Stability of a viscous liquid film flowing down a periodic surface

Trifonov, Yu. Ya.

doi:10.1016/j.ijmultiphaseflow.2007.05.004

Cited by 73 publications

(37 citation statements)

References 17 publications

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“…Recent experiments, however, in which the flow is taken to be essentially two-dimensional in a streamwise cross-sectional plane, have demonstrated that there is a strong coupling between inertia and topography for the case of gravity-driven flow over surfaces containing spanwise periodic rectangular ; Argyriadi, Vlachogiannis and Bontozoglou, 2006) or wavy (Wierschem, Lepski and Aksel, 2005) features. The experimentally-observed rise in critical Reynolds number with increasing topography steepness that occurs has also been predicted theoretically by several authors, see for example , Trifonov (2007) and Dávalos-Orozco (2007; conversely, it has been reported recently that undulating surfaces may have a destabilising influence on the flow if the surface tension is sufficiently high (Heining and The present work has two main strands in relation to gravity-driven film flow at finite Reynolds number in the presence of an electric field normal to it: two-dimensional flow over dis-crete steep and smooth periodically varying spanwise topography revisited; three-dimensional flow over localised steep topography, the exploration of which is considered for the first time. In both cases, the hydrodynamics is modelled using the approach of Veremieiev et al (2010) and the governing equation set solved numerically.…”

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confidence: 81%

Electrified thin film flow at finite Reynolds number on planar substrates featuring topography

Veremieiev

Thompson

Scholle

et al. 2012

International Journal of Multiphase Flow

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. (2012) 'Electried thin lm ow at nite Reynolds number on planar substrates featuring topography.', International journal of multiphase ow., 44 . pp. 48-69. Further information on publisher's website:http://dx.doi.org/10.1016/j.ijmultiphaseow.2012.03.010Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in International Journal of Multiphase Flow. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in International Journal of Multiphase Flow, 44, September 2012, 10.1016/j.ijmultiphaseow.2012 Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe flow of a gravity-driven thin liquid film over a substrate containing topography, in the presence of a normal electric field, is investigated. The liquid is assumed to be a perfect conductor and the air above it a perfect dielectric. Of particular interest is the interplay between inertia, for finite values of the Reynolds number, Re, and electric field strength, expressed in terms of the Weber number, We, on the resultant free-surface disturbance away from planarity. The hydrodynamics of the film are modelled via a depth-averaged form of the Navier-Stokes equations which is coupled to a Fourier series separable solution of Laplace's equation for the electric potential: detailed steady-state solutions of the coupled equation set are obtained numerically.The case of two-dimensional flow over different forms of discrete and periodically varying spanwise topography is explored. In the case of the familiar free-surface capillary peaks and depressions that arise for steep topography, and become more pronounced with increasing Re, greater electric field strength affects them differently. In particular, it is found that for topography heights commensurate with the long-wave approximation: (i) the capillary ridge associated with a step-down topography at first increases before decreasing, both monotonically, with increasing We; (ii) the free-surface hump which arises at a step-up topography continues to increase monotonically with increasing We, the increase achieved being smaller the larger the value of Re.A series of results for the more practically relevant problem of three-dimensional film flow over substrate containing a localised squa...

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confidence: 81%

Electrified thin film flow at finite Reynolds number on planar substrates featuring topography

Veremieiev

Thompson

Scholle

et al. 2012

International Journal of Multiphase Flow

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“…Indeed, it has been shown (Trifonov 2007;Nguyen & Bontozoglou 2011) that the periodic, steady deformation of the free surface imposed by the wall, becomes generally more pronounced as inclination increases. It is also consistent with the enhanced stability of the orthogonal wall.…”

Section: Discussionmentioning

confidence: 99%

“…As a consequence of all of the above (and as implicitly suggested by Trifonov (2007)) it might be of interest to check the following potential rule of thumb: the critical Reynolds, Re cr , be estimated to leading-order by the classical result of longwave analysis for a flat wall, taking into account not only the first, but also the second term in the expansion, which introduces a finite-wavelength effect. Then, the role of periodic corrugations may be roughly accounted for by an appropriate choice of the disturbance wavelength.…”

Section: Investigation Of the Primary Instability Thresholdmentioning

confidence: 99%

“…The paper by Trifonov (2007) is unique, in that it solves the steady version of the full Navier-Stokes equations for a vertical sinusoidal wall, and uses Floquet theory to predict the linear stability of these solutions. His most interesting prediction is that the flow may remain stable even up to Re = 10-20 with sufficiently steep corrugations in a range L b = 1-5, and that stability also depends on surface tension (Kapitza number).…”

Section: Introductionmentioning

confidence: 99%

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Experimental evidence for a short-wave global mode in film flow along periodic corrugations

2013

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The primary instability of liquid film flow along periodically corrugated substrates is studied experimentally. Two different wall shapes, of the same wavelength and height, are tested for a wide range of inclinations. It is found that, beyond a specific inclination, a new instability mode occurs before the classical, convective, long-wave one. This is a short, travelling wave, which is highly regular and persistently twodimensional, and appears to be a global mode. The exact shape of the corrugations has a leading-order effect on the inclination at which the new mode appears and on its wavelength at inception. Compared with the behaviour of film flow on a flat substrate, the presently tested periodic walls are found to delay very significantly, but each one to a different extent, the onset of the primary instability. This delay increases with inclination, and presents a distinct discontinuity when transition from the long-to the short-wave mode takes place.

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“…Adaptive time-stepping is performed by keeping the LTE for u within a specified tolerance that in practice automatically restricts the LTE for v and h and provides a means of increasing the time step in a controlled manner. The LTE for u at the predictor stage can be expressed via a Taylor series expansion of equation (44) in the form:…”

Section: Temporal Discretisationmentioning

confidence: 99%

Inertial thin film flow on planar surfaces featuring topography

et al. 2010

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Published paperAbstract A range of problems is investigated, involving the gravity-driven inertial flow of a thin viscous liquid film over a planar surface containing topographical features, modelled via a depth-averaged form of the governing unsteady Navier-Stokes equations. The discrete analogue of the resulting coupled equation set, employing a staggered mesh arrangement for the dependent variables, is solved accurately using an efficient Full Approximation Storage (FAS) algorithm and Full Multigrid (FMG) technique together with adaptive timestepping and proper treatment of the nonlinear convective terms. A unique, comprehensive set of results is presented for both one-and two-dimensional topographical features, and errors quantified via detailed comparisons drawn with complementary experimental data and predictions from finite element analyses where they exist. It is found in the case of one-dimensional (spanwise) topography that for small Reynolds number and shallow/short features the depth-averaged form produces results that are in close agreement with corresponding finite element solutions of the full free-surface problem. For the case of flow over two-dimensional (localised) topography the free-surface disturbance observed is influenced significantly by the presence of inertia. It leads, as in the case of spanwise topography, to an increase in the magnitude and severity of the capillary ridge/trough patterns which form.

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Stability of a viscous liquid film flowing down a periodic surface

Cited by 73 publications

References 17 publications

Electrified thin film flow at finite Reynolds number on planar substrates featuring topography

Electrified thin film flow at finite Reynolds number on planar substrates featuring topography

Experimental evidence for a short-wave global mode in film flow along periodic corrugations

Inertial thin film flow on planar surfaces featuring topography

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