Pattern formation in the flow of thin films down an incline: Constant flux configuration

Kondic, Lou; Diez, Javier A.

doi:10.1063/1.1409965

Cited by 92 publications

(122 citation statements)

References 33 publications

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“…This paper presents a detailed analysis of the Riemann problem where we identify several types of solutions that emerge, including classical shock solutions, rarefaction waves and singular shocks. Such solutions have been shown to exist for other fluid systems in the literature such as the flow of clear, thin films down an incline [12,16]. One-dimensional solutions show that the flow develops a traveling-wave solution given by a compressive shock, which moves with constant velocity; the latter is given by a characteristic speed which satisfies the Rankine-Hugoniot jump condition.…”

Section: Introductionmentioning

confidence: 91%

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Hyperbolic systems of conservation laws in gravity-driven, particle-laden thin-film flows

Mavromoustaki¹,

Bertozzi²

2014

J Eng Math

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Our study focuses on gravity-driven, particle-laden flows which are pertinent to a wide range of industrial and geophysical settings in which transport of suspensions occur. In the present study we employ a previously derived model by Murisic et al. (Physica D: Nonlinear Phenomena, 240, 2011) which uses the lubrication approximation to describe particle-laden films on an incline. The model consists of a coupled system of hyperbolic conservation laws for the interface position and the particle concentration. While it has been shown that the model compares well quantitatively with experiments, it lacks analysis. The objectives of this paper focus on the study of the Riemann problem for this system of conservation laws and how the results relate to experiments. We investigate the governing system analytically and numerically; the equations exhibit rich mathematical structures including double-shock wave solutions, rarefaction waves and singular shocks.

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Section: Introductionmentioning

confidence: 91%

“…We note that the exact shape of the profile depends on the initial particle concentration and the relation employed to describe the effective viscosity of the slurry. (15) and (16). The solutions depict the relationship of the particle volume fractionφ as a function of the rescaled normal direction z * .…”

Section: Equilibrium Modelmentioning

confidence: 99%

Hyperbolic systems of conservation laws in gravity-driven, particle-laden thin-film flows

Mavromoustaki¹,

Bertozzi²

2014

J Eng Math

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“…Kondic and Diez [6] investigated the affect of small perturbations in the substrate on a stable front; the resulting rivulet formation was found to be very similar to that observed when contact line perturbations are applied to the advancing front. The use of striped substrates in the control of rivulet spacing has also been investigated, Kondic and Diez [7].…”

Section: Introductionmentioning

confidence: 73%

“…The initial film profile consists of a front perturbed with a superposition of N modes with random length, l j ∈ [−0.2, 0.2], and differing wavelength, λ 0,j , as in [6] via:…”

Section: Problem Formulationmentioning

confidence: 99%

“…The fluid is considered to be incompressible with constant density, ρ, and viscosity, µ, and variable surface tension, σ, given by σ = σ 0σ = σ 0 + τ X with σ 0 the value of surface tension at X = 0 and τ (= ∂σ/∂X) a constant surface tension gradient [4]. The film is considered to be fully wetting; a precursor film of thickness, H * , located ahead of the advancing front, alleviates the singularity associated with the attendant contact line [6,8,9]. The long-wave approximation is invoked on the assumption that the asymptotic film thickness, H 0 , is small compared to the capillary length,…”

Section: Introductionmentioning

confidence: 99%

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Gravity-driven thin film flow: The influence of topography and surface tension gradient on rivulet formation

Slade¹,

Veremieiev²,

Lee³

et al. 2013

Chemical Engineering and Processing: Process Intensification

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. (2013) 'Gravity-driven thin lm ow : the in uence of topography and surface tension gradient on rivulet formation.', Chemical engineering and processing : process intensi cation., 68 . pp. 7-12. Further information on publisher's website:http://dx.doi.org/10.1016/j.cep.2012.07.003Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Chemical Engineering and Processing: Process Intensi cation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Chemical Engineering and Processing: Process Intensi cation, 68, June 2013, 10.1016/j.cep.2012.07.003. 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-pro t 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 evolution of an advancing fluid front formed by a gravity-driven thin film flowing down a planar substrate is considered, with particular reference to the presence of Marangoni stresses and/or surface topography. The system is modelled using lubrication theory and solved via an efficient, adaptive multigrid method that incorporates automatic, errorcontrolled grid refinement/derefinement and time stepping. The detailed three dimensional numerical results obtained reveal that, for the problems investigated, while both of the above features affect the merger of rivulets by either delaying or promoting the same, topography influences the direction of growth.

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Waves in a rivulet falling down an inclined cylinder

2020

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In the long‐wave approximation, a theoretical model is developed to describe waves in a rivulet flowing down the lower surface of an inclined cylinder. The model equations are derived by the weighted residual method by projecting the Navier–Stokes equations onto the constructed system of basic orthogonal polynomials. The simplest case of quasi‐two‐dimensional waves is studied in detail. The stability of the rivulet flow is analyzed and dispersion dependences for linear waves are obtained. The characteristics of nonlinear steady‐state traveling waves have been obtained by numerical method for the first time, and the spatial development of forced waves has been studied. The results of calculations are in good agreement with the available experimental data for various liquids in a wide range of parameters.

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Pattern formation in the flow of thin films down an incline: Constant flux configuration

Cited by 92 publications

References 33 publications

Hyperbolic systems of conservation laws in gravity-driven, particle-laden thin-film flows

Hyperbolic systems of conservation laws in gravity-driven, particle-laden thin-film flows

Gravity-driven thin film flow: The influence of topography and surface tension gradient on rivulet formation

Waves in a rivulet falling down an inclined cylinder

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