Linear stability analysis of evaporating falling liquid films

Mohamed, Hammam; Biancofiore, Luca

doi:10.1016/j.ijmultiphaseflow.2020.103354

Cited by 6 publications

(6 citation statements)

References 46 publications

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“…(v) K represents the nonequilibrium parameter, which measures the degree of departure from equilibrium for the liquid−air interface. 68,69 (vi) Da is the Damkoḧler number and it measures the ratio of particle deposition rate to particle diffusion rate. 52 (vii) Pe is the Peclet number, which quantifies the balance between convection and diffusion of particle concentration.…”

Section: ■ Mathematical Modelmentioning

confidence: 99%

Numerical Analysis of the Dispersion and Deposition of Particles in Evaporating Sessile Droplets

Erdem,

Denner,

Biancofiore

2024

Langmuir

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Section: ■ Mathematical Modelmentioning

confidence: 99%

Numerical Analysis of the Dispersion and Deposition of Particles in Evaporating Sessile Droplets

Erdem,

Denner,

Biancofiore

2024

Langmuir

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“…Finally, there exist a plethora of applications that involve volatile liquid films falling down a heated surface. The instabilities induced by thermocapillary forces (S-mode) or vapour recoil (E-mode) were only examined in the 2-D configurations in the classical Orr-Sommerfeld problem (Mohamed & Biancofiore 2020) or in the long-wave expansion regime (Mohamed, Dallaston & Biancofiore 2021). The analysis of the effect of spanwise confinement on this kind of instabilities is of great benefit due to the intrinsic spanwise nature of the thermal instabilities.…”

Section: Future Workmentioning

confidence: 99%

“…The evolution equation can be utilised to obtain a dispersion relation of the temporal amplification rate in the regions of small wavenumbers and weak inertia. Various physical effects were considered while studying the local stability of falling films such as heating and phase change (Mohamed & Biancofiore 2020), shearing gas (Lavalle et al 2019) and flexible inclined surface (Alexander, Kirk & Papageorgiou 2020). For the wide range of mathematical approaches and physical effects considered while studying the interface evolution and local stability of falling films, refer to the reviews by Oron, Davis & Bankoff (1997), Craster & Matar (2009) and Kalliadasis et al (2012).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The effect of side walls on the stability of falling films

Mohamed¹,

Sesterhenn²,

Biancofiore³

2023

J. Fluid Mech.

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We study the influence of side walls on the stability of falling liquid films. We combine a temporal biglobal stability analysis based on the linearised Navier–Stokes equations with experiments measuring the spatial growth rate of sinusoidal waves flowing downstream an inclined channel. Very good agreement was found when comparing the theoretical and experimental results. Strong lateral confinement of the channel stabilises the flow. In the wavenumber-Reynolds number space, the instability region experiences a fragmentation due to selective damping of moderate wavenumbers. For this range of parameters, the three-dimensional confined problem shows several prominent stability modes which are classified into two categories, the well-known Kapitza hydrodynamic instability mode (H-mode) and a new unstable mode, we refer to it as wall-mode (W-mode). The two mode types are stabilised differently, where the H-modes are stabilised at small wavenumbers, while the W-modes experience stabilisation at high wavenumbers, and at sufficiently small channel widths, only the W-mode is observed. The reason behind the unique H-modes stabilisation is that they become analogous to waveguide modes, which can not propagate below a certain cut-off wavenumber. The spatial structure of the eigenmodes experiences significant restructuring at wavenumbers smaller than the most damped wavenumber. The mode switching preserves the spatial symmetry of the unstable mode.

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“…26 Also, these equations are valid for only particular systems and climate conditions like those when the measurements were made. Mohamed and Biancofiore (2020) 31 utilized kinetic energy theory models to calculate the evaporation rate.…”

Section: Introductionmentioning

confidence: 99%

An experimental investigation of the potential of empirical correlations derived based on Dalton’s law and similarity theory to predict evaporation rate from still water surface

Aldarabseh

Merati

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper investigates applicability of two approaches (similarity theory and Dalton’s law) in predicting evaporation rate. Results showed that conventional Dalton’s based models could not be used to predict evaporation rate at all convection regimes. New formula as a function of vapor density difference was developed to predict evaporation rate at natural turbulent convection. However, it cannot be able to get an acceptable result. Another two formulas were developed to predict evaporation rate at forced and mixed convection regimes after considering the nonlinear relationship between evaporation rate and vapor pressure difference. Evaporation rate is proportional to exponent (n) of partial vapor pressure difference. This exponent was written as a function of higher-order polynomial of air velocity to get a good match between experimental results and predicted value, and satisfactory results were achieved. Similarity theory is an analogy between heat and mass transfer method used to predict evaporation rate from still free water surface. Results show that evaporation rate obtained from similarity method is much larger than actual evaporation rate. Similarity theory considers the effect of vapor density difference. It can be observed that experimental and similarity method results agree at natural turbulent convection. It is noteworthy that similarity theory cannot predict the evaporation rate from still water surface at forced convection. In this convection regime, evaporated water surface is not completely smooth, which violates the assumption of the similarity theory. Nonlinear regression analysis was conducted to evaluate empirical correlation of Sherwood number for mixed convection under turbulent conditions with the exponent n as a logarithmic function of the ratio(Grm/〖Re〗^2 ), then derived new formula that can be used to evaluate evaporation rate at mixed convection regime, and results are in good agreement with experimental results. Laboratory measurements are made using large wave tank-wind tunnel combination in which wind speed is controlled.

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Linear stability analysis of evaporating falling liquid films

Cited by 6 publications

References 46 publications

Numerical Analysis of the Dispersion and Deposition of Particles in Evaporating Sessile Droplets

Numerical Analysis of the Dispersion and Deposition of Particles in Evaporating Sessile Droplets

The effect of side walls on the stability of falling films

An experimental investigation of the potential of empirical correlations derived based on Dalton’s law and similarity theory to predict evaporation rate from still water surface

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