Instabilities of three-dimensional viscous falling films

Joo, Sang Woo; Davis, Stephen H.

doi:10.1017/s0022112092002489

Cited by 106 publications

(52 citation statements)

References 15 publications

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“…Suslov (2006) developed a more complicated algorithm to compute the absolute-convective stability boundary in the given parameter space. Joo & Davis (1992) analysed instabilities in a falling film using Benney's long-wave evolution equation, and confirmed that the instability is of the convective type. A detailed analysis of the linear stability characteristics of a falling film is given in Kalliadasis et al (2012).…”

Section: Introductionmentioning

confidence: 79%

Absolute and convective instabilities in counter-current gas–liquid film flows

2014

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Absolute and convective instabilities in counter-current gas-liquid film flows. Mechanics, 763, Additional Information: Journal of Fluid• This is the accepted manuscript of an article subsequently published in We consider a thin liquid film flowing down an inclined plate in the presence of a countercurrent turbulent gas. By making appropriate assumptions, Tseluiko & Kalliadasis (2011) developed low-dimensional non-local models for the liquid problem, namely a long-wave model and a weighted integral-boundary-layer model, that incorporate the effect of the turbulent gas. By utilising these models, along with the Orr-Sommerfeld problem formulated using the full governing equations for the liquid phase and associated boundary conditions, we explore the linear stability of the gas-liquid system. In addition, we devise a generalised methodology to investigate absolute and convective instabilities in the nonlocal equations describing the gas-liquid flow. We observe that at low gas flow rates, the system is convectively unstable with the localised disturbances being convected downwards. As the gas flow rate is increased, the instability becomes absolute and localised disturbances spread across the whole domain. As the gas flow rate is further increased, the system again becomes convectively unstable with the localised disturbances propagating upwards. We find that the upper limit of the absolute instability region is close to the 'flooding' point associated with the appearance of large-amplitude standing waves, as obtained in Tseluiko & Kalliadasis (2011), and our analysis can therefore be used to predict the onset of flooding. We also find that an increase in the angle of inclination of the channel requires an increased gas flow rate for the onset of absolute instability. We generally find good agreement between the results obtained using the full equations and the reduced models. Moreover, we find that the weighted integral-boundary-layer model generally provides better agreement with the results for the full equations than the longwave model. Such an analysis is important for understanding the ranges of validity of the reduced model equations. In addition, a comparison of our theoretical predictions with the experiments of Zapke & Kröger (2000a) shows a fairly good agreement. We supplement our stability analysis with time-dependent computations of the linearised weighted integral-boundary-layer model. To provide some insight into the mechanisms of instability, we perform an energy budget analysis.

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Section: Introductionmentioning

confidence: 79%

Absolute and convective instabilities in counter-current gas–liquid film flows

2014

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“…The instability evolves into a nonlinear wavetrain and for heated substrates may lead to film rupture [15]. Transverse instabilities may also be present, leading at long times to a pattern of rivulets with a characteristic transverse wavenumber [16,17]. A recent overview of long wave evolution equations for thin films can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

Thin liquid films on a slightly inclined heated plate

Thiele

Knobloch

2004

Physica D: Nonlinear Phenomena

114

121

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The behavior of a thin liquid film on a uniformly heated substrate is considered. When the substrate is horizontal and the Marangoni number sufficiently large the film breaks up into a periodic array of drops. When the substrate is slightly inclined this drop-like state slides down the substrate. The relation between these states is discussed and their stability properties with respect to longitudinal perturbations are determined. The results shed light on the multiplicity of states accessible to systems of this type and on the possible transitions among them.

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“…Joo and Davis [21] also studied the 3D behaviour of such pure hydrodynamic instabilities. They found that for perturbations in the stream-wise direction the spanwise direction is always unstable and its growth is slow and grows with the Re number.…”

Section: Hydrodynamic Instabilitymentioning

confidence: 99%