Drag reduction and improvement of material transport in creeping films

Scholle, Markus; Rund, Armin; Aksel, Nuri

doi:10.1007/s00419-005-0414-5

Cited by 32 publications

(13 citation statements)

References 31 publications

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“…Gramlich et al 21 applied a localized heat source at the bottom to modify the capillary ridge by Marangoni forces in the flow over an edge. Scholle et al 22 presented a different approach by varying the topography. They found that particular topographies lead to a drag reduction in Stokes flow which is comparable with the shark-skin effect in turbulent flow.…”

Section: Introductionmentioning

confidence: 99%

Velocity field reconstruction in gravity-driven flow over unknown topography

Heining

2011

Physics of Fluids

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A numerical method for reconstructing the velocity field of a viscous liquid flowing over unknown topography is presented. For a given fluid this procedure allows one to determine the velocity field as well as the topographic structure from the free-surface shape only. First, we confirm the results with previous computations in the thin-film limit and then generalize the numerical solution to arbitrary film thicknesses and focus on the velocity field. It is documented that even smoothly corrugated free-surface shapes require strongly undulated topographies to maintain the flow structure. Finally, we discuss details of the implementation in applications, solvability in general, and sensitivity of the solution.

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Section: Introductionmentioning

confidence: 99%

Velocity field reconstruction in gravity-driven flow over unknown topography

Heining

2011

Physics of Fluids

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“…A similar effect was reported by Tseluiko et al 15 who concluded that applying an electric field may lead to a suppression of the capillary ridge. Scholle et al 23 considered creeping films and found that special bottom topographies in the a͒ Author to whom correspondence should be addressed. Telephone: ϩ49921557262.…”

Section: Introductionmentioning

confidence: 99%

Bottom reconstruction in thin-film flow over topography: Steady solution and linear stability

Heining

Aksel

2009

Physics of Fluids

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We consider viscous gravity-driven films flowing over undulated substrates. Instead of the widely studied direct problem of finding the free surface for a given bottom topography, we focus on the inverse problem: Given a specific free surface shape, we seek the corresponding bottom topography which causes this free surface profile. As an asymptotic approach for thin films and moderate Reynolds numbers, we apply the weighted-residual integral boundary-layer method which enables us to derive a set of two evolution equations for the film thickness and the flow rate. We prescribe the free surface as a monofrequent periodic function and discuss the influence of inertia, film thickness, and surface tension on the shape of the corresponding substrate. For small free surface undulations, we can solve the bottom contour analytically and study its parametric dependence. The analytical results are then validated with numerical simulations. Furthermore, we consider the stability of the corresponding direct problem, which reveals that the bottom topography is stabilizing or destabilizing, depending on surface tension.

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“…Such eddies were later shown to act as "fluid roller bearings" for the improvement of material transport in creeping films. 26 Other aspects have also been considered, such as the effect of inertia on eddies and on the breakup of the associated separatrix by the "turnstile lobe mechanism" 27 and, very recently, the effect of an applied electric field on the free-surface profile and eddy generation within the film. 28 The only analytical work of direct relevance to have explored the effect of inertia is that of Trifonov, 29 who considered the problem of a viscous liquid film flowing down a vertical one-dimensional periodic surface for a wide range of Reynolds numbers with regard to the presence of recirculating flow due to boundary-layer separation.…”

Section: Introductionmentioning

confidence: 99%

Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

et al. 2008

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The formation and presence of eddies within thick gravity-driven free-surface film flow over a corrugated substrate are considered, with the governing equations solved semianalytically using a complex variable method for Stokes flow and numerically via a full finite element formulation for the more general problem when inertia is significant. The effect of varying geometry ͑involving changes in the film thickness or the amplitude and wavelength of the substrate͒ and inertia is explored separately. For Stokes-like flow and varying geometry, excellent agreement is found between prediction and existing flow visualizations and measured eddy center locations associated with the switch from attached to locally detached flow. It is argued that an appropriate measure of the influence of inertia at the substrate is in terms of a local Reynolds number based on the characteristic corrugation length scale. Since, for small local Reynolds numbers, the local flow structure there becomes effectively decoupled from the inertia-dominated overlying film and immune from instabilities at the free-surface; the influence of inertia manifests itself as a skewing of the dividing streamline ͑separatrix͒. It is shown that the formation and presence of eddies can be manipulated in one of two ways. While an decrease/increase in the corrugation steepness leads to the disappearance/appearance of kinematically induced eddies, an increase/decrease in the inertia present in the system leads to the appearance/disappearance of inertially induced eddies. A critical corrugation steepness for a given film thickness is defined, demarking the transition from a kinematically to an inertially induced local eddy flow structure and vice versa.

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Drag reduction and improvement of material transport in creeping films

Cited by 32 publications

References 31 publications

Velocity field reconstruction in gravity-driven flow over unknown topography

Velocity field reconstruction in gravity-driven flow over unknown topography

Bottom reconstruction in thin-film flow over topography: Steady solution and linear stability

Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

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