Beating capillarity in thin film flows

Sellier, Mathieu; Panda, Satyananda

doi:10.1002/fld.2086

Cited by 21 publications

(12 citation statements)

References 18 publications

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“…Later, an extension to the three-dimensional topography 24 was presented in Ref. 25. Heining and Aksel 26 derived a weighted-residual integral boundary-layer model 27 ͑WRIBL͒ which allows for studies for higher Reynolds numbers.…”

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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“…Furthermore, we note that for applications with noisy input data (2.25) can be integrated once to eliminate the derivative of u 2 S . Compared with previous approaches (Sellier 2008;Sellier & Panda 2010;Heining 2011), the present method can be formulated without higher derivatives of the input data. This is an immense advantage since the input data contains possible noise which is amplified by taking the derivative up to the third-order (see ).…”

Section: Integral Boundary-layer Model For the Inverse Problemmentioning

confidence: 92%

“…Instead of prescribing a fixed topography, another quantity for example the free surface shape or the free surface velocity is prescribed but the topography and the flow field are unknown. First results on the inverse problem for film flows have been published by Sellier (2008), Sellier & Panda (2010) and Heining, Sellier & Aksel (2012) who derived the inverse solution in the lubrication approximation for creeping thin films. They studied the case where a target free-surface shape is achieved by modifying the topography shape.…”

Section: Introductionmentioning

confidence: 98%

Flow domain identification from free surface velocity in thin inertial films

2013

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We consider the flow of a viscous liquid along an unknown topography. A new strategy is presented to reconstruct the topography and the free surface shape from one component of the free surface velocity only. In contrast to the classical approach in inverse problems based on optimization theory we derive an ordinary differential equation which can be solved directly to obtain the inverse solution. This is achieved by averaging the Navier-Stokes equation and coupling the function parameterizing the flow domain with the free surface velocity. Even though we consider nonlinear systems including inertia and surface tension, the inverse problem can be solved analytically with a Fourier series approach. We test our method on a variety of benchmark problems and show that the analytical solution can be applied to reconstruct the flow domain from noisy input data. It is also demonstrated that the asymptotic approach agrees very well with numerical results of the Navier-Stokes equation. The results are finally confirmed with an experimental study where we measure the free surface velocity for the film flow over a trench and compare the reconstructed topography with the measured one.

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“…From a more fundamental point of view, one wishes to understand these strongly nonlinear fingering dynamics [4]. Thin film flows have been extensively studied experimentally [5,6], analytically [1,[7][8][9][10], and numerically [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Karlsen and Lie [11] proposed an unconditionally stable scheme based on operator splitting combined with a front…”

Section: Introductionmentioning

confidence: 99%

Numerical studies of the fingering phenomena for the thin film equation

Lee

Yoon

et al. 2010

Numerical Methods in Fluids

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SUMMARYWe present a new interpretation of the fingering phenomena of the thin liquid film layer through numerical investigations. The governing partial differential equation is h t +(h 2 −h 3 ) x =−∇ ·(h 3 ∇ h), which arises in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, y, t) is the liquid film height. A robust and accurate finite difference method is developed for the thin liquid film equation. For the advection part (h 2 −h 3 ) x , we use an implicit essentially nonoscillatory (ENO)-type scheme and get a good stability property. For the diffusion part −∇ ·(h 3 ∇ h), we use an implicit Euler's method. The resulting nonlinear discrete system is solved by an efficient nonlinear multigrid method. Numerical experiments indicate that higher the film thickness, the faster the film front evolves. The concave front has higher film thickness than the convex front. Therefore, the concave front has higher speed than the convex front and this leads to the fingering phenomena.

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Beating capillarity in thin film flows

Cited by 21 publications

References 18 publications

Velocity field reconstruction in gravity-driven flow over unknown topography

Velocity field reconstruction in gravity-driven flow over unknown topography

Flow domain identification from free surface velocity in thin inertial films

Numerical studies of the fingering phenomena for the thin film equation

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