Free-surface thin-film flows over topography: influence of inertia and viscoelasticity

Saprykin, Sergey; Koopmans, R. J.; Kalliadasis, Serafim

doi:10.1017/s0022112007004752

Cited by 47 publications

(43 citation statements)

References 29 publications

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“…The mathematical formulation of the latter, in which the resulting equations are expressed in terms of the film thickness and mean flow rate, can be traced back to Shkadov 1967Shkadov /1968, who used it to predict solitary waves in thin films on flat substrates. Recently, Saprykin, Koopmans and Kalliadasis 2007 [34] extended Shkadov's idea to explore the influence of inertia and viscoelasticity on thin film flow over step-down topography taken to be in vertical alignment. A key feature of the integral-boundary-layer approximation is the assumption that the velocity profile across the film has a self-similar parabolic form.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Inertial thin film flow on planar surfaces featuring topography

et al. 2010

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“…is the unit normal vector pointing outward from the free surface; K = −∇·n is twice the mean curvature of the free surface that, following for example Saprykin et al (2007), is taken to be positive when the surface is concave upwards; P A is the pressure of the surrounding air. In what follows the pressure variable is shifted, P → P + P A , to denote instead a reference pressure.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Indeed, not only was lubrication theory shown to produce accurate results in regions of parameter space where it is not strictly valid, the authors were able to quantify the expected error in terms of Reynolds number and topography height/depth by a detailed comparison with complementary finite element solutions of the full Navier-Stokes equations for the case of spanwise topography. Veremieiev et al (2010) recently considered the same problem; this time undertaking a detailed investigation of the effect of inertia using a model based on depth-averaging the governing unsteady Navier-Stokes equations, a method akin to the integral boundary layer approximation developed by Shkadov (1967Shkadov ( , 1968 for flow over flat substrates and subsequently utilised for the case when surface topography is present by Trifonov (2004) and Saprykin et al (2007). Not only were they able to isolate and identify the role of inertia, the results obtained lend further support to the suitability of the long-wave approximation for resolving gravity-driven flows when the topography depth/height to film thickness ratio is sufficiently small and the Reynolds number is not too large.…”

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confidence: 99%

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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“…Khayat [17] presented transient results using the lubrication approximation for a viscoelastic liquid film following the Oldroyd-B model, which is extruded in the direction of a wall including smooth topographic features. More recently, Saprykin et al [18] examined the combined influence of inertia and viscoelasticity for steady and transient thin film flows when the substrate is an isolated step. In their model, they employed the long-wave approximation and assumed that De 1 in order to derive explicit expressions for the polymeric stresses in terms of the components of the rate of strain tensor.…”

Section: Introductionmentioning

confidence: 99%