases

Respiratory pandemic and indoor aeraulics of classrooms

Heating and Evaporation of Mono-component Droplets

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