Thin film flow on surfaces containing arbitrary occlusions

Sellier, Mathieu; Lee, Yeaw Chu; Thompson, H. M.; Gaskell, Philip

doi:10.1016/j.compfluid.2008.01.008

Cited by 28 publications

(22 citation statements)

References 34 publications

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“…This package has been proven particularly convenient and accurate to model thin layer flows. 17 Details on the implementation can be found in Refs. 17 and 18.…”

Section: B Solution Proceduresmentioning

confidence: 99%

Modeling the coalescence of sessile droplets

Sellier

Trelluyer

2009

Biomicrofluidics

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This paper proposes a simple scenario to describe the coalescence of sessile droplets. This scenario predicts a power-law growth of the bridge between the droplets. The exponent of this power law depends on the driving mechanism for the spreading of each droplet. To validate this simple idea, the coalescence is simulated numerically and a basic experiment is performed. The fluid dynamics problem is formulated in the lubrication approximation framework and the governing equations are solved in the commercial finite element software COMSOL. Although a direct comparison of the numerical results with experiment is difficult because of the sensitivity of the coalescence to the initial and operating conditions, the key features of the event are qualitatively captured by the simulation and the characteristic time scale of the dynamics recovered. The experiment consists of inducing coalescence by pumping a droplet through a substrate which grows and ultimately coalesces with another droplet resting on the substrate. The coalescence was recorded using high-speed imaging and also confirmed the power-law growth of the neck.

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“…This package has been proven particularly convenient and accurate to model thin layer flows. 17 Details on the implementation can be found in Refs. 17 and 18.…”

Section: B Solution Proceduresmentioning

confidence: 99%

Modeling the coalescence of sessile droplets

Sellier

Trelluyer

2009

Biomicrofluidics

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“…This same algorithm was used in a detailed study of the flow of gravity-driven thin liquid films on non-porous substrates with topography, showing that the long wavelength approximation leads to very good solutions, even in regions of parameter space where it is not strictly valid [13]. The methodology has subsequently been refined to embody error-controlled automatic mesh adaption [14,15] leading to significant further improvement in solution times without loss of accuracy, and to include additional physics [16] -in this case evaporation.…”

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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“…The finite element package COMSOL is used here to solve the governing equations on the solution domain. The ability of this commercial package to accurately solve the pertaining governing equations has recently been demonstrated in [19].…”

Section: Solution Methodsmentioning

confidence: 99%

“…• If the cross-flow pressure gradient vanishes (* p ex /*y = 0), the streamlines are in the positive x-direction and dy is equal to zero in Equation (25) according to Equation (19). Equation (25) reduces to an ode, which can easily be integrated to yield…”

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confidence: 99%

Beating capillarity in thin film flows

Sellier

Panda

2009

Numerical Methods in Fluids

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SUMMARYThe combination of substrate unevenness and capillarity is known to induce far-reaching perturbations at the free surface of thin liquid films. These might be undesired and this paper explores the possibility to control the free surface of thin liquid films to give it a prescribed profile by a suitable design of the underlying substrate. This corresponds to the inverse of the widely studied forward problem, which considers the effect of substrate unevenness on a free surface. Assuming that the steady free surface profile can be described by the lubrication approximation, this optimal control problem is shown to be governed by a first-order partial differential equation, which is solved numerically using the method of characteristics. The proposed method is successfully tested for a range of desired free surface profiles and the domain of existence of a solution to the inverse problem is probed. Expectedly, it is shown that, owing to surface tension, not all free surface profiles can be achieved but in some cases capillarity can be beaten and a prescribed free surface profile obtained.

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Thin film flow on surfaces containing arbitrary occlusions

Cited by 28 publications

References 34 publications

Modeling the coalescence of sessile droplets

Modeling the coalescence of sessile droplets

Inertial thin film flow on planar surfaces featuring topography

Beating capillarity in thin film flows

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