Electrowetting of a 3D drop: numerical modelling with electrostatic vector fields

Ciarlet, Patrick; Scheid, Claire

doi:10.1051/m2an/2010014

Cited by 3 publications

(4 citation statements)

References 29 publications

(47 reference statements)

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“…Capillary surfaces [15,26] of variable contact angle, e.g., not equal to 90 • , are an active field of research [1,12,48,57] and many questions are open regarding the existence of equilibrium shapes for contact angles between 90 • and 180 • . Moreover, including G complicates the problem further; see Remark 4.3.…”

Section: Lower-level Problem Formulationmentioning

confidence: 99%

“…Effectively, this means that θ cl is set to a fixed value at each material point of Σ when computing the equilibrium solution of (3.10). There is some justification for this in the context of electrowetting [12,23,40,72,73,74,77]. In this case, it is well known that one can control the local contact angle by applying an electric field to the droplet [50].…”

Section: Interpretation and Handling Of The Controlmentioning

confidence: 99%

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Droplet Footprint Control

Laurain¹,

Walker²

2015

SIAM J. Control Optim.

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Controlling droplet shape via surface tension has numerous technological applications, such as droplet lenses and lab-on-a-chip. This motivates a partial differential equationconstrained shape optimization approach for controlling the shape of droplets on flat substrates by controlling the surface tension of the substrate. We use shape differential calculus to derive an L 2 gradient flow approach to compute equilibrium shapes for sessile droplets on substrates. We then develop a gradient-based optimization method to find the substrate surface tension coefficient yielding an equilibrium droplet shape with a desired footprint (i.e., the liquid-solid interface has a desired shape). Moreover, we prove a sensitivity result with respect to the substrate surface tensions for the free boundary problem associated with the footprint. Numerical results are also presented to showcase the method.

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Section: Lower-level Problem Formulationmentioning

confidence: 99%

Section: Interpretation and Handling Of The Controlmentioning

confidence: 99%

Droplet Footprint Control

Laurain¹,

Walker²

2015

SIAM J. Control Optim.

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“…Several works have been concerned with the modeling of electrowetting. The approaches include experimental relations and scaling laws [34,62], empirical models [41], studies concerning the dependence of the contact angle ( [24,55]) or the shape of the droplet ( [42,17]) on the applied voltage, lattice Boltzmann methods [4,3] and others. Of relevance to our present discussion are the works [64,63] and [20,23].…”

Section: Introductionmentioning

confidence: 99%

A Diffuse Interface Model for Electrowetting With Moving Contact Lines

Nochetto

Salgado

2013

Math. Models Methods Appl. Sci.

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We introduce a diffuse interface model for the phenomenon of electrowetting on dielectric and present an analysis of the arising system of equations. Moreover, we study discretization techniques for the problem. The model takes into account different material parameters on each phase and incorporates the most important physical processes, such as incompressibility, electrostatics and dynamic contact lines; necessary to properly reflect the relevant phenomena. The arising nonlinear system couples the variable density incompressible Navier-Stokes equations for velocity and pressure with a Cahn-Hilliard type equation for the phase variable and chemical potential, a convection diffusion equation for the electric charges and a Poisson equation for the electric potential. Numerical experiments are presented, which illustrate the wide range of effects the model is able to capture, such as splitting and coalescence of droplets.

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“…Below, we focus on the original version of Costabel and Dauge. See [50][51][52][53][54][55][56] for applications in electromagnetism in a homogeneous material. It it especially of interest when the domain Ω is a non-convex polyhedron 3 , so we focus on this geometrical configuration from now on.…”

Section: A Conforming Variational Formulation In a Weighted Spacementioning

confidence: 99%

Variational methods for solving numerically magnetostatic systems

Ciarlet,

Jamelot

2024

Adv Comput Math

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In this paper, we study some techniques for solving numerically magnetostatic systems. We consider fairly general assumptions on the magnetic permeability tensor. It is elliptic, but can be nonhermitian. In particular, we revisit existing classical variational methods and propose new numerical methods. The numerical approximation is either based on the classical edge finite elements, or on continuous Lagrange finite elements. For the first type of discretization, we rely on the design of a new, mixed variational formulation that is obtained with the help of T -coercivity. The numerical method can be related to a perturbed approach for solving mixed problems in electromagnetism. For the second type of discretization, we rely on an augmented variational formulation obtained with the help of the Weighted Regularization Method.

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Electrowetting of a 3D drop: numerical modelling with electrostatic vector fields

Cited by 3 publications

References 29 publications

Droplet Footprint Control

Droplet Footprint Control

A Diffuse Interface Model for Electrowetting With Moving Contact Lines

Variational methods for solving numerically magnetostatic systems

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