Liquid Drops on a Rough Surface

Feldman, William M.; Kim, Inwon C.

doi:10.1002/cpa.21793

Cited by 10 publications

(4 citation statements)

References 30 publications

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“…We also mention the paper of the second author and Kim [16] which considers a capillary problem on a rough surface. This is quite a different problem, but there are loose analogies.…”

Section: Literaturementioning

confidence: 99%

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Quantitative convergence of the “bulk” free boundary in an oscillatory obstacle problem

Abedin,

Feldman

2023

Interfaces Free Bound.

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We consider an oscillatory obstacle problem where the coincidence set and free boundary are also highly oscillatory. We establish a rate of convergence for a regularized notion of free boundary to the free boundary of a corresponding classical obstacle problem, assuming the latter is regular. The convergence rate is linear in the minimal length scale determined by the fine properties of a corrector function.' " .x/ WD ' 0 .x/ C " p .x="/:

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“…We also mention the paper of the second author and Kim [16] which considers a capillary problem on a rough surface. This is quite a different problem, but there are loose analogies.…”

Section: Literaturementioning

confidence: 99%

“…This is quite a different problem, but there are loose analogies. In [16] the surface roughness also results in a singular oscillatory contact set and contact line, and a notion of "bulk" can be used in a similar way to recover free boundary regularity at large scales.…”

Section: Literaturementioning

confidence: 99%

Quantitative convergence of the “bulk” free boundary in an oscillatory obstacle problem

Abedin,

Feldman

2023

Interfaces Free Bound.

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“…[5,22,14,37]; (ii) Area functional G(u, ∇u) = 1 + |∇u| 2 + σ, c.f. [6,7,15]; (iii) free energy for droplets on inclined groove-textured surface; see (3.30)…”

Section: Dynamics Of a Droplet With Topological Changes As A Gradient...mentioning

confidence: 99%

“…On one hand, for the quasi-static dynamics, i.e. the capillary surface is determined by an elliptic equation, there are many analysis results on the global existence and homogenization problems; see [5,19,22,14] for capillary surface described by a harmonic equation and see [6,7,8,15] for capillary surface described by spatial-constant mean curvature equation. On the other hand, for the pure mean curvature flow with an obstacle but without contact line dynamics, we refer to [1,26] for local existence and uniqueness of a regular solution by constructing a minimizing movement sequence.…”

Section: Introductionmentioning

confidence: 99%

Projection method for droplet dynamics on groove-textured surface with merging and splitting

Gao¹,

Liu²

2020

Preprint

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We study the full dynamics of droplets placed on an inclined groove-textured surface with merging and splitting. The motion of droplets can be determined by the contact line dynamics and motion by mean curvature, which are driven by the competition between surfaces tensions of three phases and gravitational effect. We reformulate the dynamics as a gradient flow on a Hilbert manifold with boundary, which can be further reduced to a parabolic variational inequality under some differentiable assumptions. To efficiently solve the parabolic variational inequality, the convergence and stability of projection method for obstacle problem in Hilbert space is revisited using Trotter-Kato's product formula. Based on this, we proposed a projection scheme for the droplets dynamics, which incorporates both the obstacle information and the phase transition information when merging and splitting happen. Several challenging examples including splitting and merging of droplets are demonstrated.

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Spreading Equilibria Under Mildly Singular Potentials: Pancakes Versus Droplets

Durastanti

Giacomelli

2022

J Nonlinear Sci

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We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive singularity at short ranges, global minimizers are compactly supported and display a microscopic contact angle of $$\pi /2$$ π / 2 . Depending on the form of the potential, the macroscopic shape can either be droplet-like or pancake-like, with a transition profile between the two at zero spreading coefficient for purely repulsive potentials. These results generalize, complete, and give mathematical rigor to de Gennes’ formal discussion of spreading equilibria. Uniqueness and non-uniqueness phenomena are also discussed.

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Liquid Drops on a Rough Surface

Cited by 10 publications

References 30 publications

Quantitative convergence of the “bulk” free boundary in an oscillatory obstacle problem

Quantitative convergence of the “bulk” free boundary in an oscillatory obstacle problem

Projection method for droplet dynamics on groove-textured surface with merging and splitting

Spreading Equilibria Under Mildly Singular Potentials: Pancakes Versus Droplets

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