Electrically driven mixing in anisotropic electrolytes: an optimal control approach

Luisa Plato (WIAS Berlin) is going to talk about: "Electrically driven mixing in anisotropic electrolytes: an optimal control approach"

Mixing fluids on lab-on-a-chip devices is challenging: flows at this scale are highly viscous, and mechanical stirring is impractical. An alternative is to drive the flow electrically. Applying an electric field to an electrolyte moves the ions, and they in turn set the fluid in motion. We model this by an anisotropic, time-dependent Stokes–Nernst–Planck–Poisson system. The control is the electric potential applied on the boundary, subject to upper and lower bounds, and the aim is to choose the potential so as to maximize the mixing over a given time horizon. In this talk, we prove the existence of an optimal control, present a finite element discretization of the system, and show first numerical results for the discrete optimal control problem, computed with automatically derived adjoints.