Prof. Dr. Michael Hintermüller
Dr. Soheil Hajian
Humboldt Universität Berlin
A number of emerging key technologies in microbiology, medical diagnostic devices, personal genomics, as well as
next-generation low-energy OLED displays and liquid lenses make use of a phenomenon known as electrowetting on dielectric (EWOD).
Electrowetting involves the manipulation of small (microscopic) droplets on a dielectric surface by the actuation of the underlying
current. In fact, droplets in a typical EWOD device are situated between two separated hydrophobic surfaces, one of which
contains an array of controllable electrodes.
The air-liquid-solid contact angle can then by changed by varying the voltages on separate electrodes, which causes the droplets to move. Thus,
the voltages are a natural choice for influencing (controlling) the motion of a droplet.
The project pursues both sharp interface and phase field models, respectively, for the movement of droplets in an EWOD device.
Both models make use of a macroscopic description for contact line pinning, which is due to contact angle hysteresis as well as molecular adhesion at the solid-liquid-air interface, for a faithful representation of the droplets velocity and cover different aspects properly.
Due to the non-trivial dependencies
on the moving interface
in the sharp interface context, the proof of existence of an optimal control remains impossible without further restrictive assumptions or constraints, e.g., on the geometry, and the complexity of the phase field model poses severe challenges for a fast (real-time) numerical solution as needed for EWOD devices. For these reasons, instead of computing time-discrete or optimal controls the project work pursues an idea from model predictive control (MPC).