Micro Structures in Thin Coating Layers: Micro Structure Evolution and Macroscopic Contact Angle

Dohmen, Jonas; Grunewald, Natalie; Otto, Félix; Rumpf, Martin

doi:10.1007/978-3-540-77203-3_7

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…As for a dynamic description of evolving liquid drops, many different models are available: see, for instance, [2,15,16,20,22,23]. In general, regularity near the contact line, or even the topology of the drop, is largely unknown for drops that are not global minimizers except drops with strong geometric properties (for example, see Feldman and Kim [18]).…”

Section: Literaturementioning

confidence: 99%

Liquid Drops on a Rough Surface

Feldman

Kim

2018

Comm Pure Appl Math

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We consider a liquid drop sitting on a rough solid surface at equilibrium, a volume-constrained minimizer of the total interfacial energy. The large-scale shape of such a drop strongly depends on the microstructure of the solid surface. Surface roughness enhances hydrophilicity and hydrophobicity properties of the surface, altering the equilibrium contact angle between the drop and the surface. Our goal is to understand the shape of the drop with fixed small-scale roughness. To achieve this, we develop a quantitative description of the drop and its contact line in the context of periodic homogenization theory, building on the qualitative theory of Alberti and DeSimone.

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Section: Literaturementioning

confidence: 99%

Liquid Drops on a Rough Surface

Feldman

Kim

2018

Comm Pure Appl Math

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“…To this end, we approximate the squared distance via a quadrature rule involving the metric g and obtain a semi-implicit optimization problem for the mass distribution u at time t k+1 and a flux quantity f , where u and f are coupled via a time-discrete conservation law. For planar surfaces and thin coatings consisting of a resin and a solvent component, such a scheme has already been investigated by Dohmen et al [12] Düring et al [13] also derived a numerical scheme for a fourth order PDE using an underlying gradient flow structure. Similar to our approach, they applied direct numerical integration of the underlying Wasserstein-type transport problem for the nonlinear fourth order Derrida-Lebowitz-Speer-Spohn equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical Gradient Flow Discretization of Viscous Thin Films on Curved Geometries

Rumpf

Vantzos

2013

Math. Models Methods Appl. Sci.

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The evolution of a viscous thin film on a curved geometry is numerically approximated based on the natural time discretization of the underlying gradient flow. This discretization leads to a variational problem to be solved at each time step, which reflects the balance between the decay of the free (gravitational and surface) energy and the viscous dissipation. Both dissipation and energy are derived from a lubrication approximation for a small ratio between the characteristic film height and the characteristic length scale of the surface. The dissipation is formulated in terms of a corresponding flux field, whereas the energy primarily depends on the fluid volume per unit surface, which is a conserved quantity. These two degrees of freedom are coupled by the underlying transport equation. Hence, one is naturally led to a PDE-constrained optimization problem, where the variational time stepping problem has to be solved under the constraint described by the transport equation. For the space discretization a discrete exterior calculus approach is investigated. Various applications demonstrate the qualitative and quantitative behavior of one- and two-dimensional thin films on curved geometries.

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Micro Structures in Thin Coating Layers: Micro Structure Evolution and Macroscopic Contact Angle

Cited by 2 publications

References 18 publications

Liquid Drops on a Rough Surface

Liquid Drops on a Rough Surface

Numerical Gradient Flow Discretization of Viscous Thin Films on Curved Geometries

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