Optimal Control of Sliding Droplets Using the Contact Angle Distribution

Bonart, Henning; Kahle, Christian

doi:10.1137/20m1317773

Cited by 1 publication

(9 citation statements)

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“…We also refer to our complementary works for an extensive description of the mathematical details. 28,29 We assume that we can influence the contact angle at the contact line with a suitable control mechanism (i.e., electrowetting). To state the optimal control problem that defines our controller, we assume that we have some general description φ of the droplet.…”

Section: ■ Methodologymentioning

confidence: 99%

“…For further details about the gradient of our model needed in the optimization routine, we refer to our recent work. 29 The liquid droplet and the surrounding air are modeled as Newtonian, isotherm, immiscible, and incompressible fluids. In this work, the common incompressible, single-field NS equation is combined with the convective CH equation to describe the interface dynamics.…”

Section: ■ Methodologymentioning

confidence: 99%

“…We refer to our other works for a detailed description of the mathematical setup. 28,29 The optimal control problem is solved using a quasi-Newton method. Gradients are derived using adjoint calculus.…”

Section: ■ Introductionmentioning

confidence: 99%

“…The dynamics of the droplet and the gas–liquid interface are described by the Cahn–Hilliard–Navier–Stokes (CHNS) equations. We refer to our other works for a detailed description of the mathematical setup. , The optimal control problem is solved using a quasi-Newton method. Gradients are derived using adjoint calculus.…”

Section: Introductionmentioning

confidence: 99%

“…54,55 See our recent works for a discussion of numerical schemes to solve the forward model eqs 3−6. 29,44 For the solution to the arising linear systems and subsystems, the software suite PETSc 3.8.4 56−58 is used. Common for Newton-based methods, the optimization is conducted iteratively.…”

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Optimal Control of Droplets on a Solid Surface Using Distributed Contact Angles

2020

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Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. However, automating them, e.g., for high-throughput applications, does rarely involve model-based optimal control strategies. In this work, we demonstrate the optimal control of both the shape and position of a droplet sliding on an inclined surface. This basic test case is a fundamental building block in plenty of microfluidic designs. The static contact angle between the solid surface, the surrounding gas, and the liquid droplet serves as the control variable. By using several control patches, e.g., like done in electrowetting, the contact angles are allowed to vary in space and time. In computer experiments, we are able to calculate mathematically optimal contact angle distributions using gradientbased optimization. The dynamics of the droplet are described by the Cahn-Hilliard-Navier-Stokes equations. We anticipate our demonstration to be the starting point for more sophisticated optimal design and control concepts.

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Section: ■ Methodologymentioning

confidence: 99%

Section: ■ Methodologymentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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