Spatial stability of a liquid film on a rotating disk

Елисеев, В. И.

doi:10.1007/bf00905629

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…They found that axisymmetric perturbations have the largest amplification factors and Coriolis forces exert a stabilizing influence. Eliseev (1983), who examined the linear stability of timeperiodic perturbations, showed that the wavelength of the perturbation determines the radial domain of the instability, which becomes wider with increasing wavelength. The range of unstable wavenumbers approaches that for the falling film case with increasing radius.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric wave regimes in viscous liquid film flow over a spinning disk

2003

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Finite-amplitude capillary waves, which can accompany the axisymmetric flow of a thin viscous film over a rotating disk, are considered. A system of approximate evolution equations for the film thickness and volumetric flow rates in the radial and azimuthal directions is derived, which contains two similarity parameters. In order to inspire confidence in this model, its steady solutions and their linear stability characteristics are compared to those of the full Navier–Stokes equations. Localized equations, which account for the presence of inertial, capillary, centrifugal and Coriolis forces, are obtained via truncation of the approximate system. Periodic solutions of these equations are then determined and found to be similar to those observed experimentally. Our results suggest that the steady quasi-periodic waves with largest amplitude compare well with experimentally observed wave profiles.

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Section: Introductionmentioning

confidence: 99%

Axisymmetric wave regimes in viscous liquid film flow over a spinning disk

2003

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“…perturbations have the largest growth rates; they also found Coriolis forces to be stabilizing. Eliseev (1983) showed that the width of the linear instability domain increases with wavelength for time-periodic disturbances and approaches that for falling fi lms with increasing radius. Sisoev and Shkadov (1987) considered the limit of large E and examined the linear stability of axisymmetric perturbations for locally uniform fl ow.…”

Section: Steady Solutions Linear Stability and Lubrication Theorymentioning

confidence: 99%

The Flow of Thin Liquid Films Over Spinning Discs

2008

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Les écoulements de fi lms liquides minces continus au-dessus de disques rotatifs présentent des avantages technologiques; en effet, l'épaisseur du fi lm peut être contrôlée par la vitesse de rotation et elle peut devenir très mince, donnant de très bonnes caractéristiques de transfert de chaleur et de matière. On présente une étude de la recherche menée sur de tels écoulements. Les principaux résultats des études expérimentales et de modélisation les plus pertinentes sont présentés. Ceux-ci démontrent que l'écoulement s'accompagne de dynamiques complexes, dont la formation d'ondes de grande amplitude. On a trouvé que ces ondes amélioraient les vitesses de transfert de matière et le mélange menant à l'intensifi cation des procédés. Des progrès importants tant dans la modélisation que l'expérimentation ont été effectués pour comprendre de manière fondamentale la dynamique des ondes et son exploitation pour des applications technologiques en milieu industriel. Cet article se termine par un résumé de l'état de l'art et des suggestions de nouvelles pistes de recherche.

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“…Steady flow in the frame of the boundary layer approximation was considered by Dorfman12 and Sisoev et al ,13 where transitions from arbitrary inlet film flow to the Nusselt solution were computed. Analysis of the linear stability of the steady axisymmetric flow was performed using asymptotic methods2, 5, 11, 14 and the full Navier–Stokes equation for finite Eckman numbers 15. 16 The simplest non‐linear evolution equations based on the lubrication approximation for radial velocity were discussed by Emslie et al 17 and recently by Momoniat and Mason,18 where additional references may be found.…”

Section: Introductionmentioning

confidence: 99%

Modelling of film flow over a spinning disk

Sisoev

Matar

Lawrence

2003

J of Chemical Tech & Biotech

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Film flows over a spinning disk are applied to intensify heat and mass transfer processes, which need large contact surfaces between a liquid and surrounding gas. An inherent property of this flow is the formation of waves, whose amplitude may have the same scale as the film thickness. Experimental observations indicate a strong dependence of heat and mass transfer processes on these surface structures, especially in the case of large amplitude waves. This paper reports mathematical modelling of this flow.

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Spatial stability of a liquid film on a rotating disk

Cited by 3 publications

References 5 publications

Axisymmetric wave regimes in viscous liquid film flow over a spinning disk

Axisymmetric wave regimes in viscous liquid film flow over a spinning disk

The Flow of Thin Liquid Films Over Spinning Discs

Modelling of film flow over a spinning disk

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