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

Abstract

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.

Virtual Stencil for Patterning and Modeling in a Quantitative Volume Using EWOD and DEP Devices for Microfluidics

“…It will result in a smaller contact angle between the liquid and the solid, which in turn changes the wetting characteristics of the liquid on the solid surface. This phenomenon is called the electro-wetting effect [44][45][46][47][48][49][50].…”

“…It will result in a smaller contact angle between the liquid and the solid, which in turn changes the wetting characteristics of the liquid on the solid surface. This phenomenon is called the electro-wetting effect [44][45][46][47][48][49][50]. According to the research results published by Lippmann in 1875, the interfacial tension γSL between liquid and solid can be controlled by an external voltage, and the derived formula is:…”

Controlling Sliding Droplets with Optimal Contact Angle Distributions and a Phase Field Model

“…We consider the following time discrete system and refer to [3] for more details. Let Ω ⊂ R n with boundary ∂Ω and t 0 < t 1 < .…”